iProverMo---2.5-0.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : SWW196+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n017.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 : Thu Jul 21 00:28:10 EDT 2022

% Result   : Theorem 5.86s 6.06s
% Output   : CNFRefutation 5.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      : 1176
% Syntax   : Number of formulae    : 10945 (2241 unt;   0 def)
%            Number of atoms       : 29936 (7323 equ)
%            Maximal formula atoms :   87 (   2 avg)
%            Number of connectives : 33310 (14319   ~;15455   |; 828   &)
%                                         ( 556 <=>;2152  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   40 (   4 avg)
%            Maximal term depth    :    7 (   1 avg)
%            Number of predicates  :   66 (  64 usr;   2 prp; 0-3 aty)
%            Number of functors    :   64 (  64 usr;  10 con; 0-3 aty)
%            Number of variables   : 26081 (1237 sgn7717   !;  34   ?)

% Comments : 
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
    ! [X21,X2,X22,X23,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),c_Groups_Otimes__class_Otimes(X3,X2,X21)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X2),c_Groups_Ominus__class_Ominus(X3,X22,X21)),c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X2),X21)),c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ominus__class_Ominus(X3,X22,X21))) ),
    file('<stdin>',fact_mult_Oprod__diff__prod) ).

fof(c_0_1,axiom,
    ! [X17,X18,X68,X65,X66] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17))
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66),X68),X17)) ) ),
    file('<stdin>',fact_nat__less__add__iff2) ).

fof(c_0_2,axiom,
    ! [X17,X18,X68,X66,X65] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X66)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17))
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X65),X68),X18),X17) ) ),
    file('<stdin>',fact_nat__less__add__iff1) ).

fof(c_0_3,axiom,
    ! [X17,X18,X68,X65,X66] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66),X68),X17)) ) ),
    file('<stdin>',fact_nat__le__add__iff2) ).

fof(c_0_4,axiom,
    ! [X17,X18,X68,X66,X65] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X66)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X65),X68),X18),X17) ) ),
    file('<stdin>',fact_nat__le__add__iff1) ).

fof(c_0_5,axiom,
    ! [X41,X24,X42,X67,X25,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41))
      <=> c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X24,X25),X67),X41)) ) ),
    file('<stdin>',fact_less__add__iff2) ).

fof(c_0_6,axiom,
    ! [X41,X24,X42,X67,X25,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41))
      <=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),X67),X42),X41) ) ),
    file('<stdin>',fact_less__add__iff1) ).

fof(c_0_7,axiom,
    ! [X41,X24,X42,X67,X25,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41))
      <=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),X67),X42),X41) ) ),
    file('<stdin>',fact_le__add__iff1) ).

fof(c_0_8,axiom,
    ! [X41,X24,X42,X67,X25,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X42,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X24,X25),X67),X41)) ) ),
    file('<stdin>',fact_le__add__iff2) ).

fof(c_0_9,axiom,
    ! [X33,X21,X2] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X21),X33) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X33),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X33)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X33),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X33)),X33)),
    file('<stdin>',fact_zdiv__zadd1__eq) ).

fof(c_0_10,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('<stdin>',fact_neg__zmod__mult__2) ).

fof(c_0_11,axiom,
    ! [X22,X23,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Ominus__class_Ominus(X3,X23,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23),X22)) ),
    file('<stdin>',fact_power2__diff) ).

fof(c_0_12,axiom,
    ! [X22,X23,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Oplus__class_Oplus(X3,X23,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23),X22)) ),
    file('<stdin>',fact_power2__sum) ).

fof(c_0_13,axiom,
    ! [X22,X23] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X23,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23),X22)),
    file('<stdin>',fact_real__sum__squared__expand) ).

fof(c_0_14,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))))
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ),
    file('<stdin>',fact_odd__0__le__power__imp__0__le) ).

fof(c_0_15,axiom,
    ! [X14,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> ( X15 != c_Groups_Ozero__class_Ozero(X3)
          | X14 != c_Groups_Ozero__class_Ozero(X3) ) ) ),
    file('<stdin>',fact_sum__power2__gt__zero__iff) ).

fof(c_0_16,axiom,
    ! [X14,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X3))
      <=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
          & X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    file('<stdin>',fact_sum__power2__le__zero__iff) ).

fof(c_0_17,axiom,
    ! [X20,X19,X52,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X52),X19),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X52),X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X53),X52),X20)) ),
    file('<stdin>',fact_nat__diff__add__eq2) ).

fof(c_0_18,axiom,
    ! [X20,X19,X52,X53,X51] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X53)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X52),X19),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X52),X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X51),X52),X19),X20) ),
    file('<stdin>',fact_nat__diff__add__eq1) ).

fof(c_0_19,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X3)) ),
    file('<stdin>',fact_not__sum__power2__lt__zero) ).

fof(c_0_20,axiom,
    ! [X57,X72,X41,X3] :
      ( ( class_Rings_Ocomm__ring(X3)
        & class_Rings_Odvd(X3) )
     => ( c_Rings_Odvd__class_Odvd(X3,X41,X72)
       => ! [X56,X59] :
            ( c_Rings_Odvd__class_Odvd(X3,X41,c_Groups_Oplus__class_Oplus(X3,X56,X57))
          <=> c_Rings_Odvd__class_Odvd(X3,X41,c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X56,c_Groups_Otimes__class_Otimes(X3,X59,X72)),X57)) ) ) ),
    file('<stdin>',fact_inf__period_I3_J) ).

fof(c_0_21,axiom,
    ! [X57,X72,X41,X3] :
      ( ( class_Rings_Ocomm__ring(X3)
        & class_Rings_Odvd(X3) )
     => ( c_Rings_Odvd__class_Odvd(X3,X41,X72)
       => ! [X56,X59] :
            ( c_Rings_Odvd__class_Odvd(X3,X41,c_Groups_Oplus__class_Oplus(X3,X56,X57))
          <=> c_Rings_Odvd__class_Odvd(X3,X41,c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X56,c_Groups_Otimes__class_Otimes(X3,X59,X72)),X57)) ) ) ),
    file('<stdin>',fact_inf__period_I4_J) ).

fof(c_0_22,axiom,
    ! [X73,X74,X39,X54,X35,X21] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X35),X54) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X73,X39)
         => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
             => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X21)
               => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,X74) ) ) ) ) ) ),
    file('<stdin>',fact_zdiv__mono2__lemma) ).

fof(c_0_23,axiom,
    ! [X73,X74,X39,X54,X35,X21] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X35),X54) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X21)
         => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X73)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
             => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X21)
               => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X74,X35) ) ) ) ) ) ),
    file('<stdin>',fact_zdiv__mono2__neg__lemma) ).

fof(c_0_24,axiom,
    ! [X42,X57,X15,X41,X25] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,X41)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X57))
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X42,X41)),X57)) ) ),
    file('<stdin>',fact_zdvd__period) ).

fof(c_0_25,axiom,
    ! [X9,X8] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X9)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X8))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X9)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X8))) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    file('<stdin>',fact_zmod__number__of__Bit1) ).

fof(c_0_26,axiom,
    ! [X54,X35,X73,X74,X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X74),X73),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X35),X54))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X73)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X73,X21)
         => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X21)
           => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X74,X35) ) ) ) ),
    file('<stdin>',fact_unique__quotient__lemma) ).

fof(c_0_27,axiom,
    ! [X54,X35,X73,X74,X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X74),X73),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X35),X54))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X54)
         => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X73)
           => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,X74) ) ) ) ),
    file('<stdin>',fact_unique__quotient__lemma__neg) ).

fof(c_0_28,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X2))) ),
    file('<stdin>',fact_pos__zmod__mult__2) ).

fof(c_0_29,axiom,
    ! [X35,X54,X21,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X54)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X33),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X33)),X54)) ) ) ),
    file('<stdin>',fact_zmult2__lemma__aux1) ).

fof(c_0_30,axiom,
    ! [X35,X21,X54,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X21)
         => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X33)),X54),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X33)) ) ) ),
    file('<stdin>',fact_zmult2__lemma__aux4) ).

fof(c_0_31,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))),c_Groups_Ozero__class_Ozero(X3)) ) ),
    file('<stdin>',fact_odd__power__less__zero) ).

fof(c_0_32,axiom,
    ! [X20,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))) = c_Groups_Otimes__class_Otimes(X3,X23,c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X23,X20))) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).

fof(c_0_33,axiom,
    ! [X9,X52,X22,X2,X23,X3] :
      ( class_Rings_Olinordered__semiring__1__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X23,X2)
       => ( c_Orderings_Oord__class_Oless(X3,X22,X2)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X52)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X9)
             => ( c_Groups_Oplus__class_Oplus(X3,X52,X9) = c_Groups_Oone__class_Oone(X3)
               => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X52,X23),c_Groups_Otimes__class_Otimes(X3,X9,X22)),X2) ) ) ) ) ) ),
    file('<stdin>',fact_convex__bound__lt) ).

fof(c_0_34,axiom,
    ! [X9,X52,X22,X2,X23,X3] :
      ( class_Rings_Olinordered__semiring__1(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X23,X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X22,X2)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X52)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X9)
             => ( c_Groups_Oplus__class_Oplus(X3,X52,X9) = c_Groups_Oone__class_Oone(X3)
               => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X52,X23),c_Groups_Otimes__class_Otimes(X3,X9,X22)),X2) ) ) ) ) ) ),
    file('<stdin>',fact_convex__bound__le) ).

fof(c_0_35,axiom,
    ! [X35,X54,X21,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X54)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X33)),X54),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
    file('<stdin>',fact_zmult2__lemma__aux2) ).

fof(c_0_36,axiom,
    ! [X35,X21,X54,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X21)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X33)),X54)) ) ) ),
    file('<stdin>',fact_zmult2__lemma__aux3) ).

fof(c_0_37,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
    file('<stdin>',fact_neg__zdiv__mult__2) ).

fof(c_0_38,axiom,
    ! [X4,X55,X3] :
      ( ( class_Rings_Odvd(X3)
        & class_Rings_Osemiring__0(X3) )
     => ( ? [X56] : hBOOL(hAPP(X55,c_Groups_Otimes__class_Otimes(X3,X4,X56)))
      <=> ? [X56] :
            ( c_Rings_Odvd__class_Odvd(X3,X4,c_Groups_Oplus__class_Oplus(X3,X56,c_Groups_Ozero__class_Ozero(X3)))
            & hBOOL(hAPP(X55,X56)) ) ) ),
    file('<stdin>',fact_unity__coeff__ex) ).

fof(c_0_39,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('<stdin>',fact_sum__power2__ge__zero) ).

fof(c_0_40,axiom,
    ! [X17,X18,X68,X65,X66] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17)
      <=> X18 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66),X68),X17) ) ),
    file('<stdin>',fact_nat__eq__add__iff2) ).

fof(c_0_41,axiom,
    ! [X17,X18,X68,X66,X65] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X66)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17)
      <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X65),X68),X18) = X17 ) ),
    file('<stdin>',fact_nat__eq__add__iff1) ).

fof(c_0_42,axiom,
    ! [X21,X2,X22,X23,X3] :
      ( class_Rings_Oring(X3)
     => c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),c_Groups_Otimes__class_Otimes(X3,X2,X21)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,c_Groups_Ominus__class_Ominus(X3,X22,X21)),c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X2),X21)) ),
    file('<stdin>',fact_mult__diff__mult) ).

fof(c_0_43,axiom,
    ! [X14,X15,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X15,X15),c_Groups_Otimes__class_Otimes(X3,X14,X14)))
      <=> ( X15 != c_Groups_Ozero__class_Ozero(X3)
          | X14 != c_Groups_Ozero__class_Ozero(X3) ) ) ),
    file('<stdin>',fact_sum__squares__gt__zero__iff) ).

fof(c_0_44,axiom,
    ! [X14,X15,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X15,X15),c_Groups_Otimes__class_Otimes(X3,X14,X14)),c_Groups_Ozero__class_Ozero(X3))
      <=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
          & X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    file('<stdin>',fact_sum__squares__le__zero__iff) ).

fof(c_0_45,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__ring(X3)
     => ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X23),c_Groups_Otimes__class_Otimes(X3,X22,X22)),c_Groups_Ozero__class_Ozero(X3)) ),
    file('<stdin>',fact_not__sum__squares__lt__zero) ).

fof(c_0_46,axiom,
    ! [X20,X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))) = c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    file('<stdin>',fact_power__odd__eq) ).

fof(c_0_47,axiom,
    ! [X41,X24,X42,X67,X25,X3] :
      ( class_Rings_Oring(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41)
      <=> X42 = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X24,X25),X67),X41) ) ),
    file('<stdin>',fact_eq__add__iff2) ).

fof(c_0_48,axiom,
    ! [X41,X24,X42,X67,X25,X3] :
      ( class_Rings_Oring(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41)
      <=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),X67),X42) = X41 ) ),
    file('<stdin>',fact_eq__add__iff1) ).

fof(c_0_49,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X2) ),
    file('<stdin>',fact_pos__zdiv__mult__2) ).

fof(c_0_50,axiom,
    ! [X7,X2,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X7)),c_Groups_Ozero__class_Ozero(X3))
       => X2 = c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_even__power__le__0__imp__0) ).

fof(c_0_51,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
         => c_Orderings_Oord__class_Oless(X3,X23,X22) ) ) ),
    file('<stdin>',fact_power2__less__imp__less) ).

fof(c_0_52,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
         => c_Orderings_Oord__class_Oless__eq(X3,X23,X22) ) ) ),
    file('<stdin>',fact_power2__le__imp__le) ).

fof(c_0_53,axiom,
    ! [X33,X21,X45,X2,X3] :
      ( class_Rings_Osemiring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X45),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X21,X45),X33)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X45),X33) ),
    file('<stdin>',fact_combine__common__factor) ).

fof(c_0_54,axiom,
    ! [X46,X15,X14,X16,X3] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X16,X14),c_Groups_Otimes__class_Otimes(X3,X15,X46)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X16,X46),c_Groups_Otimes__class_Otimes(X3,X15,X14))
      <=> ( X16 = X15
          | X14 = X46 ) ) ),
    file('<stdin>',fact_crossproduct__eq) ).

fof(c_0_55,axiom,
    ! [X41,X42,X24,X25,X3] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
     => ( ( X25 != X24
          & X42 != X41 )
      <=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X42),c_Groups_Otimes__class_Otimes(X3,X24,X41)) != c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X41),c_Groups_Otimes__class_Otimes(X3,X24,X42)) ) ),
    file('<stdin>',fact_crossproduct__noteq) ).

fof(c_0_56,axiom,
    ! [X7,X51,X52,X53] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X52),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X52),X7)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X52),X7),
    file('<stdin>',fact_left__add__mult__distrib) ).

fof(c_0_57,axiom,
    ! [X73,X74,X39] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X73)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X74,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
    file('<stdin>',fact_q__neg__lemma) ).

fof(c_0_58,axiom,
    ! [X73,X74,X39] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X73,X39)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X74) ) ) ),
    file('<stdin>',fact_q__pos__lemma) ).

fof(c_0_59,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
    file('<stdin>',fact_mod__mult__eq) ).

fof(c_0_60,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Oring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
    file('<stdin>',fact_mod__diff__eq) ).

fof(c_0_61,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
    file('<stdin>',fact_mod__add__eq) ).

fof(c_0_62,axiom,
    ! [X19,X20,X7] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20),X19)),X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X19),X20),
    file('<stdin>',fact_mod__mult__self4) ).

fof(c_0_63,axiom,
    ! [X14,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X3)
      <=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
          & X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    file('<stdin>',fact_sum__power2__eq__zero__iff) ).

fof(c_0_64,axiom,
    ! [X14,X15] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> ( X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        & X14 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    file('<stdin>',fact_realpow__two__sum__zero__iff) ).

fof(c_0_65,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oone__class_Oone(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20)),c_Power_Opower__class_Opower(X3,X2,X20)) ) ) ),
    file('<stdin>',fact_power__Suc__less) ).

fof(c_0_66,axiom,
    ! [X24,X25,X55] :
      ( hBOOL(hAPP(X55,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24)))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
         => hBOOL(hAPP(X55,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [X69] :
            ( X25 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X69)
           => hBOOL(hAPP(X55,X69)) ) ) ),
    file('<stdin>',fact_nat__diff__split) ).

fof(c_0_67,axiom,
    ! [X24,X25,X55] :
      ( hBOOL(hAPP(X55,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24)))
    <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
            & ~ hBOOL(hAPP(X55,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
          | ? [X69] :
              ( X25 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X69)
              & ~ hBOOL(hAPP(X55,X69)) ) ) ),
    file('<stdin>',fact_nat__diff__split__asm) ).

fof(c_0_68,axiom,
    ! [X39,X21,X43,X33,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Divides_Odiv__class_Omod(X3,X2,X33) = c_Divides_Odiv__class_Omod(X3,X43,X33)
       => ( c_Divides_Odiv__class_Omod(X3,X21,X33) = c_Divides_Odiv__class_Omod(X3,X39,X33)
         => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X43,X39),X33) ) ) ),
    file('<stdin>',fact_mod__mult__cong) ).

fof(c_0_69,axiom,
    ! [X39,X21,X43,X33,X2,X3] :
      ( class_Divides_Oring__div(X3)
     => ( c_Divides_Odiv__class_Omod(X3,X2,X33) = c_Divides_Odiv__class_Omod(X3,X43,X33)
       => ( c_Divides_Odiv__class_Omod(X3,X21,X33) = c_Divides_Odiv__class_Omod(X3,X39,X33)
         => c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X43,X39),X33) ) ) ),
    file('<stdin>',fact_mod__diff__cong) ).

fof(c_0_70,axiom,
    ! [X39,X21,X43,X33,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Divides_Odiv__class_Omod(X3,X2,X33) = c_Divides_Odiv__class_Omod(X3,X43,X33)
       => ( c_Divides_Odiv__class_Omod(X3,X21,X33) = c_Divides_Odiv__class_Omod(X3,X39,X33)
         => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X43,X39),X33) ) ) ),
    file('<stdin>',fact_mod__add__cong) ).

fof(c_0_71,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Ocomm__ring__1(X3)
     => c_Groups_Ominus__class_Ominus(X3,c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(X3,X22,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X22),c_Groups_Oplus__class_Oplus(X3,X23,X22)) ),
    file('<stdin>',fact_realpow__two__diff) ).

fof(c_0_72,axiom,
    ! [X46] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X46),X46),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('<stdin>',fact_odd__less__0) ).

fof(c_0_73,axiom,
    ! [X22,X78,X79,X80] :
      ( X80 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X79,X78),X22)
     => ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
           => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
              & c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X79) ) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X22)
              & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
       => ( X79 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,X80,X79) = X22 ) ) ),
    file('<stdin>',fact_divmod__int__rel__mod__eq) ).

fof(c_0_74,axiom,
    ! [X26,X27,X28,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,X29,c_Groups_Otimes__class_Otimes(X3,X28,c_Groups_Otimes__class_Otimes(X3,X27,X26))) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

fof(c_0_75,axiom,
    ! [X26,X27,X28,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,X27,c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),X26)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

fof(c_0_76,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,X33,X34)
         => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
             => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
    file('<stdin>',fact_mult__strict__mono) ).

fof(c_0_77,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,X33,X34)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
             => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
    file('<stdin>',fact_mult__strict__mono_H) ).

fof(c_0_78,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
           => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
             => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
    file('<stdin>',fact_mult__less__le__imp__less) ).

fof(c_0_79,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,X33,X34)
         => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
             => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
    file('<stdin>',fact_mult__le__less__imp__less) ).

fof(c_0_80,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Oordered__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
             => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
    file('<stdin>',fact_mult__mono_H) ).

fof(c_0_81,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Oordered__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
             => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
    file('<stdin>',fact_mult__mono) ).

fof(c_0_82,axiom,
    ! [X23] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('<stdin>',fact_four__x__squared) ).

fof(c_0_83,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X18)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X17)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X5),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X5))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ) ),
    file('<stdin>',fact_le__diff__iff) ).

fof(c_0_84,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X18)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X17)
       => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X5),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X5))
        <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ) ),
    file('<stdin>',fact_less__diff__iff) ).

fof(c_0_85,axiom,
    ! [X22,X20,X38,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X20)
       => c_Power_Opower__class_Opower(X3,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X20),X38)) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X38)),X22) ) ),
    file('<stdin>',fact_lemma__realpow__diff) ).

fof(c_0_86,axiom,
    ! [X18,X17,X5] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X18)))
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5,X17) ),
    file('<stdin>',fact_zdvd__reduce) ).

fof(c_0_87,axiom,
    ! [X21,X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)),c_Power_Opower__class_Opower(X3,X21,c_Nat_OSuc(X20)))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ) ),
    file('<stdin>',fact_power__le__imp__le__base) ).

fof(c_0_88,axiom,
    ! [X22,X23,X10,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X10,X23)
       => ( c_Rings_Odvd__class_Odvd(X3,X10,X22)
         => c_Divides_Odiv__class_Odiv(X3,c_Groups_Oplus__class_Oplus(X3,X23,X22),X10) = c_Groups_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Odiv(X3,X23,X10),c_Divides_Odiv__class_Odiv(X3,X22,X10)) ) ) ),
    file('<stdin>',fact_div__add) ).

fof(c_0_89,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__ring(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X23),c_Groups_Otimes__class_Otimes(X3,X22,X22))) ),
    file('<stdin>',fact_sum__squares__ge__zero) ).

fof(c_0_90,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
       => c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20))) ) ),
    file('<stdin>',fact_power__less__power__Suc) ).

fof(c_0_91,axiom,
    ! [X21,X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X21,X20))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
    file('<stdin>',fact_power__less__imp__less__base) ).

fof(c_0_92,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X42)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
        <=> c_Orderings_Oord__class_Oless__eq(X3,X25,X24) ) ) ),
    file('<stdin>',fact_mult__le__cancel__left__pos) ).

fof(c_0_93,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
        <=> c_Orderings_Oord__class_Oless__eq(X3,X24,X25) ) ) ),
    file('<stdin>',fact_mult__le__cancel__left__neg) ).

fof(c_0_94,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Rings_Olinordered__semiring(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
    file('<stdin>',fact_mult__right__less__imp__less) ).

fof(c_0_95,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
    file('<stdin>',fact_mult__less__imp__less__right) ).

fof(c_0_96,axiom,
    ! [X21,X2,X33,X3] :
      ( class_Rings_Olinordered__semiring(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
    file('<stdin>',fact_mult__left__less__imp__less) ).

fof(c_0_97,axiom,
    ! [X21,X2,X33,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
    file('<stdin>',fact_mult__less__imp__less__left) ).

fof(c_0_98,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33))
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ) ),
    file('<stdin>',fact_mult__right__le__imp__le) ).

fof(c_0_99,axiom,
    ! [X21,X2,X33,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21))
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ) ),
    file('<stdin>',fact_mult__left__le__imp__le) ).

fof(c_0_100,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X42)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
        <=> c_Orderings_Oord__class_Oless(X3,X25,X24) ) ) ),
    file('<stdin>',fact_mult__less__cancel__left__pos) ).

fof(c_0_101,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
        <=> c_Orderings_Oord__class_Oless(X3,X24,X25) ) ) ),
    file('<stdin>',fact_mult__less__cancel__left__neg) ).

fof(c_0_102,axiom,
    ! [X14,X15,X24,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X24)
       => ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X24,X15),c_Power_Opower__class_Opower(X3,X24,X14))
        <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14) ) ) ),
    file('<stdin>',fact_power__strict__increasing__iff) ).

fof(c_0_103,axiom,
    ! [X20,X19,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X19),c_Power_Opower__class_Opower(X3,X2,X20))
         => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ) ) ),
    file('<stdin>',fact_power__less__imp__less__exp) ).

fof(c_0_104,axiom,
    ! [X14,X15,X24,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X24)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X24,X15),c_Power_Opower__class_Opower(X3,X24,X14))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14) ) ) ),
    file('<stdin>',fact_power__increasing__iff) ).

fof(c_0_105,axiom,
    ! [X20,X19,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X19),c_Power_Opower__class_Opower(X3,X2,X20))
         => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ) ) ),
    file('<stdin>',fact_power__le__imp__le__exp) ).

fof(c_0_106,axiom,
    ! [X9,X21,X2,X30] :
      ( ( class_Int_Onumber(X30)
        & class_Rings_Oring(X30) )
     => c_Groups_Otimes__class_Otimes(X30,c_Groups_Ominus__class_Ominus(X30,X2,X21),c_Int_Onumber__class_Onumber__of(X30,X9)) = c_Groups_Ominus__class_Ominus(X30,c_Groups_Otimes__class_Otimes(X30,X2,c_Int_Onumber__class_Onumber__of(X30,X9)),c_Groups_Otimes__class_Otimes(X30,X21,c_Int_Onumber__class_Onumber__of(X30,X9))) ),
    file('<stdin>',fact_left__diff__distrib__number__of) ).

fof(c_0_107,axiom,
    ! [X33,X21,X9,X30] :
      ( ( class_Int_Onumber(X30)
        & class_Rings_Oring(X30) )
     => c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),c_Groups_Ominus__class_Ominus(X30,X21,X33)) = c_Groups_Ominus__class_Ominus(X30,c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),X21),c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),X33)) ),
    file('<stdin>',fact_right__diff__distrib__number__of) ).

fof(c_0_108,axiom,
    ! [X9,X21,X2,X30] :
      ( ( class_Int_Onumber(X30)
        & class_Rings_Osemiring(X30) )
     => c_Groups_Otimes__class_Otimes(X30,c_Groups_Oplus__class_Oplus(X30,X2,X21),c_Int_Onumber__class_Onumber__of(X30,X9)) = c_Groups_Oplus__class_Oplus(X30,c_Groups_Otimes__class_Otimes(X30,X2,c_Int_Onumber__class_Onumber__of(X30,X9)),c_Groups_Otimes__class_Otimes(X30,X21,c_Int_Onumber__class_Onumber__of(X30,X9))) ),
    file('<stdin>',fact_left__distrib__number__of) ).

fof(c_0_109,axiom,
    ! [X33,X21,X9,X30] :
      ( ( class_Int_Onumber(X30)
        & class_Rings_Osemiring(X30) )
     => c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),c_Groups_Oplus__class_Oplus(X30,X21,X33)) = c_Groups_Oplus__class_Oplus(X30,c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),X21),c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),X33)) ),
    file('<stdin>',fact_right__distrib__number__of) ).

fof(c_0_110,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))) ),
    file('<stdin>',fact_zero__le__even__power_H) ).

fof(c_0_111,axiom,
    ! [X7,X32,X9] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
       => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32),X7)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
       => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32),X7)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X32)),X7) ) ),
    file('<stdin>',fact_nat__number__of__mult__left) ).

fof(c_0_112,axiom,
    ! [X20,X19,X53] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X19),c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X20))
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X53)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ) ),
    file('<stdin>',fact_power__dvd__imp__le) ).

fof(c_0_113,axiom,
    ! [X14,X15,X46] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X46)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X46),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X14,X46))
      <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14) ) ),
    file('<stdin>',fact_real__mult__less__iff1) ).

fof(c_0_114,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ),
    file('<stdin>',fact_mult__le__cancel1) ).

fof(c_0_115,axiom,
    ! [X17,X5,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X5),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X5))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ),
    file('<stdin>',fact_mult__le__cancel2) ).

fof(c_0_116,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ),
    file('<stdin>',fact_nat__mult__le__cancel1) ).

fof(c_0_117,axiom,
    ! [X14,X15,X46] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X46)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X46,X15),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X46,X14))
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14) ) ),
    file('<stdin>',fact_real__mult__le__cancel__iff2) ).

fof(c_0_118,axiom,
    ! [X14,X15,X46] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X46)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X46),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X14,X46))
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14) ) ),
    file('<stdin>',fact_real__mult__le__cancel__iff1) ).

fof(c_0_119,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X19),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20))
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X20) ) ),
    file('<stdin>',fact_dvd__mult__cancel) ).

fof(c_0_120,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,X17) ) ),
    file('<stdin>',fact_nat__mult__dvd__cancel1) ).

fof(c_0_121,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ),
    file('<stdin>',fact_nat__mult__less__cancel1) ).

fof(c_0_122,axiom,
    ! [X20,X19,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X19),c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X20))
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ) ),
    file('<stdin>',fact_nat__power__less__imp__less) ).

fof(c_0_123,axiom,
    ! [X2,X62,X20,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X62)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oone__class_Oone(X3))
           => c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X62),c_Power_Opower__class_Opower(X3,X2,X20)) ) ) ) ),
    file('<stdin>',fact_power__strict__decreasing) ).

fof(c_0_124,axiom,
    ! [X2,X62,X20,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X62)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Oone__class_Oone(X3))
           => c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X62),c_Power_Opower__class_Opower(X3,X2,X20)) ) ) ) ),
    file('<stdin>',fact_power__decreasing) ).

fof(c_0_125,axiom,
    ! [X24,X42,X25,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X25,X42),c_Groups_Otimes__class_Otimes(X3,X24,X42))
      <=> ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X42)
            & c_Orderings_Oord__class_Oless(X3,X25,X24) )
          | ( c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Ozero__class_Ozero(X3))
            & c_Orderings_Oord__class_Oless(X3,X24,X25) ) ) ) ),
    file('<stdin>',fact_mult__less__cancel__right__disj) ).

fof(c_0_126,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
      <=> ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X42)
            & c_Orderings_Oord__class_Oless(X3,X25,X24) )
          | ( c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Ozero__class_Ozero(X3))
            & c_Orderings_Oord__class_Oless(X3,X24,X25) ) ) ) ),
    file('<stdin>',fact_mult__less__cancel__left__disj) ).

fof(c_0_127,axiom,
    ! [X20,X21,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
           => c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X21,X20)) ) ) ) ),
    file('<stdin>',fact_power__strict__mono) ).

fof(c_0_128,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) ),
    file('<stdin>',fact_zmod__simps_I4_J) ).

fof(c_0_129,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) ),
    file('<stdin>',fact_mod__mult__left__eq) ).

fof(c_0_130,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
    file('<stdin>',fact_mod__mult__right__eq) ).

fof(c_0_131,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Oring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
    file('<stdin>',fact_mod__diff__right__eq) ).

fof(c_0_132,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Oring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) ),
    file('<stdin>',fact_mod__diff__left__eq) ).

fof(c_0_133,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) ),
    file('<stdin>',fact_zmod__simps_I1_J) ).

fof(c_0_134,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) ),
    file('<stdin>',fact_zmod__simps_I2_J) ).

fof(c_0_135,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) ),
    file('<stdin>',fact_mod__add__left__eq) ).

fof(c_0_136,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
    file('<stdin>',fact_mod__add__right__eq) ).

fof(c_0_137,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Oplus__class_Oplus(X3,X33,X34)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(c_0_138,axiom,
    ! [X26,X27,X28,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X27),c_Groups_Otimes__class_Otimes(X3,X28,X26)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

fof(c_0_139,axiom,
    ! [X33,X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Groups_Ominus__class_Ominus(X3,c_Int_Onumber__class_Onumber__of(X3,X8),X33)) = c_Groups_Ominus__class_Ominus(X3,c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)),X33) ),
    file('<stdin>',fact_add__number__of__diff1) ).

fof(c_0_140,axiom,
    ! [X10,X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X8),X10)) = c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)),X10) ),
    file('<stdin>',fact_add__number__of__left) ).

fof(c_0_141,axiom,
    ! [X10,X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,X8),X10)) = c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)),X10) ),
    file('<stdin>',fact_mult__number__of__left) ).

fof(c_0_142,axiom,
    ! [X23,X20,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
       => c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X23) = c_Power_Opower__class_Opower(X3,X23,X20) ) ),
    file('<stdin>',fact_realpow__minus__mult) ).

fof(c_0_143,axiom,
    ! [X20,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,X23,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20)) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X23,X20)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).

fof(c_0_144,axiom,
    ! [X34,X33,X21,X2,X54,X3] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
     => ( X54 != c_Groups_Ozero__class_Ozero(X3)
       => ( ( X2 = X21
            & X33 != X34 )
         => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Otimes__class_Otimes(X3,X54,X33)) != c_Groups_Oplus__class_Oplus(X3,X21,c_Groups_Otimes__class_Otimes(X3,X54,X34)) ) ) ),
    file('<stdin>',fact_add__scale__eq__noteq) ).

fof(c_0_145,axiom,
    ! [X20,X23,X22,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X22,X23)
       => c_Power_Opower__class_Opower(X3,c_Divides_Odiv__class_Odiv(X3,X23,X22),X20) = c_Divides_Odiv__class_Odiv(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X20)) ) ),
    file('<stdin>',fact_div__power) ).

fof(c_0_146,axiom,
    ! [X21,X39,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X21)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X39)) ) ) ),
    file('<stdin>',fact_zdiv__mono2) ).

fof(c_0_147,axiom,
    ! [X21,X39,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X21)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X39),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21)) ) ) ),
    file('<stdin>',fact_zdiv__mono2__neg) ).

fof(c_0_148,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X23)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
           => X23 = X22 ) ) ) ),
    file('<stdin>',fact_power2__eq__imp__eq) ).

fof(c_0_149,axiom,
    ! [X33,X21,X2] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X21),X33) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X33)),X33),
    file('<stdin>',fact_zmod__zmult1__eq) ).

fof(c_0_150,axiom,
    ! [X33,X21,X2] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X33)),X33) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X21),X33),
    file('<stdin>',fact_zmod__simps_I3_J) ).

fof(c_0_151,axiom,
    ! [X19,X22,X23] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X19)),X19) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,X22),X19),
    file('<stdin>',fact_zdiff__zmod__right) ).

fof(c_0_152,axiom,
    ! [X22,X19,X23] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X19),X22),X19) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,X22),X19),
    file('<stdin>',fact_zdiff__zmod__left) ).

fof(c_0_153,axiom,
    ! [X22,X19,X23] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X19),X22),X19) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X22),X19),
    file('<stdin>',fact_zpower__zmod) ).

fof(c_0_154,axiom,
    ! [X19,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7)),X19) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X51),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X19)) ),
    file('<stdin>',fact_diff__Suc__diff__eq2) ).

fof(c_0_155,axiom,
    ! [X19,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),c_Nat_OSuc(X51)) ),
    file('<stdin>',fact_diff__Suc__diff__eq1) ).

fof(c_0_156,axiom,
    ! [X19,X21,X20,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X2,X20),X21)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
         => c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X2,X19),X21) ) ) ),
    file('<stdin>',fact_power__le__dvd) ).

fof(c_0_157,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X17))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
    file('<stdin>',fact_Suc__mult__le__cancel1) ).

fof(c_0_158,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X17))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
    file('<stdin>',fact_Suc__mult__less__cancel1) ).

fof(c_0_159,axiom,
    ! [X20,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin) ),
    file('<stdin>',fact_power__m1__odd) ).

fof(c_0_160,axiom,
    ! [X24,X42,X25,X3] :
      ( class_Rings_Oidom(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X25,X42),c_Groups_Otimes__class_Otimes(X3,X24,X42))
      <=> ( X42 = c_Groups_Ozero__class_Ozero(X3)
          | c_Rings_Odvd__class_Odvd(X3,X25,X24) ) ) ),
    file('<stdin>',fact_dvd__mult__cancel__right) ).

fof(c_0_161,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Rings_Oidom(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
      <=> ( X42 = c_Groups_Ozero__class_Ozero(X3)
          | c_Rings_Odvd__class_Odvd(X3,X25,X24) ) ) ),
    file('<stdin>',fact_dvd__mult__cancel__left) ).

fof(c_0_162,axiom,
    ! [X66,X65,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X65)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X5))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X5),X65) ) ),
    file('<stdin>',fact_le__diff__conv2) ).

fof(c_0_163,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
       => c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20))) ) ),
    file('<stdin>',fact_power__gt1__lemma) ).

fof(c_0_164,axiom,
    ! [X24,X42,X25,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X25,X42),c_Groups_Oplus__class_Oplus(X3,X24,X42))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X25,X24) ) ),
    file('<stdin>',fact_add__le__cancel__right) ).

fof(c_0_165,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X42,X25),c_Groups_Oplus__class_Oplus(X3,X42,X24))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X25,X24) ) ),
    file('<stdin>',fact_add__le__cancel__left) ).

fof(c_0_166,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X33))
       => c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ),
    file('<stdin>',fact_add__le__imp__le__right) ).

fof(c_0_167,axiom,
    ! [X21,X2,X33,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X33,X2),c_Groups_Oplus__class_Oplus(X3,X33,X21))
       => c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ),
    file('<stdin>',fact_add__le__imp__le__left) ).

fof(c_0_168,axiom,
    ! [X21,X2,X33,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X33,X2),c_Groups_Oplus__class_Oplus(X3,X33,X21))
       => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ),
    file('<stdin>',fact_add__less__imp__less__left) ).

fof(c_0_169,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X33))
       => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ),
    file('<stdin>',fact_add__less__imp__less__right) ).

fof(c_0_170,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X42,X25),c_Groups_Oplus__class_Oplus(X3,X42,X24))
      <=> c_Orderings_Oord__class_Oless(X3,X25,X24) ) ),
    file('<stdin>',fact_add__less__cancel__left) ).

fof(c_0_171,axiom,
    ! [X24,X42,X25,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X25,X42),c_Groups_Oplus__class_Oplus(X3,X24,X42))
      <=> c_Orderings_Oord__class_Oless(X3,X25,X24) ) ),
    file('<stdin>',fact_add__less__cancel__right) ).

fof(c_0_172,axiom,
    ! [X35,X54,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X35))
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    file('<stdin>',fact_self__quotient__aux2) ).

fof(c_0_173,axiom,
    ! [X20,X19,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X19)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20)
       => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X7),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20) ) ),
    file('<stdin>',fact_Nat_Odiff__diff__eq) ).

fof(c_0_174,axiom,
    ! [X35,X54,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X35))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X2)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X35) ) ) ),
    file('<stdin>',fact_self__quotient__aux1) ).

fof(c_0_175,axiom,
    ! [X55,X17,X18] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
       => hBOOL(hAPP(hAPP(X55,X17),X18)) )
     => ( ( X18 = X17
         => hBOOL(hAPP(hAPP(X55,X17),X18)) )
       => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
           => hBOOL(hAPP(hAPP(X55,X17),X18)) )
         => hBOOL(hAPP(hAPP(X55,X17),X18)) ) ) ),
    file('<stdin>',fact_nat__less__cases) ).

fof(c_0_176,axiom,
    ! [X20,X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20)) = c_Power_Opower__class_Opower(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('<stdin>',fact_power__even__eq) ).

fof(c_0_177,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20))
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X19)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
         => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X20) ) ) ),
    file('<stdin>',fact_dvd__diffD1) ).

fof(c_0_178,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20))
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X20)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
         => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X19) ) ) ),
    file('<stdin>',fact_dvd__diffD) ).

fof(c_0_179,axiom,
    ! [X24,X25,X17] :
      ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X25,X17),c_Power_Opower__class_Opower(tc_Nat_Onat,X24,X17))
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24) ) ),
    file('<stdin>',fact_pow__divides__eq__nat) ).

fof(c_0_180,axiom,
    ! [X21,X20,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X20),c_Power_Opower__class_Opower(tc_Nat_Onat,X21,X20))
     => ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21) ) ),
    file('<stdin>',fact_pow__divides__pow__nat) ).

fof(c_0_181,axiom,
    ! [X21,X20,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X20),c_Power_Opower__class_Opower(tc_Int_Oint,X21,X20))
     => ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X21) ) ),
    file('<stdin>',fact_pow__divides__pow__int) ).

fof(c_0_182,axiom,
    ! [X24,X25,X17] :
      ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X25,X17),c_Power_Opower__class_Opower(tc_Int_Oint,X24,X17))
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,X24) ) ),
    file('<stdin>',fact_pow__divides__eq__int) ).

fof(c_0_183,axiom,
    ! [X23,X3] :
      ( class_Rings_Oring__1(X3)
     => c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X23),c_Groups_Oone__class_Oone(X3)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X23,c_Groups_Oone__class_Oone(X3)),c_Groups_Ominus__class_Ominus(X3,X23,c_Groups_Oone__class_Oone(X3))) ),
    file('<stdin>',fact_real__squared__diff__one__factored) ).

fof(c_0_184,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X19),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X20))
     => ( X7 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X19,X20) ) ),
    file('<stdin>',fact_zdvd__mult__cancel) ).

fof(c_0_185,axiom,
    ! [X57,X18,X5] :
      ( X5 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X18,X57)
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X18),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X57)) ) ),
    file('<stdin>',fact_zdvd__mono) ).

fof(c_0_186,axiom,
    ! [X17,X18,X5] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
    <=> ( X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,X17) ) ),
    file('<stdin>',fact_nat__mult__dvd__cancel__disj) ).

fof(c_0_187,axiom,
    ! [X17,X5,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X5),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X5))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ),
    file('<stdin>',fact_mult__less__cancel2) ).

fof(c_0_188,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ),
    file('<stdin>',fact_mult__less__cancel1) ).

fof(c_0_189,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X17))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
    file('<stdin>',fact_nat__add__left__cancel__le) ).

fof(c_0_190,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X17))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
    file('<stdin>',fact_nat__add__left__cancel__less) ).

fof(c_0_191,axiom,
    ! [X21,X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Power_Opower__class_Opower(X3,X2,X20) = c_Power_Opower__class_Opower(X3,X21,X20)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
           => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
             => X2 = X21 ) ) ) ) ),
    file('<stdin>',fact_power__eq__imp__eq__base) ).

fof(c_0_192,axiom,
    ! [X20,X21,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X21,X20)) ) ) ),
    file('<stdin>',fact_power__mono) ).

fof(c_0_193,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Oordered__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ) ),
    file('<stdin>',fact_mult__right__mono) ).

fof(c_0_194,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Oordered__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
    file('<stdin>',fact_mult__left__mono) ).

fof(c_0_195,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Oordered__comm__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
    file('<stdin>',fact_comm__mult__left__mono) ).

fof(c_0_196,axiom,
    ! [X33,X2,X21,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X21,X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ) ),
    file('<stdin>',fact_mult__right__mono__neg) ).

fof(c_0_197,axiom,
    ! [X33,X2,X21,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X21,X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
    file('<stdin>',fact_mult__left__mono__neg) ).

fof(c_0_198,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ) ),
    file('<stdin>',fact_mult__strict__right__mono) ).

fof(c_0_199,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
    file('<stdin>',fact_mult__strict__left__mono) ).

fof(c_0_200,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Olinordered__comm__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
    file('<stdin>',fact_comm__mult__strict__left__mono) ).

fof(c_0_201,axiom,
    ! [X33,X2,X21,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X21,X2)
       => ( c_Orderings_Oord__class_Oless(X3,X33,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ) ),
    file('<stdin>',fact_mult__strict__right__mono__neg) ).

fof(c_0_202,axiom,
    ! [X33,X2,X21,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X21,X2)
       => ( c_Orderings_Oord__class_Oless(X3,X33,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
    file('<stdin>',fact_mult__strict__left__mono__neg) ).

fof(c_0_203,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X23)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
         => ( c_Orderings_Oord__class_Oless__eq(X3,X22,c_Groups_Oone__class_Oone(X3))
           => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),X23) ) ) ) ),
    file('<stdin>',fact_mult__right__le__one__le) ).

fof(c_0_204,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X23)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
         => ( c_Orderings_Oord__class_Oless__eq(X3,X22,c_Groups_Oone__class_Oone(X3))
           => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X22,X23),X23) ) ) ) ),
    file('<stdin>',fact_mult__left__le__one__le) ).

fof(c_0_205,axiom,
    ! [X2,X62,X20,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X62)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
         => c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X2,X62)) ) ) ),
    file('<stdin>',fact_power__strict__increasing) ).

fof(c_0_206,axiom,
    ! [X2,X62,X20,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X62)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X2)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X2,X62)) ) ) ),
    file('<stdin>',fact_power__increasing) ).

fof(c_0_207,axiom,
    ! [X16,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)))
      <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
            & X15 != c_Groups_Ozero__class_Ozero(X3) )
          | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
            & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
    file('<stdin>',fact_zero__less__power__eq__number__of) ).

fof(c_0_208,axiom,
    ! [X19,X20,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19),X7)) ),
    file('<stdin>',fact_le__add__diff) ).

fof(c_0_209,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ) ) ),
    file('<stdin>',fact_add__less__le__mono) ).

fof(c_0_210,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,X33,X34)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ) ) ),
    file('<stdin>',fact_add__le__less__mono) ).

fof(c_0_211,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ) ) ),
    file('<stdin>',fact_add__mono) ).

fof(c_0_212,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,X33,X34)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ) ) ),
    file('<stdin>',fact_add__strict__mono) ).

fof(c_0_213,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
       => ( c_Rings_Odvd__class_Odvd(X3,X33,X34)
         => c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ),
    file('<stdin>',fact_mult__dvd__mono) ).

fof(c_0_214,axiom,
    ! [X19,X20,X3] :
      ( class_Power_Opower(X3)
     => ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X3,X19,X20) = c_Groups_Oone__class_Oone(X3) )
        & ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X3,X19,X20) = c_Groups_Otimes__class_Otimes(X3,X19,c_Power_Opower__class_Opower(X3,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    file('<stdin>',fact_realpow__num__eq__if) ).

fof(c_0_215,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X21) ) ),
    file('<stdin>',fact_mod__pos__neg__trivial) ).

fof(c_0_216,axiom,
    ! [X19,X20,X22,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X23,X22)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
         => c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X19)) ) ) ),
    file('<stdin>',fact_dvd__power__le) ).

fof(c_0_217,axiom,
    ! [X14,X15,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X15,X15),c_Groups_Otimes__class_Otimes(X3,X14,X14)) = c_Groups_Ozero__class_Ozero(X3)
      <=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
          & X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    file('<stdin>',fact_sum__squares__eq__zero__iff) ).

fof(c_0_218,axiom,
    ! [X16,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)),c_Groups_Ozero__class_Ozero(X3))
      <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
              & c_Orderings_Oord__class_Oless__eq(X3,X15,c_Groups_Ozero__class_Ozero(X3)) )
            | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
              & X15 = c_Groups_Ozero__class_Ozero(X3) ) ) ) ) ),
    file('<stdin>',fact_power__le__zero__eq__number__of) ).

fof(c_0_219,axiom,
    ! [X16,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)))
      <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
          | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
            & c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
    file('<stdin>',fact_zero__le__power__eq__number__of) ).

fof(c_0_220,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) = c_Groups_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X3,X2,X21),X33) ),
    file('<stdin>',fact_mod__mult__mult2) ).

fof(c_0_221,axiom,
    ! [X21,X2,X33,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) = c_Groups_Otimes__class_Otimes(X3,X33,c_Divides_Odiv__class_Omod(X3,X2,X21)) ),
    file('<stdin>',fact_mod__mult__mult1) ).

fof(c_0_222,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Otimes__class_Otimes(X3,X33,X21)),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
    file('<stdin>',fact_mod__mult__self1) ).

fof(c_0_223,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X33)),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
    file('<stdin>',fact_mod__mult__self2) ).

fof(c_0_224,axiom,
    ! [X44,X22,X23,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X22),X44) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X44),c_Groups_Otimes__class_Otimes(X3,X22,X44)) ),
    file('<stdin>',fact_mult__left_Odiff) ).

fof(c_0_225,axiom,
    ! [X21,X43,X2,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X2,X43),X21) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Otimes__class_Otimes(X3,X43,X21)) ),
    file('<stdin>',fact_mult_Odiff__left) ).

fof(c_0_226,axiom,
    ! [X22,X23,X40,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,X40,c_Groups_Ominus__class_Ominus(X3,X23,X22)) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X40,X23),c_Groups_Otimes__class_Otimes(X3,X40,X22)) ),
    file('<stdin>',fact_mult__right_Odiff) ).

fof(c_0_227,axiom,
    ! [X39,X21,X2,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ominus__class_Ominus(X3,X21,X39)) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Otimes__class_Otimes(X3,X2,X39)) ),
    file('<stdin>',fact_mult_Odiff__right) ).

fof(c_0_228,axiom,
    ! [X20,X21,X2,X3] :
      ( class_Groups_Ocomm__monoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X20) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X21,X20)) ),
    file('<stdin>',fact_power__mult__distrib) ).

fof(c_0_229,axiom,
    ! [X21,X19,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X19),c_Groups_Otimes__class_Otimes(X3,X21,X19)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X19) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(c_0_230,axiom,
    ! [X44,X22,X23,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X23,X22),X44) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X44),c_Groups_Otimes__class_Otimes(X3,X22,X44)) ),
    file('<stdin>',fact_mult__left_Oadd) ).

fof(c_0_231,axiom,
    ! [X21,X43,X2,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X43),X21) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Otimes__class_Otimes(X3,X43,X21)) ),
    file('<stdin>',fact_mult_Oadd__left) ).

fof(c_0_232,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(c_0_233,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ),
    file('<stdin>',fact_comm__semiring__class_Odistrib) ).

fof(c_0_234,axiom,
    ! [X22,X23,X40,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,X40,c_Groups_Oplus__class_Oplus(X3,X23,X22)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X40,X23),c_Groups_Otimes__class_Otimes(X3,X40,X22)) ),
    file('<stdin>',fact_mult__right_Oadd) ).

fof(c_0_235,axiom,
    ! [X10,X22,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X23,c_Groups_Oplus__class_Oplus(X3,X22,X10)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),c_Groups_Otimes__class_Otimes(X3,X23,X10)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(c_0_236,axiom,
    ! [X39,X21,X2,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Oplus__class_Oplus(X3,X21,X39)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Otimes__class_Otimes(X3,X2,X39)) ),
    file('<stdin>',fact_mult_Oadd__right) ).

fof(c_0_237,axiom,
    ! [X35,X22,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),X35) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X35),c_Power_Opower__class_Opower(X3,X22,X35)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).

fof(c_0_238,axiom,
    ! [X20,X19,X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X2,X19),c_Power_Opower__class_Opower(X3,X2,X20)) ),
    file('<stdin>',fact_power__add) ).

fof(c_0_239,axiom,
    ! [X35,X38,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X38),c_Power_Opower__class_Opower(X3,X23,X35)) = c_Power_Opower__class_Opower(X3,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X35)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

fof(c_0_240,axiom,
    ! [X21,X43,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X43)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X43,X21)) ) ),
    file('<stdin>',fact_zdiv__mono1) ).

fof(c_0_241,axiom,
    ! [X21,X43,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X43)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X43,X21),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21)) ) ),
    file('<stdin>',fact_zdiv__mono1__neg) ).

fof(c_0_242,axiom,
    ! [X22,X23,X10] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X10)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,X22)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X10,X23),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X10,X22)) ) ),
    file('<stdin>',fact_real__mult__less__mono2) ).

fof(c_0_243,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X53),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X51)) ) ),
    file('<stdin>',fact_mult__less__mono2) ).

fof(c_0_244,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X7)) ) ),
    file('<stdin>',fact_mult__less__mono1) ).

fof(c_0_245,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X53,X51)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X53),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X51)) ) ),
    file('<stdin>',fact_zmult__zless__mono2) ).

fof(c_0_246,axiom,
    ! [X38,X19] :
      ( ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Power_Opower__class_Opower(tc_Nat_Onat,X38,X19) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Power_Opower__class_Opower(tc_Nat_Onat,X38,X19) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X38,c_Power_Opower__class_Opower(tc_Nat_Onat,X38,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
    file('<stdin>',fact_power__eq__if) ).

fof(c_0_247,axiom,
    ! [X20,X19] :
      ( ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20)) ) ),
    file('<stdin>',fact_mult__eq__if) ).

fof(c_0_248,axiom,
    ! [X5,X17,X55] :
      ( hBOOL(hAPP(X55,c_Divides_Odiv__class_Omod(tc_Int_Oint,X17,X5)))
    <=> ( ( X5 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X55,X17)) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
         => ! [X77,X58] :
              ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X58)
                & c_Orderings_Oord__class_Oless(tc_Int_Oint,X58,X5)
                & X17 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
             => hBOOL(hAPP(X55,X58)) ) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => ! [X77,X58] :
              ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X58)
                & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                & X17 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
             => hBOOL(hAPP(X55,X58)) ) ) ) ),
    file('<stdin>',fact_split__zmod) ).

fof(c_0_249,axiom,
    ! [X10,X70,X8,X71] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X71,X8)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X70,X10)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X71,X70),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X10)) ) ),
    file('<stdin>',fact_zadd__zless__mono) ).

fof(c_0_250,axiom,
    ! [X6,X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X6)) ) ),
    file('<stdin>',fact_mult__le__mono) ).

fof(c_0_251,axiom,
    ! [X6,X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X6)) ) ),
    file('<stdin>',fact_add__le__mono) ).

fof(c_0_252,axiom,
    ! [X6,X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X6)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X19)) ) ),
    file('<stdin>',fact_diff__less__mono2) ).

fof(c_0_253,axiom,
    ! [X33,X21,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X21)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X2)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X33),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X33)) ) ),
    file('<stdin>',fact_diff__less__mono) ).

fof(c_0_254,axiom,
    ! [X6,X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X6)) ) ),
    file('<stdin>',fact_add__less__mono) ).

fof(c_0_255,axiom,
    ! [X25,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      <=> X25 != c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_zero__less__power2) ).

fof(c_0_256,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21))
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21) ) ) ),
    file('<stdin>',fact_zero__less__mult__pos) ).

fof(c_0_257,axiom,
    ! [X2,X21,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X21,X2))
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21) ) ) ),
    file('<stdin>',fact_zero__less__mult__pos2) ).

fof(c_0_258,axiom,
    ! [X15] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
    <=> ? [X31] : X15 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X31),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('<stdin>',fact_odd__equiv__def) ).

fof(c_0_259,axiom,
    ! [X24,X25] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X25,X24))
      <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,X25)
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24) ) ) ),
    file('<stdin>',fact_nonneg1__imp__zdiv__pos__iff) ).

fof(c_0_260,axiom,
    ! [X2,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ~ c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X3)) ),
    file('<stdin>',fact_power2__less__0) ).

fof(c_0_261,axiom,
    ! [X8,X9] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X9)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X8))) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))),
    file('<stdin>',fact_zmod__number__of__Bit0) ).

fof(c_0_262,axiom,
    ! [X14,X15] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X15),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X14,X14)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> ( X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        & X14 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    file('<stdin>',fact_real__two__squares__add__zero__iff) ).

fof(c_0_263,axiom,
    ! [X19,X20,X7] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20),X19),X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),
    file('<stdin>',fact_mod__mult__self3) ).

fof(c_0_264,axiom,
    ! [X7,X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),X7) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X7)),
    file('<stdin>',fact_mod__mult__distrib) ).

fof(c_0_265,axiom,
    ! [X20,X19,X7] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X19),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20)),
    file('<stdin>',fact_mod__mult__distrib2) ).

fof(c_0_266,axiom,
    ! [X8,X12,X13] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X12),X8) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X13,X8),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X12,X8)),
    file('<stdin>',fact_real__add__mult__distrib) ).

fof(c_0_267,axiom,
    ! [X7,X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X7) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X7)),
    file('<stdin>',fact_diff__mult__distrib) ).

fof(c_0_268,axiom,
    ! [X20,X19,X7] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X19),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20)),
    file('<stdin>',fact_diff__mult__distrib2) ).

fof(c_0_269,axiom,
    ! [X12,X13,X8] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X13,X12)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X13),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X12)),
    file('<stdin>',fact_zdiff__zmult__distrib2) ).

fof(c_0_270,axiom,
    ! [X8,X12,X13] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X13,X12),X8) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,X8),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12,X8)),
    file('<stdin>',fact_zdiff__zmult__distrib) ).

fof(c_0_271,axiom,
    ! [X8,X12,X13] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,X12),X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,X8),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12,X8)),
    file('<stdin>',fact_zadd__zmult__distrib) ).

fof(c_0_272,axiom,
    ! [X12,X13,X8] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,X12)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X13),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X12)),
    file('<stdin>',fact_zadd__zmult__distrib2) ).

fof(c_0_273,axiom,
    ! [X7,X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X7)),
    file('<stdin>',fact_add__mult__distrib) ).

fof(c_0_274,axiom,
    ! [X20,X19,X7] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X19),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20)),
    file('<stdin>',fact_add__mult__distrib2) ).

fof(c_0_275,axiom,
    ! [X10,X22,X23] : c_Power_Opower__class_Opower(tc_Int_Oint,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X10)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X22),c_Power_Opower__class_Opower(tc_Int_Oint,X23,X10)),
    file('<stdin>',fact_zpower__zadd__distrib) ).

fof(c_0_276,axiom,
    ! [X5,X65,X66] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X66,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X5))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X5),X65) ),
    file('<stdin>',fact_less__diff__conv) ).

fof(c_0_277,axiom,
    ! [X66,X5,X65] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X5),X66)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X5)) ),
    file('<stdin>',fact_le__diff__conv) ).

fof(c_0_278,axiom,
    ! [X16,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)),c_Groups_Ozero__class_Ozero(X3))
      <=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
          & c_Orderings_Oord__class_Oless(X3,X15,c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    file('<stdin>',fact_power__less__zero__eq__number__of) ).

fof(c_0_279,axiom,
    ! [X20,X19,X7,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X7,c_Divides_Odiv__class_Omod(X3,X19,X20))
       => ( c_Rings_Odvd__class_Odvd(X3,X7,X20)
         => c_Rings_Odvd__class_Odvd(X3,X7,X19) ) ) ),
    file('<stdin>',fact_dvd__mod__imp__dvd) ).

fof(c_0_280,axiom,
    ! [X18,X17,X5,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X5,X17)
       => ( c_Rings_Odvd__class_Odvd(X3,X5,c_Divides_Odiv__class_Omod(X3,X18,X17))
        <=> c_Rings_Odvd__class_Odvd(X3,X5,X18) ) ) ),
    file('<stdin>',fact_dvd__mod__iff) ).

fof(c_0_281,axiom,
    ! [X21,X2,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
     => c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X33)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),X33) ),
    file('<stdin>',fact_zdiv__zmult2__eq) ).

fof(c_0_282,axiom,
    ! [X53,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),X51) ),
    file('<stdin>',fact_diff__diff__right) ).

fof(c_0_283,axiom,
    ! [X53,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X7) ),
    file('<stdin>',fact_add__diff__assoc) ).

fof(c_0_284,axiom,
    ! [X53,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7)) ),
    file('<stdin>',fact_diff__add__assoc) ).

fof(c_0_285,axiom,
    ! [X53,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7),X53) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X53),X7) ),
    file('<stdin>',fact_add__diff__assoc2) ).

fof(c_0_286,axiom,
    ! [X53,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X53),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7),X53) ),
    file('<stdin>',fact_diff__add__assoc2) ).

fof(c_0_287,axiom,
    ! [X25,X24] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X25,X24))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25) ) ),
    file('<stdin>',fact_pos__imp__zdiv__nonneg__iff) ).

fof(c_0_288,axiom,
    ! [X25,X24] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X25,X24))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('<stdin>',fact_neg__imp__zdiv__nonneg__iff) ).

fof(c_0_289,axiom,
    ! [X16,X15] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)))
    <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) ) ),
    file('<stdin>',fact_zero__less__power__nat__eq__number__of) ).

fof(c_0_290,axiom,
    ! [X66,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X66,X5))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X66) ) ),
    file('<stdin>',fact_pos__imp__zdiv__pos__iff) ).

fof(c_0_291,axiom,
    ! [X24,X25,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X25,X24))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X25)
            & c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X24) )
          | ( c_Orderings_Oord__class_Oless__eq(X3,X25,c_Groups_Ozero__class_Ozero(X3))
            & c_Orderings_Oord__class_Oless__eq(X3,X24,c_Groups_Ozero__class_Ozero(X3)) ) ) ) ),
    file('<stdin>',fact_zero__le__mult__iff) ).

fof(c_0_292,axiom,
    ! [X24,X25,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X25,X24),c_Groups_Ozero__class_Ozero(X3))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X25)
            & c_Orderings_Oord__class_Oless__eq(X3,X24,c_Groups_Ozero__class_Ozero(X3)) )
          | ( c_Orderings_Oord__class_Oless__eq(X3,X25,c_Groups_Ozero__class_Ozero(X3))
            & c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X24) ) ) ) ),
    file('<stdin>',fact_mult__le__0__iff) ).

fof(c_0_293,axiom,
    ! [X21,X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)) = c_Power_Opower__class_Opower(X3,X21,c_Nat_OSuc(X20))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
           => X2 = X21 ) ) ) ),
    file('<stdin>',fact_power__inject__base) ).

fof(c_0_294,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X20)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) ),
    file('<stdin>',fact_Suc__diff__eq__diff__pred) ).

fof(c_0_295,axiom,
    ! [X20,X19] :
      ( ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20) = X20 )
      & ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20)) ) ),
    file('<stdin>',fact_add__eq__if) ).

fof(c_0_296,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X20))
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X20)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X19) ) ),
    file('<stdin>',fact_zdvd__zmod__imp__zdvd) ).

fof(c_0_297,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X19,X20))
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X20)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X19) ) ),
    file('<stdin>',fact_zdvd__zdiffD) ).

fof(c_0_298,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oone__class_Oone(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)),c_Groups_Oone__class_Oone(X3)) ) ) ),
    file('<stdin>',fact_power__Suc__less__one) ).

fof(c_0_299,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17))
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18)
        & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17) ) ),
    file('<stdin>',fact_one__le__mult__iff) ).

fof(c_0_300,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)) ) ),
    file('<stdin>',fact_one__less__mult) ).

fof(c_0_301,axiom,
    ! [X22,X23,X20,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X23,X22)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X20)) ) ) ),
    file('<stdin>',fact_power__mono__odd) ).

fof(c_0_302,axiom,
    ! [X20,X54,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X54)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X54,c_Groups_Oone__class_Oone(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X54,c_Nat_OSuc(X20)),X54) ) ) ),
    file('<stdin>',fact_realpow__Suc__le__self) ).

fof(c_0_303,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    file('<stdin>',fact_add__nonpos__neg) ).

fof(c_0_304,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    file('<stdin>',fact_add__neg__nonpos) ).

fof(c_0_305,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X2,X21)) ) ) ),
    file('<stdin>',fact_add__nonneg__pos) ).

fof(c_0_306,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X2,X21)) ) ) ),
    file('<stdin>',fact_add__pos__nonneg) ).

fof(c_0_307,axiom,
    ! [X20,X19,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X19)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X20)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Otimes__class_Otimes(X3,X19,X20)) ) ) ),
    file('<stdin>',fact_less__1__mult) ).

fof(c_0_308,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    file('<stdin>',fact_add__nonpos__nonpos) ).

fof(c_0_309,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X2,X21)) ) ) ),
    file('<stdin>',fact_add__nonneg__nonneg) ).

fof(c_0_310,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__cancel__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ) ),
    file('<stdin>',fact_mult__nonneg__nonneg) ).

fof(c_0_311,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__cancel__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    file('<stdin>',fact_mult__nonneg__nonpos) ).

fof(c_0_312,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__cancel__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X21,X2),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    file('<stdin>',fact_mult__nonneg__nonpos2) ).

fof(c_0_313,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__cancel__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    file('<stdin>',fact_mult__nonpos__nonneg) ).

fof(c_0_314,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ) ),
    file('<stdin>',fact_mult__nonpos__nonpos) ).

fof(c_0_315,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
            & c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21) )
          | ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
            & c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3)) ) )
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ),
    file('<stdin>',fact_split__mult__pos__le) ).

fof(c_0_316,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__cancel__semiring(X3)
     => ( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
            & c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3)) )
          | ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
            & c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21) ) )
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ),
    file('<stdin>',fact_split__mult__neg__le) ).

fof(c_0_317,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X2,X21)) ) ) ),
    file('<stdin>',fact_add__pos__pos) ).

fof(c_0_318,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    file('<stdin>',fact_add__neg__neg) ).

fof(c_0_319,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ) ),
    file('<stdin>',fact_mult__pos__pos) ).

fof(c_0_320,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    file('<stdin>',fact_mult__pos__neg) ).

fof(c_0_321,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X21,X2),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    file('<stdin>',fact_mult__pos__neg2) ).

fof(c_0_322,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    file('<stdin>',fact_mult__neg__pos) ).

fof(c_0_323,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ) ),
    file('<stdin>',fact_mult__neg__neg) ).

fof(c_0_324,axiom,
    ! [X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X19))),
    file('<stdin>',fact_le__cube) ).

fof(c_0_325,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) ) ),
    file('<stdin>',fact_add__gr__0) ).

fof(c_0_326,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19)) ) ),
    file('<stdin>',fact_n__less__n__mult__m) ).

fof(c_0_327,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)) ) ),
    file('<stdin>',fact_n__less__m__mult__n) ).

fof(c_0_328,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X33)) ) ),
    file('<stdin>',fact_add__right__mono) ).

fof(c_0_329,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X33,X2),c_Groups_Oplus__class_Oplus(X3,X33,X21)) ) ),
    file('<stdin>',fact_add__left__mono) ).

fof(c_0_330,axiom,
    ! [X20,X22,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X23,X22)
       => c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X20)) ) ),
    file('<stdin>',fact_dvd__power__same) ).

fof(c_0_331,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X33,X2),c_Groups_Oplus__class_Oplus(X3,X33,X21)) ) ),
    file('<stdin>',fact_add__strict__left__mono) ).

fof(c_0_332,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X33)) ) ),
    file('<stdin>',fact_add__strict__right__mono) ).

fof(c_0_333,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
       => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X3,X2,X20)) ) ) ),
    file('<stdin>',fact_one__less__power) ).

fof(c_0_334,axiom,
    ! [X2,X20,X19,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
       => c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X2,X19),c_Power_Opower__class_Opower(X3,X2,X20)) ) ),
    file('<stdin>',fact_le__imp__power__dvd) ).

fof(c_0_335,axiom,
    ! [X10,X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X22) )
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X23) ) ) ),
    file('<stdin>',fact_dvd_Oless__trans) ).

fof(c_0_336,axiom,
    ! [X14,X17,X15] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,X17) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X17)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X15,X14)) ),
    file('<stdin>',fact_zmod__eq__dvd__iff) ).

fof(c_0_337,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X21,X33)
         => c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
    file('<stdin>',fact_add__strict__increasing2) ).

fof(c_0_338,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,X33)
         => c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
    file('<stdin>',fact_add__strict__increasing) ).

fof(c_0_339,axiom,
    ! [X2,X21,X33,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,X2)
         => c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
    file('<stdin>',fact_add__increasing2) ).

fof(c_0_340,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,X33)
         => c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
    file('<stdin>',fact_add__increasing) ).

fof(c_0_341,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X21,X33)
         => c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
    file('<stdin>',fact_pos__add__strict) ).

fof(c_0_342,axiom,
    ! [X16,X61,X3] :
      ( ( class_Int_Onumber(X3)
        & class_Orderings_Olinorder(X3) )
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X61),c_Int_Onumber__class_Onumber__of(X3,X16))
      <=> ~ c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X16),c_Int_Onumber__class_Onumber__of(X3,X61)) ) ),
    file('<stdin>',fact_le__number__of__eq__not__less) ).

fof(c_0_343,axiom,
    ! [X17,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,X17))
      <=> ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
            & X15 != c_Groups_Ozero__class_Ozero(X3) )
          | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
            & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
    file('<stdin>',fact_zero__less__power__eq) ).

fof(c_0_344,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
       => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X19,X20)
         => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X20,X19)
           => X19 = X20 ) ) ) ),
    file('<stdin>',fact_zdvd__antisym__nonneg) ).

fof(c_0_345,axiom,
    ! [X17,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X15,X17),c_Groups_Ozero__class_Ozero(X3))
      <=> ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
              & c_Orderings_Oord__class_Oless__eq(X3,X15,c_Groups_Ozero__class_Ozero(X3)) )
            | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
              & X15 = c_Groups_Ozero__class_Ozero(X3) ) ) ) ) ),
    file('<stdin>',fact_power__le__zero__eq) ).

fof(c_0_346,axiom,
    ! [X17,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,X17))
      <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
          | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
            & c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
    file('<stdin>',fact_zero__le__power__eq) ).

fof(c_0_347,axiom,
    ! [X17,X25,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X25,X17))
      <=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X25)
          | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ) ),
    file('<stdin>',fact_zero__le__power__iff) ).

fof(c_0_348,axiom,
    ! [X15,X17,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,X17))
        <=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ),
    file('<stdin>',fact_zero__le__odd__power) ).

fof(c_0_349,axiom,
    ! [X6,X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X6),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X6)) ),
    file('<stdin>',fact_diff__le__mono) ).

fof(c_0_350,axiom,
    ! [X6,X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X19)) ),
    file('<stdin>',fact_diff__le__mono2) ).

fof(c_0_351,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,X51)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X53),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X51)) ),
    file('<stdin>',fact_zadd__left__mono) ).

fof(c_0_352,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X53),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X51)) ),
    file('<stdin>',fact_mult__le__mono2) ).

fof(c_0_353,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X7)) ),
    file('<stdin>',fact_mult__le__mono1) ).

fof(c_0_354,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X7)) ),
    file('<stdin>',fact_add__le__mono1) ).

fof(c_0_355,axiom,
    ! [X10,X22,X23] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X23),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X22)) ),
    file('<stdin>',fact_real__add__left__mono) ).

fof(c_0_356,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X7)) ),
    file('<stdin>',fact_add__less__mono1) ).

fof(c_0_357,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X53,X51)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X53,X7),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X51,X7)) ),
    file('<stdin>',fact_zadd__strict__right__mono) ).

fof(c_0_358,axiom,
    ! [X19,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X19),X19) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oone__class_Oone(X3)),X19) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

fof(c_0_359,axiom,
    ! [X2,X19,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X19,c_Groups_Otimes__class_Otimes(X3,X2,X19)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oone__class_Oone(X3)),X19) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(c_0_360,axiom,
    ! [X20,X19,X7,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X7,X19)
       => ( c_Rings_Odvd__class_Odvd(X3,X7,X20)
         => c_Rings_Odvd__class_Odvd(X3,X7,c_Divides_Odiv__class_Omod(X3,X19,X20)) ) ) ),
    file('<stdin>',fact_dvd__mod) ).

fof(c_0_361,axiom,
    ! [X10,X22,X23,X3] :
      ( class_Rings_Ocomm__ring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X23,X22)
       => ( c_Rings_Odvd__class_Odvd(X3,X23,X10)
         => c_Rings_Odvd__class_Odvd(X3,X23,c_Groups_Ominus__class_Ominus(X3,X22,X10)) ) ) ),
    file('<stdin>',fact_dvd__diff) ).

fof(c_0_362,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
       => ( c_Rings_Odvd__class_Odvd(X3,X2,X33)
         => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Oplus__class_Oplus(X3,X21,X33)) ) ) ),
    file('<stdin>',fact_dvd__add) ).

fof(c_0_363,axiom,
    ! [X17] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
    <=> ? [X1] : X17 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) ),
    file('<stdin>',fact_odd__Suc__mult__two__ex) ).

fof(c_0_364,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X18),X18)
      <=> X17 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('<stdin>',fact_dvd__mult__cancel2) ).

fof(c_0_365,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17),X18)
      <=> X17 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('<stdin>',fact_dvd__mult__cancel1) ).

fof(c_0_366,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('<stdin>',fact_div__nonneg__neg__le0) ).

fof(c_0_367,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('<stdin>',fact_div__nonpos__pos__le0) ).

fof(c_0_368,axiom,
    ! [X22,X23] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X22)) ) ),
    file('<stdin>',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).

fof(c_0_369,axiom,
    ! [X22,X23] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ) ),
    file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

fof(c_0_370,axiom,
    ! [X22,X23] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
    file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(c_0_371,axiom,
    ! [X22,X23] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X23)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X22)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X23,X22)) ) ),
    file('<stdin>',fact_real__mult__order) ).

fof(c_0_372,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) ) ),
    file('<stdin>',fact_nat__0__less__mult__iff) ).

fof(c_0_373,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X18)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X17)
       => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X5) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X5)
        <=> X18 = X17 ) ) ),
    file('<stdin>',fact_eq__diff__iff) ).

fof(c_0_374,axiom,
    ! [X7,X23] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X7)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X23,X7),X23) ) ),
    file('<stdin>',fact_int__div__less__self) ).

fof(c_0_375,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X19) ) ),
    file('<stdin>',fact_diff__less) ).

fof(c_0_376,axiom,
    ! [X25,X3] :
      ( class_Groups_Olinordered__ab__group__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X25,X25),c_Groups_Ozero__class_Ozero(X3))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X25,c_Groups_Ozero__class_Ozero(X3)) ) ),
    file('<stdin>',fact_double__add__le__zero__iff__single__add__le__zero) ).

fof(c_0_377,axiom,
    ! [X25,X3] :
      ( class_Groups_Olinordered__ab__group__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X25,X25))
      <=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X25) ) ),
    file('<stdin>',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(c_0_378,axiom,
    ! [X25,X3] :
      ( class_Groups_Olinordered__ab__group__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X25,X25),c_Groups_Ozero__class_Ozero(X3))
      <=> c_Orderings_Oord__class_Oless(X3,X25,c_Groups_Ozero__class_Ozero(X3)) ) ),
    file('<stdin>',fact_double__add__less__zero__iff__single__add__less__zero) ).

fof(c_0_379,axiom,
    ! [X25,X3] :
      ( class_Groups_Olinordered__ab__group__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X25,X25))
      <=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X25) ) ),
    file('<stdin>',fact_zero__less__double__add__iff__zero__less__single__add) ).

fof(c_0_380,axiom,
    ! [X17,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X15,X17),c_Groups_Ozero__class_Ozero(X3))
      <=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
          & c_Orderings_Oord__class_Oless(X3,X15,c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    file('<stdin>',fact_power__less__zero__eq) ).

fof(c_0_381,axiom,
    ! [X25,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X25,X25),c_Groups_Ozero__class_Ozero(X3))
      <=> c_Orderings_Oord__class_Oless(X3,X25,c_Groups_Ozero__class_Ozero(X3)) ) ),
    file('<stdin>',fact_even__less__0__iff) ).

fof(c_0_382,axiom,
    ! [X7,X20,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),X20),c_Nat_OSuc(X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X7),
    file('<stdin>',fact_Suc__diff__diff) ).

fof(c_0_383,axiom,
    ! [X20,X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X2,X20),X2) = c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20)) ),
    file('<stdin>',fact_power__commutes) ).

fof(c_0_384,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oab__semigroup__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X21,X33)) ),
    file('<stdin>',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(c_0_385,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oab__semigroup__mult(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X33)) ),
    file('<stdin>',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

fof(c_0_386,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),X21) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(c_0_387,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X21,X33)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(c_0_388,axiom,
    ! [X34,X33,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X33,X34)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),X34) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(c_0_389,axiom,
    ! [X34,X33,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X33,X34)) = c_Groups_Oplus__class_Oplus(X3,X33,c_Groups_Oplus__class_Oplus(X3,X2,X34)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(c_0_390,axiom,
    ! [X26,X27,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X29,c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,X27,c_Groups_Otimes__class_Otimes(X3,X29,X26)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(c_0_391,axiom,
    ! [X26,X27,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X29,c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X27),X26) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

fof(c_0_392,axiom,
    ! [X27,X28,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),X27) = c_Groups_Otimes__class_Otimes(X3,X29,c_Groups_Otimes__class_Otimes(X3,X28,X27)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(c_0_393,axiom,
    ! [X27,X28,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),X27) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X27),X28) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

fof(c_0_394,axiom,
    ! [X20,X19,X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)) = c_Power_Opower__class_Opower(X3,c_Power_Opower__class_Opower(X3,X2,X19),X20) ),
    file('<stdin>',fact_power__mult) ).

fof(c_0_395,axiom,
    ! [X35,X38,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,c_Power_Opower__class_Opower(X3,X23,X38),X35) = c_Power_Opower__class_Opower(X3,X23,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X38,X35)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

fof(c_0_396,axiom,
    ! [X24,X25,X3] :
      ( class_Groups_Oordered__ab__group__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X25,X24)
      <=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),c_Groups_Ozero__class_Ozero(X3)) ) ),
    file('<stdin>',fact_less__iff__diff__less__0) ).

fof(c_0_397,axiom,
    ! [X24,X25,X3] :
      ( class_Groups_Oordered__ab__group__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X25,X24)
      <=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),c_Groups_Ozero__class_Ozero(X3)) ) ),
    file('<stdin>',fact_le__iff__diff__le__0) ).

fof(c_0_398,axiom,
    ! [X20,X19] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)),X20),
    file('<stdin>',fact_mod__Suc__eq__Suc__mod) ).

fof(c_0_399,axiom,
    ! [X6,X7] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X7),X6) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X6)),X6),
    file('<stdin>',fact_mult__Bit1) ).

fof(c_0_400,axiom,
    ! [X20,X19,X75] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X75,X19)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X75,X20)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X75,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X20)) ) ),
    file('<stdin>',fact_zdvd__zmod) ).

fof(c_0_401,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X19)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X20)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) ) ),
    file('<stdin>',fact_dvd__diff__nat) ).

fof(c_0_402,axiom,
    ! [X15] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('<stdin>',fact_neq__one__mod__two) ).

fof(c_0_403,axiom,
    ! [X41,X42,X24,X25,X3] :
      ( class_Groups_Oordered__ab__group__add(X3)
     => ( c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ominus__class_Ominus(X3,X42,X41)
       => ( c_Orderings_Oord__class_Oless(X3,X25,X24)
        <=> c_Orderings_Oord__class_Oless(X3,X42,X41) ) ) ),
    file('<stdin>',fact_diff__eq__diff__less) ).

fof(c_0_404,axiom,
    ! [X41,X42,X24,X25,X3] :
      ( class_Groups_Oordered__ab__group__add(X3)
     => ( c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ominus__class_Ominus(X3,X42,X41)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X25,X24)
        <=> c_Orderings_Oord__class_Oless__eq(X3,X42,X41) ) ) ),
    file('<stdin>',fact_diff__eq__diff__less__eq) ).

fof(c_0_405,axiom,
    ! [X32,X9] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
       => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X32)) ) ) ) ),
    file('<stdin>',fact_add__nat__number__of) ).

fof(c_0_406,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33)
       => c_Rings_Odvd__class_Odvd(X3,X21,X33) ) ),
    file('<stdin>',fact_dvd__mult__right) ).

fof(c_0_407,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33)
       => c_Rings_Odvd__class_Odvd(X3,X2,X33) ) ),
    file('<stdin>',fact_dvd__mult__left) ).

fof(c_0_408,axiom,
    ! [X7,X51,X53] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X51),X7) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X7),X51),
    file('<stdin>',fact_diff__commute) ).

fof(c_0_409,axiom,
    ! [X11,X12,X13] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X13,X12),X11) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X13,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X12,X11)),
    file('<stdin>',fact_real__mult__assoc) ).

fof(c_0_410,axiom,
    ! [X20,X7,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),
    file('<stdin>',fact_diff__cancel2) ).

fof(c_0_411,axiom,
    ! [X20,X19,X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X19),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),
    file('<stdin>',fact_diff__cancel) ).

fof(c_0_412,axiom,
    ! [X7,X51,X53] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X51),X7) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X7)),
    file('<stdin>',fact_diff__diff__left) ).

fof(c_0_413,axiom,
    ! [X11,X12,X13] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,X12),X11) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,X11)),
    file('<stdin>',fact_zadd__assoc) ).

fof(c_0_414,axiom,
    ! [X10,X22,X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X10)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X10)),
    file('<stdin>',fact_zadd__left__commute) ).

fof(c_0_415,axiom,
    ! [X10,X22,X23] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X22),X10) = c_Power_Opower__class_Opower(tc_Int_Oint,X23,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X10)),
    file('<stdin>',fact_zpower__zpower) ).

fof(c_0_416,axiom,
    ! [X7,X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X7)),
    file('<stdin>',fact_nat__add__assoc) ).

fof(c_0_417,axiom,
    ! [X10,X22,X23] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X10)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X10)),
    file('<stdin>',fact_nat__add__left__commute) ).

fof(c_0_418,axiom,
    ! [X7,X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20),X7) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X7)),
    file('<stdin>',fact_nat__mult__assoc) ).

fof(c_0_419,axiom,
    ! [X11,X12,X13] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,X12),X11) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12,X11)),
    file('<stdin>',fact_zmult__assoc) ).

fof(c_0_420,axiom,
    ! [X46,X16] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X46,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X46)
        | X16 = X46 ) ),
    file('<stdin>',fact_zless__add1__eq) ).

fof(c_0_421,axiom,
    ! [X17,X15] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X17))
    <=> ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) ) ),
    file('<stdin>',fact_zero__less__power__nat__eq) ).

fof(c_0_422,axiom,
    ! [X17,X15] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X17))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
        | X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('<stdin>',fact_nat__zero__less__power__iff) ).

fof(c_0_423,axiom,
    ! [X46,X16] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X46,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,X46) ),
    file('<stdin>',fact_zle__add1__eq__le) ).

fof(c_0_424,axiom,
    ! [X46,X16] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Groups_Oone__class_Oone(tc_Int_Oint)),X46)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X46) ),
    file('<stdin>',fact_add1__zle__eq) ).

fof(c_0_425,axiom,
    ! [X46,X16] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X46,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X46) ),
    file('<stdin>',fact_zle__diff1__eq) ).

fof(c_0_426,axiom,
    ! [X2,X21,X33,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X33,X21)
       => c_Divides_Odiv__class_Omod(X3,c_Divides_Odiv__class_Omod(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,X2,X33) ) ),
    file('<stdin>',fact_mod__mod__cancel) ).

fof(c_0_427,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('<stdin>',fact_less__bin__lemma) ).

fof(c_0_428,axiom,
    ! [X18,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X18))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
    file('<stdin>',fact_zero__less__diff) ).

fof(c_0_429,axiom,
    ! [X14,X15] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X15,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('<stdin>',fact_real__le__eq__diff) ).

fof(c_0_430,axiom,
    ! [X10,X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X23) ) ) ),
    file('<stdin>',fact_dvd_Oless__le__trans) ).

fof(c_0_431,axiom,
    ! [X10,X22,X23] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
     => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X22) )
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X23) ) ) ),
    file('<stdin>',fact_dvd_Ole__less__trans) ).

fof(c_0_432,axiom,
    ! [X20,X19,X6,X7] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X20)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ) ),
    file('<stdin>',fact_less__add__eq__less) ).

fof(c_0_433,axiom,
    ! [X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
     => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
      <=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    file('<stdin>',fact_even__num__iff) ).

fof(c_0_434,axiom,
    ! [X20,X7,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),X20)
     => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
         => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20) ) ),
    file('<stdin>',fact_add__leE) ).

fof(c_0_435,axiom,
    ! [X20,X7,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
    file('<stdin>',fact_add__leD1) ).

fof(c_0_436,axiom,
    ! [X20,X7,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20) ),
    file('<stdin>',fact_add__leD2) ).

fof(c_0_437,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X7)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X7) ),
    file('<stdin>',fact_add__lessD1) ).

fof(c_0_438,axiom,
    ! [X17,X5] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X5))
    <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5,X17) ),
    file('<stdin>',fact_dvd__reduce) ).

fof(c_0_439,axiom,
    ! [X9] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9))
     => c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('<stdin>',fact_expand__Suc) ).

fof(c_0_440,axiom,
    ! [X14,X15,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X14)
         => ( c_Groups_Oplus__class_Oplus(X3,X15,X14) = c_Groups_Ozero__class_Ozero(X3)
          <=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
              & X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ) ) ),
    file('<stdin>',fact_add__nonneg__eq__0__iff) ).

fof(c_0_441,axiom,
    ! [X14,X15,X3] :
      ( ( class_Divides_Osemiring__div(X3)
        & class_Int_Onumber(X3) )
     => ( c_Rings_Odvd__class_Odvd(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Divides_Odiv__class_Omod(X3,c_Int_Onumber__class_Onumber__of(X3,X14),c_Int_Onumber__class_Onumber__of(X3,X15)) = c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_dvd__eq__mod__eq__0__number__of) ).

fof(c_0_442,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) ),
    file('<stdin>',fact_le__mod__geq) ).

fof(c_0_443,axiom,
    ! [X60,X61] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X60))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X61,X60)
         => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X60) )
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,X61,X60) ) ),
    file('<stdin>',fact_less__nat__number__of) ).

fof(c_0_444,axiom,
    ! [X15] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
    <=> ? [X31] : X15 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31)) ),
    file('<stdin>',fact_odd__nat__equiv__def2) ).

fof(c_0_445,axiom,
    ! [X20,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20)) = c_Groups_Oone__class_Oone(X3) ),
    file('<stdin>',fact_power__m1__even) ).

fof(c_0_446,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
       => c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20))) ) ),
    file('<stdin>',fact_power__gt1) ).

fof(c_0_447,axiom,
    ! [X8,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(X8)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X3,X8)),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
    file('<stdin>',fact_number__of__Bit1) ).

fof(c_0_448,axiom,
    ! [X8,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(X8)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X3,X8)),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
    file('<stdin>',fact_number__of__Bit0) ).

fof(c_0_449,axiom,
    ! [X17,X18,X25,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X25)
       => ( c_Power_Opower__class_Opower(X3,X25,X18) = c_Power_Opower__class_Opower(X3,X25,X17)
        <=> X18 = X17 ) ) ),
    file('<stdin>',fact_power__inject__exp) ).

fof(c_0_450,axiom,
    ! [X20,X19] :
      ( ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)) = X20
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)) != X20
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)) ) ),
    file('<stdin>',fact_mod__Suc) ).

fof(c_0_451,axiom,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ) ),
    file('<stdin>',fact_dvd_Oless__asym) ).

fof(c_0_452,axiom,
    ! [X21,X2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2) )
     => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21) ) ),
    file('<stdin>',fact_dvd_Oless__asym_H) ).

fof(c_0_453,axiom,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ) ),
    file('<stdin>',fact_dvd_Oless__imp__not__less) ).

fof(c_0_454,axiom,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ) ),
    file('<stdin>',fact_dvd_Oless__not__sym) ).

fof(c_0_455,axiom,
    ! [X20,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X53)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X20)) ),
    file('<stdin>',fact_nat__one__le__power) ).

fof(c_0_456,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,X20)) ) ),
    file('<stdin>',fact_zero__le__power) ).

fof(c_0_457,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X2)
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X3,X2,X20)) ) ),
    file('<stdin>',fact_one__le__power) ).

fof(c_0_458,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,X20)) ) ),
    file('<stdin>',fact_zero__less__power) ).

fof(c_0_459,axiom,
    ! [X2,X3] :
      ( class_Rings_Olinordered__ring(X3)
     => ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X2),c_Groups_Ozero__class_Ozero(X3)) ),
    file('<stdin>',fact_not__square__less__zero) ).

fof(c_0_460,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X2,X2),X2) ),
    file('<stdin>',fact_power3__eq__cube) ).

fof(c_0_461,axiom,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,X14))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14)
        | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
          & c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) )
        | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
          & ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) ) ) ),
    file('<stdin>',fact_even__difference__nat) ).

fof(c_0_462,axiom,
    ! [X2,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    file('<stdin>',fact_zero__le__power2) ).

fof(c_0_463,axiom,
    ! [X19,X53] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X19))),
    file('<stdin>',fact_less__add__Suc1) ).

fof(c_0_464,axiom,
    ! [X19,X53] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X53))),
    file('<stdin>',fact_less__add__Suc2) ).

fof(c_0_465,axiom,
    ! [X32,X9] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
       => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
       => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X32)) ) ),
    file('<stdin>',fact_mult__nat__number__of) ).

fof(c_0_466,axiom,
    ! [X20,X19] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = X19 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) ) ),
    file('<stdin>',fact_mod__if) ).

fof(c_0_467,axiom,
    ! [X20,X19] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) ),
    file('<stdin>',fact_mod__geq) ).

fof(c_0_468,axiom,
    ! [X60,X61] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X60))
    <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,X60)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,c_Int_OPls) ) ),
    file('<stdin>',fact_le__nat__number__of) ).

fof(c_0_469,axiom,
    ! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10),X10) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('<stdin>',fact_odd__nonzero) ).

fof(c_0_470,axiom,
    ! [X14,X15] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X14))
    <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X14),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('<stdin>',fact_zdvd__iff__zmod__eq__0__number__of) ).

fof(c_0_471,axiom,
    ! [X53,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Nat_OSuc(X53)),X20) ),
    file('<stdin>',fact_diff__Suc__less) ).

fof(c_0_472,axiom,
    ! [X15] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X15))
    <=> X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('<stdin>',fact_not__real__square__gt__zero) ).

fof(c_0_473,axiom,
    ! [X23,X20,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
          | X23 = c_Groups_Oone__class_Oone(X3) )
       => c_Rings_Odvd__class_Odvd(X3,X23,c_Power_Opower__class_Opower(X3,X23,X20)) ) ),
    file('<stdin>',fact_dvd__power) ).

fof(c_0_474,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
     => ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17)
      <=> X18 = X17 ) ),
    file('<stdin>',fact_nat__mult__eq__cancel1) ).

fof(c_0_475,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
       => ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,X19) ) ),
    file('<stdin>',fact_nat__dvd__not__less) ).

fof(c_0_476,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X19,X20)
       => ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X20,X19) ) ),
    file('<stdin>',fact_zdvd__not__zless) ).

fof(c_0_477,axiom,
    ! [X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
       => c_Groups_Otimes__class_Otimes(X3,X2,c_Divides_Odiv__class_Odiv(X3,X21,X2)) = X21 ) ),
    file('<stdin>',fact_dvd__mult__div__cancel) ).

fof(c_0_478,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X33)
       => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ),
    file('<stdin>',fact_dvd__mult) ).

fof(c_0_479,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
       => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ),
    file('<stdin>',fact_dvd__mult2) ).

fof(c_0_480,axiom,
    ! [X10] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10)) ),
    file('<stdin>',fact_le__imp__0__less) ).

fof(c_0_481,axiom,
    ! [X20] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20)),
    file('<stdin>',fact_two__realpow__ge__one) ).

fof(c_0_482,axiom,
    ! [X23] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
       => ( X23 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | X23 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    file('<stdin>',fact_int__pos__lt__two__imp__zero__or__one) ).

fof(c_0_483,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) ),
    file('<stdin>',fact_Suc__diff__le) ).

fof(c_0_484,axiom,
    ! [X2,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21)) ),
    file('<stdin>',fact_pos__mod__sign) ).

fof(c_0_485,axiom,
    ! [X2,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21))
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),X21) ) ),
    file('<stdin>',fact_pos__mod__conj) ).

fof(c_0_486,axiom,
    ! [X2,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('<stdin>',fact_neg__mod__sign) ).

fof(c_0_487,axiom,
    ! [X2,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21)) ) ),
    file('<stdin>',fact_neg__mod__conj) ).

fof(c_0_488,axiom,
    ! [X20,X23] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,X23,X20)) ),
    file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

fof(c_0_489,axiom,
    ! [X8,X30] :
      ( ( class_Groups_Omonoid__mult(X30)
        & class_Int_Onumber(X30) )
     => c_Power_Opower__class_Opower(X30,c_Int_Onumber__class_Onumber__of(X30,X8),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X8),c_Int_Onumber__class_Onumber__of(X30,X8)) ),
    file('<stdin>',fact_power2__eq__square__number__of) ).

fof(c_0_490,axiom,
    ! [X19,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X19,X19) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3)),X19) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(c_0_491,axiom,
    ! [X10,X8] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X8,X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Groups_Oone__class_Oone(tc_Int_Oint)),X10) ),
    file('<stdin>',fact_zless__imp__add1__zle) ).

fof(c_0_492,axiom,
    ! [X51,X53] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X53),
    file('<stdin>',fact_not__add__less1) ).

fof(c_0_493,axiom,
    ! [X53,X51] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X53),X53),
    file('<stdin>',fact_not__add__less2) ).

fof(c_0_494,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),X20) ),
    file('<stdin>',fact_mod__le__divisor) ).

fof(c_0_495,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),X20) ),
    file('<stdin>',fact_mod__less__divisor) ).

fof(c_0_496,axiom,
    ! [X2,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),X21) ),
    file('<stdin>',fact_pos__mod__bound) ).

fof(c_0_497,axiom,
    ! [X2,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21)) ),
    file('<stdin>',fact_neg__mod__bound) ).

fof(c_0_498,axiom,
    ! [X7,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X7),X19) ),
    file('<stdin>',fact_zmod__le__nonneg__dividend) ).

fof(c_0_499,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
    <=> ? [X59] : X17 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X59)) ),
    file('<stdin>',fact_less__iff__Suc__add) ).

fof(c_0_500,axiom,
    ! [X20,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X20)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X53)) = X53 ),
    file('<stdin>',fact_diff__diff__cancel) ).

fof(c_0_501,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) = X19 ),
    file('<stdin>',fact_le__add__diff__inverse) ).

fof(c_0_502,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) = X19 ),
    file('<stdin>',fact_le__add__diff__inverse2) ).

fof(c_0_503,axiom,
    ! [X19,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X51)) ),
    file('<stdin>',fact_trans__le__add2) ).

fof(c_0_504,axiom,
    ! [X19,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X19)) ),
    file('<stdin>',fact_trans__le__add1) ).

fof(c_0_505,axiom,
    ! [X20,X7,X51] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X51,X7)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X20),X7) ),
    file('<stdin>',fact_less__imp__diff__less) ).

fof(c_0_506,axiom,
    ! [X19,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X19)) ),
    file('<stdin>',fact_trans__less__add1) ).

fof(c_0_507,axiom,
    ! [X19,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X51)) ),
    file('<stdin>',fact_trans__less__add2) ).

fof(c_0_508,axiom,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X14))
    <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ) ),
    file('<stdin>',fact_even__power__nat) ).

fof(c_0_509,axiom,
    ! [X8,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3)),c_Int_Onumber__class_Onumber__of(X3,X8)) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(X8)) ),
    file('<stdin>',fact_double__number__of__Bit0) ).

fof(c_0_510,axiom,
    ! [X14,X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X14) ) ),
    file('<stdin>',fact_le__number__of) ).

fof(c_0_511,axiom,
    ! [X14,X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,X14) ) ),
    file('<stdin>',fact_less__number__of) ).

fof(c_0_512,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
       => ( c_Rings_Odvd__class_Odvd(X3,X21,X33)
         => c_Rings_Odvd__class_Odvd(X3,X2,X33) ) ) ),
    file('<stdin>',fact_dvd__trans) ).

fof(c_0_513,axiom,
    ! [X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X8)) = c_Groups_Ominus__class_Ominus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
    file('<stdin>',fact_number__of__diff) ).

fof(c_0_514,axiom,
    ! [X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)) = c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
    file('<stdin>',fact_number__of__add) ).

fof(c_0_515,axiom,
    ! [X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)) ),
    file('<stdin>',fact_add__number__of__eq) ).

fof(c_0_516,axiom,
    ! [X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)) ),
    file('<stdin>',fact_arith__simps_I32_J) ).

fof(c_0_517,axiom,
    ! [X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)) = c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
    file('<stdin>',fact_number__of__mult) ).

fof(c_0_518,axiom,
    ! [X20,X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X2,X20),X2) ),
    file('<stdin>',fact_power__Suc2) ).

fof(c_0_519,axiom,
    ! [X20,X2,X3] :
      ( class_Power_Opower(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)) = c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20)) ),
    file('<stdin>',fact_power__Suc) ).

fof(c_0_520,axiom,
    ! [X35,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(X35)) = c_Groups_Otimes__class_Otimes(X3,X23,c_Power_Opower__class_Opower(X3,X23,X35)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).

fof(c_0_521,axiom,
    ! [X35,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X23,c_Power_Opower__class_Opower(X3,X23,X35)) = c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(X35)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).

fof(c_0_522,axiom,
    ! [X35,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X35),X23) = c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(X35)) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).

fof(c_0_523,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X20)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19) ) ),
    file('<stdin>',fact_dvd__pos__nat) ).

fof(c_0_524,axiom,
    ! [X5,X66] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X66,X5) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ( X5 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X66)
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X66,X5) )
        | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X66,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X66) ) ) ),
    file('<stdin>',fact_zdiv__eq__0__iff) ).

fof(c_0_525,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X21)
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('<stdin>',fact_div__pos__pos__trivial) ).

fof(c_0_526,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X2)
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('<stdin>',fact_div__neg__neg__trivial) ).

fof(c_0_527,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X51,X7)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X53),X7) ) ),
    file('<stdin>',fact_less__trans__Suc) ).

fof(c_0_528,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X21)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21) = X2 ) ),
    file('<stdin>',fact_mod__pos__pos__trivial) ).

fof(c_0_529,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X2)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21) = X2 ) ),
    file('<stdin>',fact_mod__neg__neg__trivial) ).

fof(c_0_530,axiom,
    ! [X20,X10] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X10,X20)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X20) ) ),
    file('<stdin>',fact_zdvd__imp__le) ).

fof(c_0_531,axiom,
    ! [X20,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X20)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20) ) ),
    file('<stdin>',fact_dvd__imp__le) ).

fof(c_0_532,axiom,
    ! [X33,X21,X2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2) )
     => ( X21 = X33
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X33)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X33,X2) ) ) ),
    file('<stdin>',fact_dvd_Oord__less__eq__trans) ).

fof(c_0_533,axiom,
    ! [X33,X21,X2] :
      ( X2 = X21
     => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X33)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X33,X21) )
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X33)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X33,X2) ) ) ),
    file('<stdin>',fact_dvd_Oord__eq__less__trans) ).

fof(c_0_534,axiom,
    ! [X5,X65,X66] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
     => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66) = X5
      <=> X65 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X66) ) ),
    file('<stdin>',fact_le__imp__diff__is__add) ).

fof(c_0_535,axiom,
    ! [X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Divides_Odiv__class_Omod(X3,X2,X21),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
    file('<stdin>',fact_mod__mod__trivial) ).

fof(c_0_536,axiom,
    ! [X2,X21,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X21,X2),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
    file('<stdin>',fact_mod__add__self1) ).

fof(c_0_537,axiom,
    ! [X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
    file('<stdin>',fact_mod__add__self2) ).

fof(c_0_538,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X20 ),
    file('<stdin>',fact_Suc__pred) ).

fof(c_0_539,axiom,
    ! [X20,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20),
    file('<stdin>',fact_diff__Suc__eq__diff__pred) ).

fof(c_0_540,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X7)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X7) ) ),
    file('<stdin>',fact_le__trans) ).

fof(c_0_541,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X53,X51)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X51,X7)
       => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X53,X7) ) ),
    file('<stdin>',fact_real__le__trans) ).

fof(c_0_542,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,X51)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X51,X7)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,X7) ) ),
    file('<stdin>',fact_zle__trans) ).

fof(c_0_543,axiom,
    ! [X10,X22,X23] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10) ) ),
    file('<stdin>',fact_dvd_Oorder__trans) ).

fof(c_0_544,axiom,
    ! [X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Groups_Oone__class_Oone(X3)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,c_Int_OBit1(c_Int_OPls))) ),
    file('<stdin>',fact_add__special_I3_J) ).

fof(c_0_545,axiom,
    ! [X8,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X3,X8)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X8)) ),
    file('<stdin>',fact_add__special_I2_J) ).

fof(c_0_546,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),X21) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X21,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('<stdin>',fact_zmod__minus1) ).

fof(c_0_547,axiom,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X15,X14))
    <=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
          & c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) )
        | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
          & ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) ) ) ),
    file('<stdin>',fact_even__difference) ).

fof(c_0_548,axiom,
    ! [X22,X23] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
       => ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
    file('<stdin>',fact_odd__plus__even) ).

fof(c_0_549,axiom,
    ! [X22,X23] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
       => ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
    file('<stdin>',fact_even__plus__odd) ).

fof(c_0_550,axiom,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X14))
    <=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
          & c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) )
        | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
          & ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) ) ) ),
    file('<stdin>',fact_even__sum) ).

fof(c_0_551,axiom,
    ! [X17,X18] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))
    <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
      <=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ),
    file('<stdin>',fact_odd__add) ).

fof(c_0_552,axiom,
    ! [X17,X18] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))
    <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
      <=> c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ),
    file('<stdin>',fact_even__add) ).

fof(c_0_553,axiom,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14))
    <=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
          & c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) )
        | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
          & ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) ) ) ),
    file('<stdin>',fact_even__sum__nat) ).

fof(c_0_554,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X20))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X20)))
        & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X20))) ) ),
    file('<stdin>',fact_number__of1) ).

fof(c_0_555,axiom,
    ! [X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)),
    file('<stdin>',fact_mult__Suc) ).

fof(c_0_556,axiom,
    ! [X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)),
    file('<stdin>',fact_mult__Suc__right) ).

fof(c_0_557,axiom,
    ! [X8,X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)),
    file('<stdin>',fact_plus__numeral__code_I9_J) ).

fof(c_0_558,axiom,
    ! [X8,X9] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)),
    file('<stdin>',fact_times__numeral__code_I5_J) ).

fof(c_0_559,axiom,
    ! [X20,X19] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) = X19 ),
    file('<stdin>',fact_add__diff__inverse) ).

fof(c_0_560,axiom,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X15,X14))
    <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) ) ),
    file('<stdin>',fact_even__product) ).

fof(c_0_561,axiom,
    ! [X22,X23] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
       => ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ) ),
    file('<stdin>',fact_odd__times__odd) ).

fof(c_0_562,axiom,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X15,X14))
    <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) ) ),
    file('<stdin>',fact_even__product__nat) ).

fof(c_0_563,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X5),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
    file('<stdin>',fact_less__eq__number__of__int__code) ).

fof(c_0_564,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X5),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
    file('<stdin>',fact_less__number__of__int__code) ).

fof(c_0_565,axiom,
    ! [X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Groups_Oone__class_Oone(X3))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,c_Int_OBit1(c_Int_OPls)) ) ),
    file('<stdin>',fact_less__special_I4_J) ).

fof(c_0_566,axiom,
    ! [X14,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X14) ) ),
    file('<stdin>',fact_less__special_I2_J) ).

fof(c_0_567,axiom,
    ! [X14,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X14) ) ),
    file('<stdin>',fact_le__special_I2_J) ).

fof(c_0_568,axiom,
    ! [X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Groups_Oone__class_Oone(X3))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,c_Int_OBit1(c_Int_OPls)) ) ),
    file('<stdin>',fact_le__special_I4_J) ).

fof(c_0_569,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => X20 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('<stdin>',fact_Suc__pred_H) ).

fof(c_0_570,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X20 ),
    file('<stdin>',fact_Suc__diff__1) ).

fof(c_0_571,axiom,
    ! [X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Groups_Ozero__class_Ozero(X3))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,c_Int_OPls) ) ),
    file('<stdin>',fact_le__special_I3_J) ).

fof(c_0_572,axiom,
    ! [X14,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X14) ) ),
    file('<stdin>',fact_le__special_I1_J) ).

fof(c_0_573,axiom,
    ! [X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Groups_Ozero__class_Ozero(X3))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,c_Int_OPls) ) ),
    file('<stdin>',fact_less__special_I3_J) ).

fof(c_0_574,axiom,
    ! [X14,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X14) ) ),
    file('<stdin>',fact_less__special_I1_J) ).

fof(c_0_575,axiom,
    ! [X23,X20,X3] :
      ( ( class_Groups_Omonoid__mult(X3)
        & class_Rings_Olinordered__ring(X3) )
     => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X23,X20)) ) ),
    file('<stdin>',fact_zero__le__even__power) ).

fof(c_0_576,axiom,
    ! [X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3))) ),
    file('<stdin>',fact_zero__less__two) ).

fof(c_0_577,axiom,
    ! [X17,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X15,X17))
    <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
        & X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('<stdin>',fact_even__power) ).

fof(c_0_578,axiom,
    ! [X20,X23] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X20)) ),
    file('<stdin>',fact_odd__pow) ).

fof(c_0_579,axiom,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ),
    file('<stdin>',fact_dvd_Oless__imp__le) ).

fof(c_0_580,axiom,
    ! [X14,X15] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15) )
    <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
        & X15 != X14 ) ),
    file('<stdin>',fact_dvd_Oless__le) ).

fof(c_0_581,axiom,
    ! [X14,X15] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
    <=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15) )
        | X15 = X14 ) ),
    file('<stdin>',fact_dvd_Ole__less) ).

fof(c_0_582,axiom,
    ! [X17,X18,X5] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X18) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X17)
    <=> X18 = X17 ),
    file('<stdin>',fact_Suc__mult__cancel1) ).

fof(c_0_583,axiom,
    ! [X41,X42,X24,X25,X3] :
      ( class_Groups_Oab__group__add(X3)
     => ( c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ominus__class_Ominus(X3,X42,X41)
       => ( X25 = X24
        <=> X42 = X41 ) ) ),
    file('<stdin>',fact_diff__eq__diff__eq) ).

fof(c_0_584,axiom,
    ! [X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oone__class_Oone(X3))) ),
    file('<stdin>',fact_less__add__one) ).

fof(c_0_585,axiom,
    ! [X16,X25,X3] :
      ( ( class_Power_Opower(X3)
        & class_Rings_Omult__zero(X3)
        & class_Rings_Ono__zero__divisors(X3)
        & class_Rings_Ozero__neq__one(X3) )
     => ( c_Power_Opower__class_Opower(X3,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)) = c_Groups_Ozero__class_Ozero(X3)
      <=> ( X25 = c_Groups_Ozero__class_Ozero(X3)
          & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('<stdin>',fact_power__eq__0__iff__number__of) ).

fof(c_0_586,axiom,
    ! [X33,X2,X21,X3] :
      ( class_Groups_Ocancel__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X21,X2) = c_Groups_Oplus__class_Oplus(X3,X33,X2)
       => X21 = X33 ) ),
    file('<stdin>',fact_add__right__imp__eq) ).

fof(c_0_587,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Ocancel__ab__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X2,X21) = c_Groups_Oplus__class_Oplus(X3,X2,X33)
       => X21 = X33 ) ),
    file('<stdin>',fact_add__imp__eq) ).

fof(c_0_588,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Ocancel__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X2,X21) = c_Groups_Oplus__class_Oplus(X3,X2,X33)
       => X21 = X33 ) ),
    file('<stdin>',fact_add__left__imp__eq) ).

fof(c_0_589,axiom,
    ! [X42,X25,X24,X3] :
      ( class_Groups_Ocancel__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X24,X25) = c_Groups_Oplus__class_Oplus(X3,X42,X25)
      <=> X24 = X42 ) ),
    file('<stdin>',fact_add__right__cancel) ).

fof(c_0_590,axiom,
    ! [X42,X24,X25,X3] :
      ( class_Groups_Ocancel__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X25,X24) = c_Groups_Oplus__class_Oplus(X3,X25,X42)
      <=> X24 = X42 ) ),
    file('<stdin>',fact_add__left__cancel) ).

fof(c_0_591,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
     => ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X18,X17) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      <=> ( X18 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X17 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    file('<stdin>',fact_pos__zmult__eq__1__iff) ).

fof(c_0_592,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18))
      <=> X17 = X18 ) ),
    file('<stdin>',fact_le__less__Suc__eq) ).

fof(c_0_593,axiom,
    ! [X25,X3] :
      ( class_Rings_Oring__1__no__zero__divisors(X3)
     => ( c_Power_Opower__class_Opower(X3,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X3)
      <=> X25 = c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_zero__eq__power2) ).

fof(c_0_594,axiom,
    ! [X17,X18] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X18) ),
    file('<stdin>',fact_not__less__eq__eq) ).

fof(c_0_595,axiom,
    ! [X17,X18] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18)) ),
    file('<stdin>',fact_not__less__eq) ).

fof(c_0_596,axiom,
    ! [X20,X19] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => X19 = X20 ) ),
    file('<stdin>',fact_diffs0__imp__equal) ).

fof(c_0_597,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
    <=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [X58] :
            ( X18 = c_Nat_OSuc(X58)
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X58,X17) ) ) ),
    file('<stdin>',fact_less__Suc__eq__0__disj) ).

fof(c_0_598,axiom,
    ! [X61] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X61) ),
    file('<stdin>',fact_less__0__number__of) ).

fof(c_0_599,axiom,
    ! [X2,X3] :
      ( class_Rings_Olinordered__ring(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X2)) ),
    file('<stdin>',fact_zero__le__square) ).

fof(c_0_600,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
    <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('<stdin>',fact_even__def) ).

fof(c_0_601,axiom,
    ! [X6,X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit1(X6)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X6)),
    file('<stdin>',fact_diff__bin__simps_I10_J) ).

fof(c_0_602,axiom,
    ! [X6,X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit0(X6)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X6)),
    file('<stdin>',fact_diff__bin__simps_I9_J) ).

fof(c_0_603,axiom,
    ! [X6,X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit0(X6)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X6)),
    file('<stdin>',fact_diff__bin__simps_I7_J) ).

fof(c_0_604,axiom,
    ! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit1(X6)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X6)),
    file('<stdin>',fact_add__Bit0__Bit1) ).

fof(c_0_605,axiom,
    ! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit0(X6)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X6)),
    file('<stdin>',fact_add__Bit1__Bit0) ).

fof(c_0_606,axiom,
    ! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit0(X6)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X6)),
    file('<stdin>',fact_add__Bit0__Bit0) ).

fof(c_0_607,axiom,
    ! [X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Odiv(X3,c_Divides_Odiv__class_Omod(X3,X2,X21),X21) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_mod__div__trivial) ).

fof(c_0_608,axiom,
    ! [X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X21) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_mod__mult__self2__is__0) ).

fof(c_0_609,axiom,
    ! [X2,X21,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X21,X2),X21) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_mod__mult__self1__is__0) ).

fof(c_0_610,axiom,
    ! [X24,X25,X42] :
      ( X42 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X42,X25) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X42,X24)
      <=> X25 = X24 ) ),
    file('<stdin>',fact_real__mult__left__cancel) ).

fof(c_0_611,axiom,
    ! [X24,X25,X42] :
      ( X42 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X25,X42) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X24,X42)
      <=> X25 = X24 ) ),
    file('<stdin>',fact_real__mult__right__cancel) ).

fof(c_0_612,axiom,
    ! [X17,X18,X5] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17)
    <=> ( X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18 = X17 ) ),
    file('<stdin>',fact_nat__mult__eq__cancel__disj) ).

fof(c_0_613,axiom,
    ! [X17,X18,X5] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17)
    <=> ( X18 = X17
        | X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('<stdin>',fact_mult__cancel1) ).

fof(c_0_614,axiom,
    ! [X17,X5,X18] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X5) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X5)
    <=> ( X18 = X17
        | X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('<stdin>',fact_mult__cancel2) ).

fof(c_0_615,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
    <=> ? [X31] : X15 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X31) ),
    file('<stdin>',fact_even__equiv__def) ).

fof(c_0_616,axiom,
    ! [X17] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
    <=> ? [X1] : X17 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
    file('<stdin>',fact_even__mult__two__ex) ).

fof(c_0_617,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X15) ),
    file('<stdin>',fact_int__even__iff__2__dvd) ).

fof(c_0_618,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
    <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X15) ),
    file('<stdin>',fact_nat__even__iff__2__dvd) ).

fof(c_0_619,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
     => ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('<stdin>',fact_less__2__cases) ).

fof(c_0_620,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
       => X19 = X20 ) ),
    file('<stdin>',fact_le__antisym) ).

fof(c_0_621,axiom,
    ! [X8,X10] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X8)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X10)
       => X10 = X8 ) ),
    file('<stdin>',fact_real__le__antisym) ).

fof(c_0_622,axiom,
    ! [X8,X10] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X8)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X10)
       => X10 = X8 ) ),
    file('<stdin>',fact_zle__antisym) ).

fof(c_0_623,axiom,
    ! [X22,X23] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
       => X23 = X22 ) ),
    file('<stdin>',fact_dvd_Oantisym) ).

fof(c_0_624,axiom,
    ! [X20,X19] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X20)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,X19)
       => X19 = X20 ) ),
    file('<stdin>',fact_dvd__antisym) ).

fof(c_0_625,axiom,
    ! [X21,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
     => ( X2 != X21
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2) ) ) ),
    file('<stdin>',fact_dvd_Ole__neq__trans) ).

fof(c_0_626,axiom,
    ! [X22,X23] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
     => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
        | X23 = X22 ) ),
    file('<stdin>',fact_dvd_Ole__imp__less__or__eq) ).

fof(c_0_627,axiom,
    ! [X15,X14] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
      <=> X15 = X14 ) ),
    file('<stdin>',fact_dvd_Oantisym__conv) ).

fof(c_0_628,axiom,
    ! [X21,X2] :
      ( X2 != X21
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2) ) ) ),
    file('<stdin>',fact_dvd_Oneq__le__trans) ).

fof(c_0_629,axiom,
    ! [X14,X15] :
      ( X15 = X14
    <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15) ) ),
    file('<stdin>',fact_dvd_Oeq__iff) ).

fof(c_0_630,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Ogroup__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X21) = X2 ),
    file('<stdin>',fact_diff__add__cancel) ).

fof(c_0_631,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Ogroup__add(X3)
     => c_Groups_Ominus__class_Ominus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X21) = X2 ),
    file('<stdin>',fact_add__diff__cancel) ).

fof(c_0_632,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X2)) ),
    file('<stdin>',fact_dvd__triv__right) ).

fof(c_0_633,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Otimes__class_Otimes(X3,X2,X21)) ),
    file('<stdin>',fact_dvd__triv__left) ).

fof(c_0_634,axiom,
    ! [X17,X5,X18] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X5)
    <=> X18 = X17 ),
    file('<stdin>',fact_nat__add__right__cancel) ).

fof(c_0_635,axiom,
    ! [X17,X18,X5] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X17)
    <=> X18 = X17 ),
    file('<stdin>',fact_nat__add__left__cancel) ).

fof(c_0_636,axiom,
    ! [X41,X18] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X18,X41) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ? [X76] : X18 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X41,X76) ),
    file('<stdin>',fact_mod__eq__0__iff) ).

fof(c_0_637,axiom,
    ! [X41,X18] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X18,X41) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ? [X76] : X18 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X41,X76) ),
    file('<stdin>',fact_zmod__eq__0__iff) ).

fof(c_0_638,axiom,
    ! [X7] : c_Int_OBit1(X7) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X7),X7),
    file('<stdin>',fact_Bit1__def) ).

fof(c_0_639,axiom,
    ! [X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)),
    file('<stdin>',fact_add__Suc) ).

fof(c_0_640,axiom,
    ! [X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)),
    file('<stdin>',fact_add__Suc__right) ).

fof(c_0_641,axiom,
    ! [X6,X7] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X7),X6) = c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X6)),
    file('<stdin>',fact_mult__Bit0) ).

fof(c_0_642,axiom,
    ! [X10,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X10) = c_Groups_Oplus__class_Oplus(X3,X10,X10) ),
    file('<stdin>',fact_mult__2) ).

fof(c_0_643,axiom,
    ! [X10,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,X10,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X3,X10,X10) ),
    file('<stdin>',fact_mult__2__right) ).

fof(c_0_644,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
    <=> ? [X59] : X17 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X59) ),
    file('<stdin>',fact_le__iff__add) ).

fof(c_0_645,axiom,
    ! [X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X23,X23) = c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

fof(c_0_646,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X3,X2,X2) ),
    file('<stdin>',fact_power2__eq__square) ).

fof(c_0_647,axiom,
    ! [X20,X19] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),c_Nat_OSuc(X19)),
    file('<stdin>',fact_diff__less__Suc) ).

fof(c_0_648,axiom,
    ! [X15] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
    <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X15,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('<stdin>',fact_odd__nat__equiv__def) ).

fof(c_0_649,axiom,
    ! [X6] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X6)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X6)),
    file('<stdin>',fact_diff__bin__simps_I3_J) ).

fof(c_0_650,axiom,
    ! [X6] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X6)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X6)),
    file('<stdin>',fact_diff__bin__simps_I6_J) ).

fof(c_0_651,axiom,
    ! [X6] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X6)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X6)),
    file('<stdin>',fact_diff__bin__simps_I5_J) ).

fof(c_0_652,axiom,
    ! [X6] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X6)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X6)),
    file('<stdin>',fact_diff__bin__simps_I4_J) ).

fof(c_0_653,axiom,
    ! [X21,X2] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('<stdin>',fact_zmod__zdiv__trivial) ).

fof(c_0_654,axiom,
    ! [X19,X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('<stdin>',fact_diff__add__0) ).

fof(c_0_655,axiom,
    ! [X19,X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19),X20) = X19,
    file('<stdin>',fact_diff__add__inverse) ).

fof(c_0_656,axiom,
    ! [X20,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20),X20) = X19,
    file('<stdin>',fact_diff__add__inverse2) ).

fof(c_0_657,axiom,
    ! [X22,X23] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
       => c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
    file('<stdin>',fact_even__plus__even) ).

fof(c_0_658,axiom,
    ! [X20,X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),X19),
    file('<stdin>',fact_mod__less__eq__dividend) ).

fof(c_0_659,axiom,
    ! [X20,X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X19),
    file('<stdin>',fact_diff__le__self) ).

fof(c_0_660,axiom,
    ! [X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X19)),
    file('<stdin>',fact_le__square) ).

fof(c_0_661,axiom,
    ! [X19,X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19)),
    file('<stdin>',fact_le__add1) ).

fof(c_0_662,axiom,
    ! [X19,X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)),
    file('<stdin>',fact_le__add2) ).

fof(c_0_663,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OBit0(X49))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
    file('<stdin>',fact_less__eq__int__code_I15_J) ).

fof(c_0_664,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit0(X4))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
    file('<stdin>',fact_rel__simps_I33_J) ).

fof(c_0_665,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OBit1(X49))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
    file('<stdin>',fact_less__int__code_I14_J) ).

fof(c_0_666,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit1(X4))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
    file('<stdin>',fact_rel__simps_I15_J) ).

fof(c_0_667,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OBit1(X49))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
    file('<stdin>',fact_less__eq__int__code_I14_J) ).

fof(c_0_668,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit1(X4))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
    file('<stdin>',fact_rel__simps_I32_J) ).

fof(c_0_669,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OBit0(X49))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
    file('<stdin>',fact_less__eq__int__code_I13_J) ).

fof(c_0_670,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit0(X4))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
    file('<stdin>',fact_rel__simps_I31_J) ).

fof(c_0_671,axiom,
    ! [X18,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),c_Nat_OSuc(X18))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X18) ),
    file('<stdin>',fact_Suc__le__mono) ).

fof(c_0_672,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OBit1(X49))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
    file('<stdin>',fact_less__eq__int__code_I16_J) ).

fof(c_0_673,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit1(X4))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
    file('<stdin>',fact_rel__simps_I34_J) ).

fof(c_0_674,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X18),c_Nat_OSuc(X17))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
    file('<stdin>',fact_Suc__less__eq) ).

fof(c_0_675,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X20))
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ),
    file('<stdin>',fact_Suc__less__SucD) ).

fof(c_0_676,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OBit0(X49))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
    file('<stdin>',fact_less__int__code_I15_J) ).

fof(c_0_677,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit0(X4))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
    file('<stdin>',fact_rel__simps_I16_J) ).

fof(c_0_678,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OBit0(X49))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
    file('<stdin>',fact_less__int__code_I13_J) ).

fof(c_0_679,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit0(X4))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
    file('<stdin>',fact_rel__simps_I14_J) ).

fof(c_0_680,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OBit1(X49))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
    file('<stdin>',fact_less__int__code_I16_J) ).

fof(c_0_681,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit1(X4))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
    file('<stdin>',fact_rel__simps_I17_J) ).

fof(c_0_682,axiom,
    ! [X16] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X16),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('<stdin>',fact_bin__less__0__simps_I3_J) ).

fof(c_0_683,axiom,
    ! [X16] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X16),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('<stdin>',fact_bin__less__0__simps_I4_J) ).

fof(c_0_684,axiom,
    ! [X24,X25,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X25,X24)
      <=> c_Divides_Odiv__class_Omod(X3,X24,X25) = c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_dvd__eq__mod__eq__0) ).

fof(c_0_685,axiom,
    ! [X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X10),
    file('<stdin>',fact_nat__mult__2__right) ).

fof(c_0_686,axiom,
    ! [X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X10) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X10),
    file('<stdin>',fact_nat__mult__2) ).

fof(c_0_687,axiom,
    ! [X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
       => c_Divides_Odiv__class_Omod(X3,X21,X2) = c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_dvd__imp__mod__0) ).

fof(c_0_688,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Nat_OSuc(X20))
     => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
       => X19 = c_Nat_OSuc(X20) ) ),
    file('<stdin>',fact_le__SucE) ).

fof(c_0_689,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
        | X18 = c_Nat_OSuc(X17) ) ),
    file('<stdin>',fact_le__Suc__eq) ).

fof(c_0_690,axiom,
    ! [X7,X21,X2,X3] :
      ( class_Rings_Odvd(X3)
     => ( X2 = c_Groups_Otimes__class_Otimes(X3,X21,X7)
       => c_Rings_Odvd__class_Odvd(X3,X21,X2) ) ),
    file('<stdin>',fact_dvdI) ).

fof(c_0_691,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X20)) ),
    file('<stdin>',fact_Suc__mono) ).

fof(c_0_692,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
        | X18 = X17 ) ),
    file('<stdin>',fact_less__Suc__eq) ).

fof(c_0_693,axiom,
    ! [X18,X17] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18))
      <=> X17 = X18 ) ),
    file('<stdin>',fact_not__less__less__Suc__eq) ).

fof(c_0_694,axiom,
    ! [X19,X20] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(X19))
       => X19 = X20 ) ),
    file('<stdin>',fact_less__antisym) ).

fof(c_0_695,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20))
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
       => X19 = X20 ) ),
    file('<stdin>',fact_less__SucE) ).

fof(c_0_696,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => ( c_Nat_OSuc(X19) != X20
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),X20) ) ),
    file('<stdin>',fact_Suc__lessI) ).

fof(c_0_697,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
    <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X15,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('<stdin>',fact_even__nat__equiv__def) ).

fof(c_0_698,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ),
    file('<stdin>',fact_Suc__le__lessD) ).

fof(c_0_699,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X18),X17)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
    file('<stdin>',fact_Suc__le__eq) ).

fof(c_0_700,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
    file('<stdin>',fact_less__Suc__eq__le) ).

fof(c_0_701,axiom,
    ! [X18,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X18) ),
    file('<stdin>',fact_less__eq__Suc__le) ).

fof(c_0_702,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
    file('<stdin>',fact_Suc__leD) ).

fof(c_0_703,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ),
    file('<stdin>',fact_Suc__lessD) ).

fof(c_0_704,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
    <=> ? [X31] : X15 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31) ),
    file('<stdin>',fact_even__nat__equiv__def2) ).

fof(c_0_705,axiom,
    ! [X46] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X46)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X46) ),
    file('<stdin>',fact_int__one__le__iff__zero__less) ).

fof(c_0_706,axiom,
    ! [X23] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
     => ( X23 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('<stdin>',fact_nat__lt__two__imp__zero__or__one) ).

fof(c_0_707,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X20) ),
    file('<stdin>',fact_Suc__leI) ).

fof(c_0_708,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) ),
    file('<stdin>',fact_le__imp__less__Suc) ).

fof(c_0_709,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) ),
    file('<stdin>',fact_le__SucI) ).

fof(c_0_710,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) ),
    file('<stdin>',fact_less__SucI) ).

fof(c_0_711,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Int_OPls) ),
    file('<stdin>',fact_rel__simps_I29_J) ).

fof(c_0_712,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X5))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X5) ),
    file('<stdin>',fact_rel__simps_I5_J) ).

fof(c_0_713,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Int_OPls) ),
    file('<stdin>',fact_rel__simps_I27_J) ).

fof(c_0_714,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X5))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X5) ),
    file('<stdin>',fact_rel__simps_I21_J) ).

fof(c_0_715,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X5))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X5) ),
    file('<stdin>',fact_rel__simps_I22_J) ).

fof(c_0_716,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X5))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X5) ),
    file('<stdin>',fact_rel__simps_I8_J) ).

fof(c_0_717,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X5))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X5) ),
    file('<stdin>',fact_rel__simps_I9_J) ).

fof(c_0_718,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OMin)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Int_OMin) ),
    file('<stdin>',fact_rel__simps_I13_J) ).

fof(c_0_719,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OMin)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Int_OMin) ),
    file('<stdin>',fact_rel__simps_I11_J) ).

fof(c_0_720,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X5))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X5) ),
    file('<stdin>',fact_rel__simps_I25_J) ).

fof(c_0_721,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OMin)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Int_OMin) ),
    file('<stdin>',fact_rel__simps_I30_J) ).

fof(c_0_722,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X5))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X5) ),
    file('<stdin>',fact_rel__simps_I26_J) ).

fof(c_0_723,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OMin)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Int_OMin) ),
    file('<stdin>',fact_rel__simps_I28_J) ).

fof(c_0_724,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Int_OPls) ),
    file('<stdin>',fact_rel__simps_I10_J) ).

fof(c_0_725,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X5))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X5) ),
    file('<stdin>',fact_rel__simps_I4_J) ).

fof(c_0_726,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Int_OPls) ),
    file('<stdin>',fact_rel__simps_I12_J) ).

fof(c_0_727,axiom,
    ! [X22,X23] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
       => c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
    file('<stdin>',fact_odd__plus__odd) ).

fof(c_0_728,axiom,
    ! [X17,X18] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
    file('<stdin>',fact_diff__is__0__eq) ).

fof(c_0_729,axiom,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => X22 != X23 ),
    file('<stdin>',fact_dvd_Oless__imp__not__eq2) ).

fof(c_0_730,axiom,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => X23 != X22 ),
    file('<stdin>',fact_dvd_Oless__imp__not__eq) ).

fof(c_0_731,axiom,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => X23 != X22 ),
    file('<stdin>',fact_dvd_Oless__imp__neq) ).

fof(c_0_732,axiom,
    ! [X33,X21,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
     => ( X21 = X33
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X33) ) ),
    file('<stdin>',fact_dvd_Oord__le__eq__trans) ).

fof(c_0_733,axiom,
    ! [X33,X21,X2] :
      ( X2 = X21
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X33)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X33) ) ),
    file('<stdin>',fact_dvd_Oord__eq__le__trans) ).

fof(c_0_734,axiom,
    ! [X16,X46] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,X16)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X46,X16)
        & X46 != X16 ) ),
    file('<stdin>',fact_zless__le) ).

fof(c_0_735,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('<stdin>',fact_diff__is__0__eq_H) ).

fof(c_0_736,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => ( X19 != X20
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ) ),
    file('<stdin>',fact_le__neq__implies__less) ).

fof(c_0_737,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
        | X18 = X17 ) ),
    file('<stdin>',fact_le__eq__less__or__eq) ).

fof(c_0_738,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
        & X18 != X17 ) ),
    file('<stdin>',fact_nat__less__le) ).

fof(c_0_739,axiom,
    ! [X14,X15] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
        & X15 != X14 ) ),
    file('<stdin>',fact_real__less__def) ).

fof(c_0_740,axiom,
    ! [X14,X15] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
    <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14)
        | X15 = X14 ) ),
    file('<stdin>',fact_less__eq__real__def) ).

fof(c_0_741,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = X19 ),
    file('<stdin>',fact_mod__less) ).

fof(c_0_742,axiom,
    ! [X16,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Int_Oring__char__0(X3) )
     => ( c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(X16)))
      <=> c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,X16)) ) ),
    file('<stdin>',fact_iszero__number__of__Bit0) ).

fof(c_0_743,axiom,
    ! [X20,X19] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
        | X19 = X20 )
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
    file('<stdin>',fact_less__or__eq__imp__le) ).

fof(c_0_744,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
    file('<stdin>',fact_less__imp__le__nat) ).

fof(c_0_745,axiom,
    ! [X22,X23] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ),
    file('<stdin>',fact_even__times__anything) ).

fof(c_0_746,axiom,
    ! [X23,X22] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
     => c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ),
    file('<stdin>',fact_anything__times__even) ).

fof(c_0_747,axiom,
    ! [X17,X25,X3] :
      ( ( class_Power_Opower(X3)
        & class_Rings_Omult__zero(X3)
        & class_Rings_Ono__zero__divisors(X3)
        & class_Rings_Ozero__neq__one(X3) )
     => ( c_Power_Opower__class_Opower(X3,X25,X17) = c_Groups_Ozero__class_Ozero(X3)
      <=> ( X25 = c_Groups_Ozero__class_Ozero(X3)
          & X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('<stdin>',fact_power__eq__0__iff) ).

fof(c_0_748,axiom,
    ! [X8,X3] :
      ( ( class_Power_Opower(X3)
        & class_Rings_Osemiring__0(X3) )
     => ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X8) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X8)) = c_Groups_Oone__class_Oone(X3) )
        & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X8) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X8)) = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    file('<stdin>',fact_power__0__left__number__of) ).

fof(c_0_749,axiom,
    ! [X20] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X20))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X20),
    file('<stdin>',fact_Suc3__eq__add__3) ).

fof(c_0_750,axiom,
    ! [X3] :
      ( class_Rings_Osemiring__1(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X3) ),
    file('<stdin>',fact_one__power2) ).

fof(c_0_751,axiom,
    ! [X3] :
      ( class_Rings_Osemiring__1(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_zero__power2) ).

fof(c_0_752,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( X23 != X22
       => ( ~ c_Orderings_Oord__class_Oless(X3,X23,X22)
         => c_Orderings_Oord__class_Oless(X3,X22,X23) ) ) ),
    file('<stdin>',fact_linorder__neqE__linordered__idom) ).

fof(c_0_753,axiom,
    ! [X20,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),
    file('<stdin>',fact_diff__Suc__Suc) ).

fof(c_0_754,axiom,
    ! [X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Nat_OSuc(X20)),
    file('<stdin>',fact_add__Suc__shift) ).

fof(c_0_755,axiom,
    ! [X33,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,X33) = c_Groups_Oplus__class_Oplus(X3,X33,X2) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(c_0_756,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,X21) = c_Groups_Otimes__class_Otimes(X3,X21,X2) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(c_0_757,axiom,
    ! [X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Ozero__class_Ozero(X3)) ),
    file('<stdin>',fact_not__one__less__zero) ).

fof(c_0_758,axiom,
    ! [X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Ozero__class_Ozero(X3)) ),
    file('<stdin>',fact_not__one__le__zero) ).

fof(c_0_759,axiom,
    ! [X17,X18] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X17 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('<stdin>',fact_add__is__1) ).

fof(c_0_760,axiom,
    ! [X17,X18] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17)
    <=> ( ( X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X17 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('<stdin>',fact_one__is__add) ).

fof(c_0_761,axiom,
    ! [X18] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('<stdin>',fact_dvd__1__iff__1) ).

fof(c_0_762,axiom,
    ! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20) = c_Nat_OSuc(c_Nat_OSuc(X20)),
    file('<stdin>',fact_add__2__eq__Suc) ).

fof(c_0_763,axiom,
    ! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X20)),
    file('<stdin>',fact_add__2__eq__Suc_H) ).

fof(c_0_764,axiom,
    ! [X23,X3] :
      ( class_Int_Onumber__ring(X3)
     => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
       => c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin) ) ),
    file('<stdin>',fact_neg__one__odd__power) ).

fof(c_0_765,axiom,
    ! [X23,X3] :
      ( class_Int_Onumber__ring(X3)
     => ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
         => c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Groups_Oone__class_Oone(X3) )
        & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
         => c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin) ) ) ),
    file('<stdin>',fact_neg__one__even__odd__power) ).

fof(c_0_766,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Ono__zero__divisors(X3)
     => ( c_Groups_Otimes__class_Otimes(X3,X2,X21) = c_Groups_Ozero__class_Ozero(X3)
       => ( X2 = c_Groups_Ozero__class_Ozero(X3)
          | X21 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    file('<stdin>',fact_divisors__zero) ).

fof(c_0_767,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Ono__zero__divisors(X3)
     => ( X2 != c_Groups_Ozero__class_Ozero(X3)
       => ( X21 != c_Groups_Ozero__class_Ozero(X3)
         => c_Groups_Otimes__class_Otimes(X3,X2,X21) != c_Groups_Ozero__class_Ozero(X3) ) ) ),
    file('<stdin>',fact_no__zero__divisors) ).

fof(c_0_768,axiom,
    ! [X24,X25,X3] :
      ( class_Rings_Oring__no__zero__divisors(X3)
     => ( c_Groups_Otimes__class_Otimes(X3,X25,X24) = c_Groups_Ozero__class_Ozero(X3)
      <=> ( X25 = c_Groups_Ozero__class_Ozero(X3)
          | X24 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    file('<stdin>',fact_mult__eq__0__iff) ).

fof(c_0_769,axiom,
    ! [X23,X3] :
      ( class_Int_Onumber__ring(X3)
     => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
       => c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Groups_Oone__class_Oone(X3) ) ),
    file('<stdin>',fact_neg__one__even__power) ).

fof(c_0_770,axiom,
    ! [X22,X23] :
      ( X23 != X22
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X22)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X23) ) ),
    file('<stdin>',fact_linorder__neqE__nat) ).

fof(c_0_771,axiom,
    ! [X17,X18] :
      ( X18 != X17
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18) ) ),
    file('<stdin>',fact_nat__neq__iff) ).

fof(c_0_772,axiom,
    ! [X22,X23] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,X22)
      | X23 = X22
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X23) ),
    file('<stdin>',fact_zless__linear) ).

fof(c_0_773,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => X2 = c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_dvd__0__left) ).

fof(c_0_774,axiom,
    ! [X10] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X10,
    file('<stdin>',fact_csqrt) ).

fof(c_0_775,axiom,
    ! [X18,X15] :
      ( c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X18) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X15 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('<stdin>',fact_nat__power__eq__Suc__0__iff) ).

fof(c_0_776,axiom,
    ! [X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('<stdin>',fact_less__Suc0) ).

fof(c_0_777,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19) ),
    file('<stdin>',fact_nat__le__linear) ).

fof(c_0_778,axiom,
    ! [X8,X10] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X8)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X10) ),
    file('<stdin>',fact_real__le__linear) ).

fof(c_0_779,axiom,
    ! [X8,X10] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X8)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X10) ),
    file('<stdin>',fact_zle__linear) ).

fof(c_0_780,axiom,
    ! [X23] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('<stdin>',fact_even__nat__mod__two__eq__zero) ).

fof(c_0_781,axiom,
    ! [X8,X10] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X10,X8) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X8,X10),
    file('<stdin>',fact_real__mult__commute) ).

fof(c_0_782,axiom,
    ! [X8,X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X10),
    file('<stdin>',fact_zadd__commute) ).

fof(c_0_783,axiom,
    ! [X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19),
    file('<stdin>',fact_nat__add__commute) ).

fof(c_0_784,axiom,
    ! [X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19),
    file('<stdin>',fact_nat__mult__commute) ).

fof(c_0_785,axiom,
    ! [X8,X10] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X10,X8) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X10),
    file('<stdin>',fact_zmult__commute) ).

fof(c_0_786,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Oring__1__no__zero__divisors(X3)
     => ( X2 != c_Groups_Ozero__class_Ozero(X3)
       => c_Power_Opower__class_Opower(X3,X2,X20) != c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_field__power__not__zero) ).

fof(c_0_787,axiom,
    ! [X25,X3] :
      ( class_Groups_Olinordered__ab__group__add(X3)
     => ( c_Groups_Ozero__class_Ozero(X3) = c_Groups_Oplus__class_Oplus(X3,X25,X25)
      <=> X25 = c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_double__zero__sym) ).

fof(c_0_788,axiom,
    ! [X25,X3] :
      ( class_Groups_Olinordered__ab__group__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X25,X25) = c_Groups_Ozero__class_Ozero(X3)
      <=> X25 = c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_double__eq__0__iff) ).

fof(c_0_789,axiom,
    ! [X23] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('<stdin>',fact_odd__nat__mod__two__eq__one) ).

fof(c_0_790,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).

fof(c_0_791,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).

fof(c_0_792,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('<stdin>',fact_pos2) ).

fof(c_0_793,axiom,
    ! [X17,X18] :
      ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X18,X17) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    <=> ( ( X18 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X17 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | ( X18 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
          & X17 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ) ) ),
    file('<stdin>',fact_zmult__eq__1__iff) ).

fof(c_0_794,axiom,
    ! [X20,X19] :
      ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X19,X20) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => ( X19 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X19 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ) ),
    file('<stdin>',fact_pos__zmult__eq__1__iff__lemma) ).

fof(c_0_795,axiom,
    ! [X17,X18] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        & X17 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('<stdin>',fact_mult__eq__1__iff) ).

fof(c_0_796,axiom,
    ! [X24,X25,X3] :
      ( class_Groups_Oab__group__add(X3)
     => ( X25 = X24
      <=> c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_eq__iff__diff__eq__0) ).

fof(c_0_797,axiom,
    ! [X24,X25,X3] :
      ( class_Groups_Ogroup__add(X3)
     => ( c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ozero__class_Ozero(X3)
      <=> X25 = X24 ) ),
    file('<stdin>',fact_right__minus__eq) ).

fof(c_0_798,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3)) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    file('<stdin>',fact_one__add__one__is__two) ).

fof(c_0_799,axiom,
    ! [X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
    <=> ? [X1] : X17 = c_Nat_OSuc(X1) ),
    file('<stdin>',fact_gr0__conv__Suc) ).

fof(c_0_800,axiom,
    ! [X25,X24,X3] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
     => ( X24 = c_Groups_Oplus__class_Oplus(X3,X24,X25)
      <=> X25 = c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_add__0__iff) ).

fof(c_0_801,axiom,
    ? [X1] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),
    file('<stdin>',fact__096EX_Am_O_An_A_061_A2_A_K_Am_096) ).

fof(c_0_802,axiom,
    ! [X8,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Int_Oring__char__0(X3) )
     => ~ c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(X8))) ),
    file('<stdin>',fact_iszero__number__of__Bit1) ).

fof(c_0_803,axiom,
    ! [X61] :
      ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,c_Int_OPls) ),
    file('<stdin>',fact_eq__number__of__0) ).

fof(c_0_804,axiom,
    ! [X61] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,c_Int_OPls) ),
    file('<stdin>',fact_eq__0__number__of) ).

fof(c_0_805,axiom,
    ! [X17,X18] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('<stdin>',fact_mult__is__0) ).

fof(c_0_806,axiom,
    ! [X2,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls)),X2) = X2 ),
    file('<stdin>',fact_mult__numeral__1) ).

fof(c_0_807,axiom,
    ! [X2,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls))) = X2 ),
    file('<stdin>',fact_mult__numeral__1__right) ).

fof(c_0_808,axiom,
    ! [X17] :
      ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) ),
    file('<stdin>',fact_neq0__conv) ).

fof(c_0_809,axiom,
    ! [X20] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X20),X20),
    file('<stdin>',fact_Suc__n__not__le__n) ).

fof(c_0_810,axiom,
    ! [X20,X19] :
      ( X19 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)
     => ( X20 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('<stdin>',fact_mult__eq__self__implies__10) ).

fof(c_0_811,axiom,
    ! [X18] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    <=> X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('<stdin>',fact_nat__dvd__1__iff__1) ).

fof(c_0_812,axiom,
    ! [X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('<stdin>',fact_le__0__eq) ).

fof(c_0_813,axiom,
    ! [X17,X18] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    <=> ( X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X17 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('<stdin>',fact_nat__mult__eq__1__iff) ).

fof(c_0_814,axiom,
    ! [X17,X18] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17)
    <=> ( X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X17 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('<stdin>',fact_nat__1__eq__mult__iff) ).

fof(c_0_815,axiom,
    ! [X17,X18] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('<stdin>',fact_add__is__0) ).

fof(c_0_816,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('<stdin>',fact_gr__implies__not0) ).

fof(c_0_817,axiom,
    ! [X20,X19] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20) = X19
     => X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('<stdin>',fact_add__eq__self__zero) ).

fof(c_0_818,axiom,
    ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('<stdin>',fact_less__nat__zero__code) ).

fof(c_0_819,axiom,
    ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('<stdin>',fact_not__less0) ).

fof(c_0_820,axiom,
    ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('<stdin>',fact_less__zeroE) ).

fof(c_0_821,axiom,
    ! [X63,X64] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X64,X63)
     => X64 != X63 ),
    file('<stdin>',fact_less__not__refl3) ).

fof(c_0_822,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
     => X19 != X20 ),
    file('<stdin>',fact_less__not__refl2) ).

fof(c_0_823,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('<stdin>',fact_bin__less__0__simps_I1_J) ).

fof(c_0_824,axiom,
    ! [X2,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls),X2) = X2 ),
    file('<stdin>',fact_add__numeral__0) ).

fof(c_0_825,axiom,
    ! [X2,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls)) = X2 ),
    file('<stdin>',fact_add__numeral__0__right) ).

fof(c_0_826,axiom,
    ! [X20,X3] :
      ( ( class_Power_Opower(X3)
        & class_Rings_Osemiring__0(X3) )
     => c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),c_Nat_OSuc(X20)) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_power__0__Suc) ).

fof(c_0_827,axiom,
    ! [X20,X3] :
      ( ( class_Power_Opower(X3)
        & class_Rings_Osemiring__0(X3) )
     => ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),X20) = c_Groups_Oone__class_Oone(X3) )
        & ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),X20) = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    file('<stdin>',fact_power__0__left) ).

fof(c_0_828,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('<stdin>',fact_nat__1__add__1) ).

fof(c_0_829,axiom,
    ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X20),
    file('<stdin>',fact_less__irrefl__nat) ).

fof(c_0_830,axiom,
    ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X20),
    file('<stdin>',fact_less__not__refl) ).

fof(c_0_831,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => ~ c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls))) ),
    file('<stdin>',fact_not__iszero__Numeral1) ).

fof(c_0_832,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
    file('<stdin>',fact_rel__simps_I3_J) ).

fof(c_0_833,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
    file('<stdin>',fact_rel__simps_I7_J) ).

fof(c_0_834,axiom,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
    file('<stdin>',fact_rel__simps_I20_J) ).

fof(c_0_835,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    file('<stdin>',fact_rel__simps_I2_J) ).

fof(c_0_836,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    file('<stdin>',fact_number__of2) ).

fof(c_0_837,axiom,
    ! [X2] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('<stdin>',fact_zmod__minus1__right) ).

fof(c_0_838,axiom,
    ! [X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oone__class_Oone(X3)) ),
    file('<stdin>',fact_zero__less__one) ).

fof(c_0_839,axiom,
    ! [X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oone__class_Oone(X3)) ),
    file('<stdin>',fact_zero__le__one) ).

fof(c_0_840,axiom,
    ! [X20] : c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('<stdin>',fact_power__Suc__0) ).

fof(c_0_841,axiom,
    ! [X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,X2,c_Groups_Oone__class_Oone(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_mod__by__1) ).

fof(c_0_842,axiom,
    ! [X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Ozero__class_Ozero(X3),X2) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_mod__0) ).

fof(c_0_843,axiom,
    ! [X20,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Oone__class_Oone(X3),X20) = c_Groups_Oone__class_Oone(X3) ),
    file('<stdin>',fact_power__one) ).

fof(c_0_844,axiom,
    ! [X23,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,X23,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_mult__right_Ozero) ).

fof(c_0_845,axiom,
    ! [X2,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_mult_Ozero__right) ).

fof(c_0_846,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(c_0_847,axiom,
    ! [X2,X3] :
      ( class_Rings_Omult__zero(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_mult__zero__right) ).

fof(c_0_848,axiom,
    ! [X22,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Ozero__class_Ozero(X3),X22) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_mult__left_Ozero) ).

fof(c_0_849,axiom,
    ! [X21,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Ozero__class_Ozero(X3),X21) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_mult_Ozero__left) ).

fof(c_0_850,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Ozero__class_Ozero(X3),X2) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(c_0_851,axiom,
    ! [X2,X3] :
      ( class_Rings_Omult__zero(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Ozero__class_Ozero(X3),X2) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_mult__zero__left) ).

fof(c_0_852,axiom,
    ! [X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( X2 != c_Groups_Ozero__class_Ozero(X3)
       => c_Divides_Odiv__class_Odiv(X3,X2,X2) = c_Groups_Oone__class_Oone(X3) ) ),
    file('<stdin>',fact_div__self) ).

fof(c_0_853,axiom,
    ! [X20] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) ),
    file('<stdin>',fact_odd__pos) ).

fof(c_0_854,axiom,
    ! [X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Odiv(X3,X2,c_Groups_Oone__class_Oone(X3)) = X2 ),
    file('<stdin>',fact_div__by__1) ).

fof(c_0_855,axiom,
    ! [X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
    file('<stdin>',fact_mod__by__0) ).

fof(c_0_856,axiom,
    ! [X2,X3] :
      ( class_Power_Opower(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X3) ),
    file('<stdin>',fact_power__0) ).

fof(c_0_857,axiom,
    ! [X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X3) ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(c_0_858,axiom,
    ! [X2,X3] :
      ( class_Groups_Ocomm__monoid__mult(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Oone__class_Oone(X3)) = X2 ),
    file('<stdin>',fact_mult_Ocomm__neutral) ).

fof(c_0_859,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Oone__class_Oone(X3)) = X2 ),
    file('<stdin>',fact_mult__1__right) ).

fof(c_0_860,axiom,
    ! [X2,X3] :
      ( class_Groups_Ocomm__monoid__mult(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oone__class_Oone(X3),X2) = X2 ),
    file('<stdin>',fact_mult__1) ).

fof(c_0_861,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oone__class_Oone(X3),X2) = X2 ),
    file('<stdin>',fact_mult__1__left) ).

fof(c_0_862,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Oone__class_Oone(X3)) = X2 ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(c_0_863,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oone__class_Oone(X3),X2) = X2 ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(c_0_864,axiom,
    ! [X2,X3] :
      ( class_Groups_Ogroup__add(X3)
     => c_Groups_Ominus__class_Ominus(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
    file('<stdin>',fact_diff__0__right) ).

fof(c_0_865,axiom,
    ! [X2,X3] :
      ( class_Groups_Ocomm__monoid__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
    file('<stdin>',fact_add_Ocomm__neutral) ).

fof(c_0_866,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
    file('<stdin>',fact_add__0__right) ).

fof(c_0_867,axiom,
    ! [X2,X3] :
      ( class_Groups_Ocomm__monoid__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X2) = X2 ),
    file('<stdin>',fact_add__0) ).

fof(c_0_868,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X2) = X2 ),
    file('<stdin>',fact_add__0__left) ).

fof(c_0_869,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X2) = X2 ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(c_0_870,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(c_0_871,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Rings_Odvd__class_Odvd(X3,c_Groups_Oone__class_Oone(X3),X2) ),
    file('<stdin>',fact_one__dvd) ).

fof(c_0_872,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Ozero__class_Ozero(X3)) ),
    file('<stdin>',fact_dvd__0__right) ).

fof(c_0_873,axiom,
    ! [X19] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('<stdin>',fact_mod__1) ).

fof(c_0_874,axiom,
    ! [X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,X2,X2) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_mod__self) ).

fof(c_0_875,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2 ),
    file('<stdin>',fact_power__one__right) ).

fof(c_0_876,axiom,
    ! [X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,X23,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X23 ),
    file('<stdin>',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(c_0_877,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => ~ c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin)) ),
    file('<stdin>',fact_nonzero__number__of__Min) ).

fof(c_0_878,axiom,
    ! [X2,X3] :
      ( class_Groups_Ogroup__add(X3)
     => c_Groups_Ominus__class_Ominus(X3,X2,X2) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_diff__self) ).

fof(c_0_879,axiom,
    ! [X7] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7),
    file('<stdin>',fact_dvd__1__left) ).

fof(c_0_880,axiom,
    ! [X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20,
    file('<stdin>',fact_diff__Suc__1) ).

fof(c_0_881,axiom,
    ! [X20] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X20)),
    file('<stdin>',fact_zero__less__Suc) ).

fof(c_0_882,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Rings_Odvd__class_Odvd(X3,X2,X2) ),
    file('<stdin>',fact_dvd__refl) ).

fof(c_0_883,axiom,
    ! [X14,X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Int_Oring__char__0(X3) )
     => ( c_Int_Onumber__class_Onumber__of(X3,X15) = c_Int_Onumber__class_Onumber__of(X3,X14)
      <=> X15 = X14 ) ),
    file('<stdin>',fact_eq__number__of) ).

fof(c_0_884,axiom,
    ! [X20] : c_Nat_OSuc(X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X20),
    file('<stdin>',fact_Suc__eq__plus1__left) ).

fof(c_0_885,axiom,
    ! [X20] : c_Nat_OSuc(X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('<stdin>',fact_Suc__eq__plus1) ).

fof(c_0_886,axiom,
    ! [X20] :
      ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) ),
    file('<stdin>',fact_gr0I) ).

fof(c_0_887,axiom,
    ! [X2] :
      ( X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('<stdin>',fact_zdiv__self) ).

fof(c_0_888,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

fof(c_0_889,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('<stdin>',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

fof(c_0_890,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('<stdin>',fact_int__0__less__1) ).

fof(c_0_891,axiom,
    ! [X20] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(X20)),
    file('<stdin>',fact_lessI) ).

fof(c_0_892,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('<stdin>',fact_numeral__3__eq__3) ).

fof(c_0_893,axiom,
    ! [X2] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      & c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X2 ),
    file('<stdin>',fact_DIVISION__BY__ZERO) ).

fof(c_0_894,axiom,
    ! [X21] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('<stdin>',fact_zmod__zero) ).

fof(c_0_895,axiom,
    ! [X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('<stdin>',fact_diff__0__eq__0) ).

fof(c_0_896,axiom,
    ! [X20] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('<stdin>',fact_mult__0) ).

fof(c_0_897,axiom,
    ! [X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('<stdin>',fact_mult__0__right) ).

fof(c_0_898,axiom,
    ! [X20] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20,
    file('<stdin>',fact_nat__mult__1__right) ).

fof(c_0_899,axiom,
    ! [X20] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X20) = X20,
    file('<stdin>',fact_nat__mult__1) ).

fof(c_0_900,axiom,
    ! [X10] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X10) = X10,
    file('<stdin>',fact_real__mult__1) ).

fof(c_0_901,axiom,
    ! [X10] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10) = X10,
    file('<stdin>',fact_zmult__1) ).

fof(c_0_902,axiom,
    ! [X10] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X10,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X10,
    file('<stdin>',fact_zmult__1__right) ).

fof(c_0_903,axiom,
    ! [X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
    file('<stdin>',fact_minus__nat_Odiff__0) ).

fof(c_0_904,axiom,
    ! [X7] : c_Int_OBit0(X7) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X7),
    file('<stdin>',fact_Bit0__def) ).

fof(c_0_905,axiom,
    ! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X10,
    file('<stdin>',fact_zadd__0__right) ).

fof(c_0_906,axiom,
    ! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10) = X10,
    file('<stdin>',fact_zadd__0) ).

fof(c_0_907,axiom,
    ! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) = X20,
    file('<stdin>',fact_plus__nat_Oadd__0) ).

fof(c_0_908,axiom,
    ! [X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
    file('<stdin>',fact_Nat_Oadd__0__right) ).

fof(c_0_909,axiom,
    ! [X20,X19] :
      ( X19 = X20
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
    file('<stdin>',fact_eq__imp__le) ).

fof(c_0_910,axiom,
    ! [X22,X23] :
      ( X23 = X22
     => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ),
    file('<stdin>',fact_dvd_Oeq__refl) ).

fof(c_0_911,axiom,
    ! [X23] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X23),
    file('<stdin>',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).

fof(c_0_912,axiom,
    ! [X23] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('<stdin>',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).

fof(c_0_913,axiom,
    ! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20),
    file('<stdin>',fact_less__eq__nat_Osimps_I1_J) ).

fof(c_0_914,axiom,
    ! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20),
    file('<stdin>',fact_le0) ).

fof(c_0_915,axiom,
    ! [X2] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('<stdin>',fact_zmod__self) ).

fof(c_0_916,axiom,
    ! [X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('<stdin>',fact_diff__self__eq__0) ).

fof(c_0_917,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('<stdin>',fact_bin__less__0__simps_I2_J) ).

fof(c_0_918,axiom,
    ! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X20),
    file('<stdin>',fact_le__refl) ).

fof(c_0_919,axiom,
    ! [X8] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X8),
    file('<stdin>',fact_real__le__refl) ).

fof(c_0_920,axiom,
    ! [X8] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X8),
    file('<stdin>',fact_zle__refl) ).

fof(c_0_921,axiom,
    ! [X23] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X23),
    file('<stdin>',fact_dvd_Oorder__refl) ).

fof(c_0_922,axiom,
    ! [X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,c_Int_OPls) = X7,
    file('<stdin>',fact_diff__bin__simps_I1_J) ).

fof(c_0_923,axiom,
    ! [X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X7) = X7,
    file('<stdin>',fact_add__Pls) ).

fof(c_0_924,axiom,
    ! [X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,c_Int_OPls) = X7,
    file('<stdin>',fact_add__Pls__right) ).

fof(c_0_925,axiom,
    ! [X8] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,X8) = c_Int_OPls,
    file('<stdin>',fact_mult__Pls) ).

fof(c_0_926,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
    file('<stdin>',fact_rel__simps_I6_J) ).

fof(c_0_927,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    file('<stdin>',fact_rel__simps_I19_J) ).

fof(c_0_928,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
    file('<stdin>',fact_rel__simps_I23_J) ).

fof(c_0_929,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
    file('<stdin>',fact_rel__simps_I24_J) ).

fof(c_0_930,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X15))
    <=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15) ),
    file('<stdin>',fact_even__Suc) ).

fof(c_0_931,axiom,
    ! [X15,X16,X3] :
      ( class_Int_Onumber(X3)
     => ( c_Int_Onumber__class_Onumber__of(X3,X16) = X15
      <=> X15 = c_Int_Onumber__class_Onumber__of(X3,X16) ) ),
    file('<stdin>',fact_number__of__reorient) ).

fof(c_0_932,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls)) ),
    file('<stdin>',fact_iszero__Numeral0) ).

fof(c_0_933,axiom,
    c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('<stdin>',fact_semiring__norm_I115_J) ).

fof(c_0_934,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('<stdin>',fact_numeral__2__eq__2) ).

fof(c_0_935,axiom,
    ! [X3] :
      ( class_Rings_Osemiring__1(X3)
     => ~ c_Int_Oiszero(X3,c_Groups_Oone__class_Oone(X3)) ),
    file('<stdin>',fact_not__iszero__1) ).

fof(c_0_936,axiom,
    ! [X46,X3] :
      ( class_Rings_Osemiring__1(X3)
     => ( c_Int_Oiszero(X3,X46)
      <=> X46 = c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_iszero__def) ).

fof(c_0_937,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),
    file('<stdin>',fact_eq__number__of__Pls__Min) ).

fof(c_0_938,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X3) ),
    file('<stdin>',fact_numeral__1__eq__1) ).

fof(c_0_939,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oone__class_Oone(X3) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls)) ),
    file('<stdin>',fact_semiring__norm_I110_J) ).

fof(c_0_940,axiom,
    ! [X3] :
      ( class_Rings_Osemiring__1(X3)
     => c_Int_Oiszero(X3,c_Groups_Ozero__class_Ozero(X3)) ),
    file('<stdin>',fact_iszero__0) ).

fof(c_0_941,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('<stdin>',fact_odd__1__nat) ).

fof(c_0_942,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('<stdin>',fact_odd__one__int) ).

fof(c_0_943,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Ozero__class_Ozero(X3) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls) ),
    file('<stdin>',fact_semiring__norm_I112_J) ).

fof(c_0_944,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_number__of__Pls) ).

fof(c_0_945,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('<stdin>',fact_numeral__1__eq__Suc__0) ).

fof(c_0_946,axiom,
    ! [X15,X3] :
      ( class_Groups_Oone(X3)
     => ( c_Groups_Oone__class_Oone(X3) = X15
      <=> X15 = c_Groups_Oone__class_Oone(X3) ) ),
    file('<stdin>',fact_one__reorient) ).

fof(c_0_947,axiom,
    ! [X15,X3] :
      ( class_Groups_Ozero(X3)
     => ( c_Groups_Ozero__class_Ozero(X3) = X15
      <=> X15 = c_Groups_Ozero__class_Ozero(X3) ) ),
    file('<stdin>',fact_zero__reorient) ).

fof(c_0_948,axiom,
    ! [X3] :
      ( class_Rings_Ozero__neq__one(X3)
     => c_Groups_Oone__class_Oone(X3) != c_Groups_Ozero__class_Ozero(X3) ),
    file('<stdin>',fact_one__neq__zero) ).

fof(c_0_949,axiom,
    ! [X3] :
      ( class_Rings_Ozero__neq__one(X3)
     => c_Groups_Ozero__class_Ozero(X3) != c_Groups_Oone__class_Oone(X3) ),
    file('<stdin>',fact_zero__neq__one) ).

fof(c_0_950,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
    file('<stdin>',fact_Numeral1__eq1__nat) ).

fof(c_0_951,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('<stdin>',fact_nat__numeral__1__eq__1) ).

fof(c_0_952,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
    file('<stdin>',fact_one__is__num__one) ).

fof(c_0_953,axiom,
    c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('<stdin>',fact_even__zero__int) ).

fof(c_0_954,axiom,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('<stdin>',fact_even__zero__nat) ).

fof(c_0_955,axiom,
    ! [X22,X23] :
      ( c_Nat_OSuc(X23) = c_Nat_OSuc(X22)
     => X23 = X22 ),
    file('<stdin>',fact_Suc__inject) ).

fof(c_0_956,axiom,
    ! [X36,X37] :
      ( c_Nat_OSuc(X37) = c_Nat_OSuc(X36)
    <=> X37 = X36 ),
    file('<stdin>',fact_nat_Oinject) ).

fof(c_0_957,axiom,
    ! [X4,X5] :
      ( c_Int_OBit0(X5) = c_Int_OBit0(X4)
    <=> X5 = X4 ),
    file('<stdin>',fact_rel__simps_I48_J) ).

fof(c_0_958,axiom,
    ! [X4,X5] :
      ( c_Int_OBit1(X5) = c_Int_OBit1(X4)
    <=> X5 = X4 ),
    file('<stdin>',fact_rel__simps_I51_J) ).

fof(c_0_959,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
    file('<stdin>',fact_zero__is__num__zero) ).

fof(c_0_960,axiom,
    ! [X7] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X7) = X7,
    file('<stdin>',fact_number__of__is__id) ).

fof(c_0_961,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
    file('<stdin>',fact_semiring__norm_I113_J) ).

fof(c_0_962,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('<stdin>',fact_nat__number__of__Pls) ).

fof(c_0_963,axiom,
    ! [X6,X7] : c_Int_OBit1(X7) != c_Int_OBit0(X6),
    file('<stdin>',fact_rel__simps_I50_J) ).

fof(c_0_964,axiom,
    ! [X6,X7] : c_Int_OBit0(X7) != c_Int_OBit1(X6),
    file('<stdin>',fact_rel__simps_I49_J) ).

fof(c_0_965,axiom,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    file('<stdin>',fact_e) ).

fof(c_0_966,axiom,
    ! [X19] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X19),
    file('<stdin>',fact_Zero__not__Suc) ).

fof(c_0_967,axiom,
    ! [X48] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X48),
    file('<stdin>',fact_nat_Osimps_I2_J) ).

fof(c_0_968,axiom,
    ! [X19] : c_Nat_OSuc(X19) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('<stdin>',fact_Suc__not__Zero) ).

fof(c_0_969,axiom,
    ! [X47] : c_Nat_OSuc(X47) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('<stdin>',fact_nat_Osimps_I3_J) ).

fof(c_0_970,axiom,
    ! [X19] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X19),
    file('<stdin>',fact_Zero__neq__Suc) ).

fof(c_0_971,axiom,
    ! [X19] : c_Nat_OSuc(X19) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('<stdin>',fact_Suc__neq__Zero) ).

fof(c_0_972,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('<stdin>',fact_One__nat__def) ).

fof(c_0_973,axiom,
    ! [X5] :
      ( c_Int_OBit1(X5) = c_Int_OMin
    <=> X5 = c_Int_OMin ),
    file('<stdin>',fact_rel__simps_I47_J) ).

fof(c_0_974,axiom,
    ! [X4] :
      ( c_Int_OMin = c_Int_OBit1(X4)
    <=> c_Int_OMin = X4 ),
    file('<stdin>',fact_rel__simps_I43_J) ).

fof(c_0_975,axiom,
    ! [X5] :
      ( c_Int_OBit0(X5) = c_Int_OPls
    <=> X5 = c_Int_OPls ),
    file('<stdin>',fact_rel__simps_I44_J) ).

fof(c_0_976,axiom,
    ! [X4] :
      ( c_Int_OPls = c_Int_OBit0(X4)
    <=> c_Int_OPls = X4 ),
    file('<stdin>',fact_rel__simps_I38_J) ).

fof(c_0_977,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('<stdin>',fact_real__zero__not__eq__one) ).

fof(c_0_978,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('<stdin>',fact_int__0__neq__1) ).

fof(c_0_979,axiom,
    ! [X20] : c_Nat_OSuc(X20) != X20,
    file('<stdin>',fact_Suc__n__not__n) ).

fof(c_0_980,axiom,
    ! [X20] : X20 != c_Nat_OSuc(X20),
    file('<stdin>',fact_n__not__Suc__n) ).

fof(c_0_981,axiom,
    ! [X7] : c_Int_OBit0(X7) != c_Int_OMin,
    file('<stdin>',fact_rel__simps_I45_J) ).

fof(c_0_982,axiom,
    ! [X6] : c_Int_OMin != c_Int_OBit0(X6),
    file('<stdin>',fact_rel__simps_I42_J) ).

fof(c_0_983,axiom,
    ! [X7] : c_Int_OBit1(X7) != c_Int_OPls,
    file('<stdin>',fact_rel__simps_I46_J) ).

fof(c_0_984,axiom,
    ! [X6] : c_Int_OPls != c_Int_OBit1(X6),
    file('<stdin>',fact_rel__simps_I39_J) ).

fof(c_0_985,axiom,
    v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('<stdin>',fact_assms_I2_J) ).

fof(c_0_986,axiom,
    v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('<stdin>',fact_n) ).

fof(c_0_987,axiom,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Odvd) ).

fof(c_0_988,axiom,
    class_Groups_Oone(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Groups_Oone) ).

fof(c_0_989,axiom,
    class_Int_Onumber(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Int_Onumber) ).

fof(c_0_990,axiom,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Oidom) ).

fof(c_0_991,axiom,
    class_Rings_Oring(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Oring) ).

fof(c_0_992,axiom,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Groups_Ozero) ).

fof(c_0_993,axiom,
    class_Power_Opower(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Power_Opower) ).

fof(c_0_994,axiom,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Oring__1) ).

fof(c_0_995,axiom,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Osemiring) ).

fof(c_0_996,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Int_Onumber__ring) ).

fof(c_0_997,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Int_Oring__char__0) ).

fof(c_0_998,axiom,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).

fof(c_0_999,axiom,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Omult__zero) ).

fof(c_0_1000,axiom,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Groups_Ogroup__add) ).

fof(c_0_1001,axiom,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Osemiring__0) ).

fof(c_0_1002,axiom,
    class_Rings_Osemiring__1(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Osemiring__1) ).

fof(c_0_1003,axiom,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Groups_Omonoid__add) ).

fof(c_0_1004,axiom,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).

fof(c_0_1005,axiom,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).

fof(c_0_1006,axiom,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).

fof(c_0_1007,axiom,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Groups_Oab__group__add) ).

fof(c_0_1008,axiom,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).

fof(c_0_1009,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

fof(c_0_1010,axiom,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).

fof(c_0_1011,axiom,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).

fof(c_0_1012,axiom,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).

fof(c_0_1013,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).

fof(c_0_1014,axiom,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).

fof(c_0_1015,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).

fof(c_0_1016,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).

fof(c_0_1017,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).

fof(c_0_1018,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).

fof(c_0_1019,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

fof(c_0_1020,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    file('<stdin>',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(c_0_1021,axiom,
    class_Rings_Odvd(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Odvd) ).

fof(c_0_1022,axiom,
    class_Groups_Oone(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Oone) ).

fof(c_0_1023,axiom,
    class_Int_Onumber(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Int_Onumber) ).

fof(c_0_1024,axiom,
    class_Rings_Oidom(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Oidom) ).

fof(c_0_1025,axiom,
    class_Rings_Oring(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Oring) ).

fof(c_0_1026,axiom,
    class_Groups_Ozero(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Ozero) ).

fof(c_0_1027,axiom,
    class_Power_Opower(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Power_Opower) ).

fof(c_0_1028,axiom,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Oring__1) ).

fof(c_0_1029,axiom,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Osemiring) ).

fof(c_0_1030,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Int_Onumber__ring) ).

fof(c_0_1031,axiom,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Int_Oring__char__0) ).

fof(c_0_1032,axiom,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Ocomm__ring) ).

fof(c_0_1033,axiom,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Omult__zero) ).

fof(c_0_1034,axiom,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Ogroup__add) ).

fof(c_0_1035,axiom,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Osemiring__0) ).

fof(c_0_1036,axiom,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Osemiring__1) ).

fof(c_0_1037,axiom,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Omonoid__add) ).

fof(c_0_1038,axiom,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).

fof(c_0_1039,axiom,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Omonoid__mult) ).

fof(c_0_1040,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Orderings_Olinorder) ).

fof(c_0_1041,axiom,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Oordered__ring) ).

fof(c_0_1042,axiom,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).

fof(c_0_1043,axiom,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Oab__group__add) ).

fof(c_0_1044,axiom,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).

fof(c_0_1045,axiom,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).

fof(c_0_1046,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

fof(c_0_1047,axiom,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__ring) ).

fof(c_0_1048,axiom,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).

fof(c_0_1049,axiom,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).

fof(c_0_1050,axiom,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Oordered__semiring) ).

fof(c_0_1051,axiom,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).

fof(c_0_1052,axiom,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).

fof(c_0_1053,axiom,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).

fof(c_0_1054,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

fof(c_0_1055,axiom,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).

fof(c_0_1056,axiom,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).

fof(c_0_1057,axiom,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).

fof(c_0_1058,axiom,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).

fof(c_0_1059,axiom,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).

fof(c_0_1060,axiom,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).

fof(c_0_1061,axiom,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).

fof(c_0_1062,axiom,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).

fof(c_0_1063,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).

fof(c_0_1064,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).

fof(c_0_1065,axiom,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).

fof(c_0_1066,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).

fof(c_0_1067,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

fof(c_0_1068,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).

fof(c_0_1069,axiom,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).

fof(c_0_1070,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).

fof(c_0_1071,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).

fof(c_0_1072,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(c_0_1073,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(c_0_1074,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    file('<stdin>',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(c_0_1075,axiom,
    class_Rings_Odvd(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Odvd) ).

fof(c_0_1076,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Oone) ).

fof(c_0_1077,axiom,
    class_Int_Onumber(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Int_Onumber) ).

fof(c_0_1078,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Ozero) ).

fof(c_0_1079,axiom,
    class_Power_Opower(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Power_Opower) ).

fof(c_0_1080,axiom,
    class_Rings_Osemiring(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Osemiring) ).

fof(c_0_1081,axiom,
    class_Rings_Omult__zero(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Omult__zero) ).

fof(c_0_1082,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Osemiring__0) ).

fof(c_0_1083,axiom,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Osemiring__1) ).

fof(c_0_1084,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Omonoid__add) ).

fof(c_0_1085,axiom,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Omonoid__mult) ).

fof(c_0_1086,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Orderings_Olinorder) ).

fof(c_0_1087,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Ozero__neq__one) ).

fof(c_0_1088,axiom,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Ocomm__semiring) ).

fof(c_0_1089,axiom,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Divides_Osemiring__div) ).

fof(c_0_1090,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

fof(c_0_1091,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

fof(c_0_1092,axiom,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

fof(c_0_1093,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Oordered__semiring) ).

fof(c_0_1094,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

fof(c_0_1095,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

fof(c_0_1096,axiom,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

fof(c_0_1097,axiom,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Olinordered__semidom) ).

fof(c_0_1098,axiom,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Olinordered__semiring) ).

fof(c_0_1099,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

fof(c_0_1100,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

fof(c_0_1101,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

fof(c_0_1102,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

fof(c_0_1103,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).

fof(c_0_1104,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

fof(c_0_1105,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

fof(c_0_1106,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).

fof(c_0_1107,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(c_0_1108,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(c_0_1109,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    file('<stdin>',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(c_0_1110,axiom,
    class_Rings_Odvd(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Odvd) ).

fof(c_0_1111,axiom,
    class_Groups_Oone(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Oone) ).

fof(c_0_1112,axiom,
    class_Int_Onumber(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Int_Onumber) ).

fof(c_0_1113,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Oidom) ).

fof(c_0_1114,axiom,
    class_Rings_Oring(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Oring) ).

fof(c_0_1115,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Ozero) ).

fof(c_0_1116,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Power_Opower) ).

fof(c_0_1117,axiom,
    class_Rings_Oring__1(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Oring__1) ).

fof(c_0_1118,axiom,
    class_Rings_Osemiring(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Osemiring) ).

fof(c_0_1119,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Int_Onumber__ring) ).

fof(c_0_1120,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Int_Oring__char__0) ).

fof(c_0_1121,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Ocomm__ring) ).

fof(c_0_1122,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Omult__zero) ).

fof(c_0_1123,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Divides_Oring__div) ).

fof(c_0_1124,axiom,
    class_Groups_Ogroup__add(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Ogroup__add) ).

fof(c_0_1125,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Osemiring__0) ).

fof(c_0_1126,axiom,
    class_Rings_Osemiring__1(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Osemiring__1) ).

fof(c_0_1127,axiom,
    class_Groups_Omonoid__add(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Omonoid__add) ).

fof(c_0_1128,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Ocomm__ring__1) ).

fof(c_0_1129,axiom,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Omonoid__mult) ).

fof(c_0_1130,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Orderings_Olinorder) ).

fof(c_0_1131,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Oordered__ring) ).

fof(c_0_1132,axiom,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Ozero__neq__one) ).

fof(c_0_1133,axiom,
    class_Groups_Oab__group__add(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Oab__group__add) ).

fof(c_0_1134,axiom,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Ocomm__semiring) ).

fof(c_0_1135,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Divides_Osemiring__div) ).

fof(c_0_1136,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

fof(c_0_1137,axiom,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Olinordered__idom) ).

fof(c_0_1138,axiom,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Olinordered__ring) ).

fof(c_0_1139,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

fof(c_0_1140,axiom,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Ono__zero__divisors) ).

fof(c_0_1141,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Oordered__semiring) ).

fof(c_0_1142,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Oab__semigroup__add) ).

fof(c_0_1143,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

fof(c_0_1144,axiom,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

fof(c_0_1145,axiom,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Olinordered__semidom) ).

fof(c_0_1146,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Olinordered__semiring) ).

fof(c_0_1147,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

fof(c_0_1148,axiom,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Oordered__ab__group__add) ).

fof(c_0_1149,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

fof(c_0_1150,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

fof(c_0_1151,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).

fof(c_0_1152,axiom,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

fof(c_0_1153,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

fof(c_0_1154,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).

fof(c_0_1155,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

fof(c_0_1156,axiom,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).

fof(c_0_1157,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).

fof(c_0_1158,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).

fof(c_0_1159,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

fof(c_0_1160,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

fof(c_0_1161,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).

fof(c_0_1162,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(c_0_1163,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(c_0_1164,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    file('<stdin>',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(c_0_1165,axiom,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    file('<stdin>',fact_Bit1__Min) ).

fof(c_0_1166,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('<stdin>',fact_Pls__def) ).

fof(c_0_1167,axiom,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    file('<stdin>',fact_Bit0__Pls) ).

fof(c_0_1168,axiom,
    c_Int_OPls != c_Int_OMin,
    file('<stdin>',fact_rel__simps_I37_J) ).

fof(c_0_1169,axiom,
    c_Int_OMin != c_Int_OPls,
    file('<stdin>',fact_rel__simps_I40_J) ).

fof(c_0_1170,plain,
    ! [X5,X17,X55] :
      ( epred1_3(X55,X17,X5)
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
         => ! [X77,X58] :
              ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X58)
                & c_Orderings_Oord__class_Oless(tc_Int_Oint,X58,X5)
                & X17 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
             => hBOOL(hAPP(X55,X58)) ) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => ! [X77,X58] :
              ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X58)
                & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                & X17 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
             => hBOOL(hAPP(X55,X58)) ) ) ) ),
    introduced(definition) ).

fof(c_0_1171,axiom,
    ! [X21,X2,X22,X23,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),c_Groups_Otimes__class_Otimes(X3,X2,X21)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X2),c_Groups_Ominus__class_Ominus(X3,X22,X21)),c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X2),X21)),c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ominus__class_Ominus(X3,X22,X21))) ),
    c_0_0 ).

fof(c_0_1172,axiom,
    ! [X17,X18,X68,X65,X66] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17))
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66),X68),X17)) ) ),
    c_0_1 ).

fof(c_0_1173,axiom,
    ! [X17,X18,X68,X66,X65] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X66)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17))
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X65),X68),X18),X17) ) ),
    c_0_2 ).

fof(c_0_1174,axiom,
    ! [X17,X18,X68,X65,X66] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66),X68),X17)) ) ),
    c_0_3 ).

fof(c_0_1175,axiom,
    ! [X17,X18,X68,X66,X65] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X66)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X65),X68),X18),X17) ) ),
    c_0_4 ).

fof(c_0_1176,axiom,
    ! [X41,X24,X42,X67,X25,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41))
      <=> c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X24,X25),X67),X41)) ) ),
    c_0_5 ).

fof(c_0_1177,axiom,
    ! [X41,X24,X42,X67,X25,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41))
      <=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),X67),X42),X41) ) ),
    c_0_6 ).

fof(c_0_1178,axiom,
    ! [X41,X24,X42,X67,X25,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41))
      <=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),X67),X42),X41) ) ),
    c_0_7 ).

fof(c_0_1179,axiom,
    ! [X41,X24,X42,X67,X25,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X42,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X24,X25),X67),X41)) ) ),
    c_0_8 ).

fof(c_0_1180,axiom,
    ! [X33,X21,X2] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X21),X33) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X33),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X33)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X33),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X33)),X33)),
    c_0_9 ).

fof(c_0_1181,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    c_0_10 ).

fof(c_0_1182,axiom,
    ! [X22,X23,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Ominus__class_Ominus(X3,X23,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23),X22)) ),
    c_0_11 ).

fof(c_0_1183,axiom,
    ! [X22,X23,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Oplus__class_Oplus(X3,X23,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23),X22)) ),
    c_0_12 ).

fof(c_0_1184,axiom,
    ! [X22,X23] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X23,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23),X22)),
    c_0_13 ).

fof(c_0_1185,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))))
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ),
    c_0_14 ).

fof(c_0_1186,axiom,
    ! [X14,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> ( X15 != c_Groups_Ozero__class_Ozero(X3)
          | X14 != c_Groups_Ozero__class_Ozero(X3) ) ) ),
    c_0_15 ).

fof(c_0_1187,axiom,
    ! [X14,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X3))
      <=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
          & X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    c_0_16 ).

fof(c_0_1188,axiom,
    ! [X20,X19,X52,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X52),X19),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X52),X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X53),X52),X20)) ),
    c_0_17 ).

fof(c_0_1189,axiom,
    ! [X20,X19,X52,X53,X51] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X53)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X52),X19),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X52),X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X51),X52),X19),X20) ),
    c_0_18 ).

fof(c_0_1190,plain,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_19]) ).

fof(c_0_1191,axiom,
    ! [X57,X72,X41,X3] :
      ( ( class_Rings_Ocomm__ring(X3)
        & class_Rings_Odvd(X3) )
     => ( c_Rings_Odvd__class_Odvd(X3,X41,X72)
       => ! [X56,X59] :
            ( c_Rings_Odvd__class_Odvd(X3,X41,c_Groups_Oplus__class_Oplus(X3,X56,X57))
          <=> c_Rings_Odvd__class_Odvd(X3,X41,c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X56,c_Groups_Otimes__class_Otimes(X3,X59,X72)),X57)) ) ) ),
    c_0_20 ).

fof(c_0_1192,axiom,
    ! [X57,X72,X41,X3] :
      ( ( class_Rings_Ocomm__ring(X3)
        & class_Rings_Odvd(X3) )
     => ( c_Rings_Odvd__class_Odvd(X3,X41,X72)
       => ! [X56,X59] :
            ( c_Rings_Odvd__class_Odvd(X3,X41,c_Groups_Oplus__class_Oplus(X3,X56,X57))
          <=> c_Rings_Odvd__class_Odvd(X3,X41,c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X56,c_Groups_Otimes__class_Otimes(X3,X59,X72)),X57)) ) ) ),
    c_0_21 ).

fof(c_0_1193,axiom,
    ! [X73,X74,X39,X54,X35,X21] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X35),X54) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X73,X39)
         => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
             => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X21)
               => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,X74) ) ) ) ) ) ),
    c_0_22 ).

fof(c_0_1194,axiom,
    ! [X73,X74,X39,X54,X35,X21] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X35),X54) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X21)
         => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X73)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
             => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X21)
               => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X74,X35) ) ) ) ) ) ),
    c_0_23 ).

fof(c_0_1195,axiom,
    ! [X42,X57,X15,X41,X25] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,X41)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X57))
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X42,X41)),X57)) ) ),
    c_0_24 ).

fof(c_0_1196,plain,
    ! [X9,X8] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X9)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X8))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X9)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X8))) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_25]) ).

fof(c_0_1197,axiom,
    ! [X54,X35,X73,X74,X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X74),X73),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X35),X54))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X73)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X73,X21)
         => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X21)
           => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X74,X35) ) ) ) ),
    c_0_26 ).

fof(c_0_1198,axiom,
    ! [X54,X35,X73,X74,X21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X74),X73),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X35),X54))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X54)
         => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X73)
           => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,X74) ) ) ) ),
    c_0_27 ).

fof(c_0_1199,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X2))) ),
    c_0_28 ).

fof(c_0_1200,axiom,
    ! [X35,X54,X21,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X54)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X33),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X33)),X54)) ) ) ),
    c_0_29 ).

fof(c_0_1201,axiom,
    ! [X35,X21,X54,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X21)
         => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X33)),X54),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X33)) ) ) ),
    c_0_30 ).

fof(c_0_1202,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))),c_Groups_Ozero__class_Ozero(X3)) ) ),
    c_0_31 ).

fof(c_0_1203,axiom,
    ! [X20,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))) = c_Groups_Otimes__class_Otimes(X3,X23,c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X23,X20))) ),
    c_0_32 ).

fof(c_0_1204,axiom,
    ! [X9,X52,X22,X2,X23,X3] :
      ( class_Rings_Olinordered__semiring__1__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X23,X2)
       => ( c_Orderings_Oord__class_Oless(X3,X22,X2)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X52)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X9)
             => ( c_Groups_Oplus__class_Oplus(X3,X52,X9) = c_Groups_Oone__class_Oone(X3)
               => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X52,X23),c_Groups_Otimes__class_Otimes(X3,X9,X22)),X2) ) ) ) ) ) ),
    c_0_33 ).

fof(c_0_1205,axiom,
    ! [X9,X52,X22,X2,X23,X3] :
      ( class_Rings_Olinordered__semiring__1(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X23,X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X22,X2)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X52)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X9)
             => ( c_Groups_Oplus__class_Oplus(X3,X52,X9) = c_Groups_Oone__class_Oone(X3)
               => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X52,X23),c_Groups_Otimes__class_Otimes(X3,X9,X22)),X2) ) ) ) ) ) ),
    c_0_34 ).

fof(c_0_1206,axiom,
    ! [X35,X54,X21,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X54)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X33)),X54),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
    c_0_35 ).

fof(c_0_1207,axiom,
    ! [X35,X21,X54,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X21)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X33)),X54)) ) ) ),
    c_0_36 ).

fof(c_0_1208,plain,
    ! [X5,X17,X55] :
      ( epred1_3(X55,X17,X5)
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
         => ! [X77,X58] :
              ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X58)
                & c_Orderings_Oord__class_Oless(tc_Int_Oint,X58,X5)
                & X17 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
             => hBOOL(hAPP(X55,X58)) ) )
        & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
         => ! [X77,X58] :
              ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X58)
                & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                & X17 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
             => hBOOL(hAPP(X55,X58)) ) ) ) ),
    c_0_1170 ).

fof(c_0_1209,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
    c_0_37 ).

fof(c_0_1210,axiom,
    ! [X4,X55,X3] :
      ( ( class_Rings_Odvd(X3)
        & class_Rings_Osemiring__0(X3) )
     => ( ? [X56] : hBOOL(hAPP(X55,c_Groups_Otimes__class_Otimes(X3,X4,X56)))
      <=> ? [X56] :
            ( c_Rings_Odvd__class_Odvd(X3,X4,c_Groups_Oplus__class_Oplus(X3,X56,c_Groups_Ozero__class_Ozero(X3)))
            & hBOOL(hAPP(X55,X56)) ) ) ),
    c_0_38 ).

fof(c_0_1211,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    c_0_39 ).

fof(c_0_1212,axiom,
    ! [X17,X18,X68,X65,X66] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17)
      <=> X18 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66),X68),X17) ) ),
    c_0_40 ).

fof(c_0_1213,axiom,
    ! [X17,X18,X68,X66,X65] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X66)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17)
      <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X65),X68),X18) = X17 ) ),
    c_0_41 ).

fof(c_0_1214,axiom,
    ! [X21,X2,X22,X23,X3] :
      ( class_Rings_Oring(X3)
     => c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),c_Groups_Otimes__class_Otimes(X3,X2,X21)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,c_Groups_Ominus__class_Ominus(X3,X22,X21)),c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X2),X21)) ),
    c_0_42 ).

fof(c_0_1215,axiom,
    ! [X14,X15,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X15,X15),c_Groups_Otimes__class_Otimes(X3,X14,X14)))
      <=> ( X15 != c_Groups_Ozero__class_Ozero(X3)
          | X14 != c_Groups_Ozero__class_Ozero(X3) ) ) ),
    c_0_43 ).

fof(c_0_1216,axiom,
    ! [X14,X15,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X15,X15),c_Groups_Otimes__class_Otimes(X3,X14,X14)),c_Groups_Ozero__class_Ozero(X3))
      <=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
          & X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    c_0_44 ).

fof(c_0_1217,plain,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__ring(X3)
     => ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X23),c_Groups_Otimes__class_Otimes(X3,X22,X22)),c_Groups_Ozero__class_Ozero(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_45]) ).

fof(c_0_1218,axiom,
    ! [X20,X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))) = c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    c_0_46 ).

fof(c_0_1219,axiom,
    ! [X41,X24,X42,X67,X25,X3] :
      ( class_Rings_Oring(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41)
      <=> X42 = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X24,X25),X67),X41) ) ),
    c_0_47 ).

fof(c_0_1220,axiom,
    ! [X41,X24,X42,X67,X25,X3] :
      ( class_Rings_Oring(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41)
      <=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),X67),X42) = X41 ) ),
    c_0_48 ).

fof(c_0_1221,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X2) ),
    c_0_49 ).

fof(c_0_1222,axiom,
    ! [X7,X2,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X7)),c_Groups_Ozero__class_Ozero(X3))
       => X2 = c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_50 ).

fof(c_0_1223,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
         => c_Orderings_Oord__class_Oless(X3,X23,X22) ) ) ),
    c_0_51 ).

fof(c_0_1224,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
         => c_Orderings_Oord__class_Oless__eq(X3,X23,X22) ) ) ),
    c_0_52 ).

fof(c_0_1225,axiom,
    ! [X33,X21,X45,X2,X3] :
      ( class_Rings_Osemiring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X45),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X21,X45),X33)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X45),X33) ),
    c_0_53 ).

fof(c_0_1226,axiom,
    ! [X46,X15,X14,X16,X3] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X16,X14),c_Groups_Otimes__class_Otimes(X3,X15,X46)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X16,X46),c_Groups_Otimes__class_Otimes(X3,X15,X14))
      <=> ( X16 = X15
          | X14 = X46 ) ) ),
    c_0_54 ).

fof(c_0_1227,axiom,
    ! [X41,X42,X24,X25,X3] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
     => ( ( X25 != X24
          & X42 != X41 )
      <=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X42),c_Groups_Otimes__class_Otimes(X3,X24,X41)) != c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X41),c_Groups_Otimes__class_Otimes(X3,X24,X42)) ) ),
    c_0_55 ).

fof(c_0_1228,axiom,
    ! [X7,X51,X52,X53] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X52),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X52),X7)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X52),X7),
    c_0_56 ).

fof(c_0_1229,axiom,
    ! [X73,X74,X39] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X73)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X74,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
    c_0_57 ).

fof(c_0_1230,axiom,
    ! [X73,X74,X39] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X73,X39)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X74) ) ) ),
    c_0_58 ).

fof(c_0_1231,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
    c_0_59 ).

fof(c_0_1232,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Oring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
    c_0_60 ).

fof(c_0_1233,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
    c_0_61 ).

fof(c_0_1234,axiom,
    ! [X19,X20,X7] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20),X19)),X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X19),X20),
    c_0_62 ).

fof(c_0_1235,axiom,
    ! [X14,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X3)
      <=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
          & X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    c_0_63 ).

fof(c_0_1236,axiom,
    ! [X14,X15] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> ( X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        & X14 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    c_0_64 ).

fof(c_0_1237,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oone__class_Oone(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20)),c_Power_Opower__class_Opower(X3,X2,X20)) ) ) ),
    c_0_65 ).

fof(c_0_1238,axiom,
    ! [X24,X25,X55] :
      ( hBOOL(hAPP(X55,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24)))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
         => hBOOL(hAPP(X55,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [X69] :
            ( X25 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X69)
           => hBOOL(hAPP(X55,X69)) ) ) ),
    c_0_66 ).

fof(c_0_1239,plain,
    ! [X24,X25,X55] :
      ( hBOOL(hAPP(X55,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24)))
    <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
            & ~ hBOOL(hAPP(X55,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
          | ? [X69] :
              ( X25 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X69)
              & ~ hBOOL(hAPP(X55,X69)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_67]) ).

fof(c_0_1240,axiom,
    ! [X39,X21,X43,X33,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Divides_Odiv__class_Omod(X3,X2,X33) = c_Divides_Odiv__class_Omod(X3,X43,X33)
       => ( c_Divides_Odiv__class_Omod(X3,X21,X33) = c_Divides_Odiv__class_Omod(X3,X39,X33)
         => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X43,X39),X33) ) ) ),
    c_0_68 ).

fof(c_0_1241,axiom,
    ! [X39,X21,X43,X33,X2,X3] :
      ( class_Divides_Oring__div(X3)
     => ( c_Divides_Odiv__class_Omod(X3,X2,X33) = c_Divides_Odiv__class_Omod(X3,X43,X33)
       => ( c_Divides_Odiv__class_Omod(X3,X21,X33) = c_Divides_Odiv__class_Omod(X3,X39,X33)
         => c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X43,X39),X33) ) ) ),
    c_0_69 ).

fof(c_0_1242,axiom,
    ! [X39,X21,X43,X33,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Divides_Odiv__class_Omod(X3,X2,X33) = c_Divides_Odiv__class_Omod(X3,X43,X33)
       => ( c_Divides_Odiv__class_Omod(X3,X21,X33) = c_Divides_Odiv__class_Omod(X3,X39,X33)
         => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X43,X39),X33) ) ) ),
    c_0_70 ).

fof(c_0_1243,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Ocomm__ring__1(X3)
     => c_Groups_Ominus__class_Ominus(X3,c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(X3,X22,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X22),c_Groups_Oplus__class_Oplus(X3,X23,X22)) ),
    c_0_71 ).

fof(c_0_1244,axiom,
    ! [X46] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X46),X46),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_72 ).

fof(c_0_1245,plain,
    ! [X22,X78,X79,X80] :
      ( X80 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X79,X78),X22)
     => ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
           => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
              & c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X79) ) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X22)
              & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
       => ( X79 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,X80,X79) = X22 ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_73]) ).

fof(c_0_1246,axiom,
    ! [X26,X27,X28,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,X29,c_Groups_Otimes__class_Otimes(X3,X28,c_Groups_Otimes__class_Otimes(X3,X27,X26))) ),
    c_0_74 ).

fof(c_0_1247,axiom,
    ! [X26,X27,X28,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,X27,c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),X26)) ),
    c_0_75 ).

fof(c_0_1248,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,X33,X34)
         => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
             => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
    c_0_76 ).

fof(c_0_1249,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,X33,X34)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
             => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
    c_0_77 ).

fof(c_0_1250,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
           => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
             => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
    c_0_78 ).

fof(c_0_1251,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,X33,X34)
         => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
             => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
    c_0_79 ).

fof(c_0_1252,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Oordered__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
             => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
    c_0_80 ).

fof(c_0_1253,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Oordered__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
           => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
             => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
    c_0_81 ).

fof(c_0_1254,axiom,
    ! [X23] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    c_0_82 ).

fof(c_0_1255,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X18)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X17)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X5),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X5))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ) ),
    c_0_83 ).

fof(c_0_1256,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X18)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X17)
       => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X5),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X5))
        <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ) ),
    c_0_84 ).

fof(c_0_1257,axiom,
    ! [X22,X20,X38,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X20)
       => c_Power_Opower__class_Opower(X3,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X20),X38)) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X38)),X22) ) ),
    c_0_85 ).

fof(c_0_1258,axiom,
    ! [X18,X17,X5] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X18)))
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5,X17) ),
    c_0_86 ).

fof(c_0_1259,axiom,
    ! [X21,X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)),c_Power_Opower__class_Opower(X3,X21,c_Nat_OSuc(X20)))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ) ),
    c_0_87 ).

fof(c_0_1260,axiom,
    ! [X22,X23,X10,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X10,X23)
       => ( c_Rings_Odvd__class_Odvd(X3,X10,X22)
         => c_Divides_Odiv__class_Odiv(X3,c_Groups_Oplus__class_Oplus(X3,X23,X22),X10) = c_Groups_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Odiv(X3,X23,X10),c_Divides_Odiv__class_Odiv(X3,X22,X10)) ) ) ),
    c_0_88 ).

fof(c_0_1261,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__ring(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X23),c_Groups_Otimes__class_Otimes(X3,X22,X22))) ),
    c_0_89 ).

fof(c_0_1262,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
       => c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20))) ) ),
    c_0_90 ).

fof(c_0_1263,axiom,
    ! [X21,X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X21,X20))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
    c_0_91 ).

fof(c_0_1264,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X42)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
        <=> c_Orderings_Oord__class_Oless__eq(X3,X25,X24) ) ) ),
    c_0_92 ).

fof(c_0_1265,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
        <=> c_Orderings_Oord__class_Oless__eq(X3,X24,X25) ) ) ),
    c_0_93 ).

fof(c_0_1266,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Rings_Olinordered__semiring(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
    c_0_94 ).

fof(c_0_1267,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
    c_0_95 ).

fof(c_0_1268,axiom,
    ! [X21,X2,X33,X3] :
      ( class_Rings_Olinordered__semiring(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
    c_0_96 ).

fof(c_0_1269,axiom,
    ! [X21,X2,X33,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
    c_0_97 ).

fof(c_0_1270,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33))
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ) ),
    c_0_98 ).

fof(c_0_1271,axiom,
    ! [X21,X2,X33,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21))
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ) ),
    c_0_99 ).

fof(c_0_1272,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X42)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
        <=> c_Orderings_Oord__class_Oless(X3,X25,X24) ) ) ),
    c_0_100 ).

fof(c_0_1273,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
        <=> c_Orderings_Oord__class_Oless(X3,X24,X25) ) ) ),
    c_0_101 ).

fof(c_0_1274,axiom,
    ! [X14,X15,X24,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X24)
       => ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X24,X15),c_Power_Opower__class_Opower(X3,X24,X14))
        <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14) ) ) ),
    c_0_102 ).

fof(c_0_1275,axiom,
    ! [X20,X19,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X19),c_Power_Opower__class_Opower(X3,X2,X20))
         => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ) ) ),
    c_0_103 ).

fof(c_0_1276,axiom,
    ! [X14,X15,X24,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X24)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X24,X15),c_Power_Opower__class_Opower(X3,X24,X14))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14) ) ) ),
    c_0_104 ).

fof(c_0_1277,axiom,
    ! [X20,X19,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X19),c_Power_Opower__class_Opower(X3,X2,X20))
         => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ) ) ),
    c_0_105 ).

fof(c_0_1278,axiom,
    ! [X9,X21,X2,X30] :
      ( ( class_Int_Onumber(X30)
        & class_Rings_Oring(X30) )
     => c_Groups_Otimes__class_Otimes(X30,c_Groups_Ominus__class_Ominus(X30,X2,X21),c_Int_Onumber__class_Onumber__of(X30,X9)) = c_Groups_Ominus__class_Ominus(X30,c_Groups_Otimes__class_Otimes(X30,X2,c_Int_Onumber__class_Onumber__of(X30,X9)),c_Groups_Otimes__class_Otimes(X30,X21,c_Int_Onumber__class_Onumber__of(X30,X9))) ),
    c_0_106 ).

fof(c_0_1279,axiom,
    ! [X33,X21,X9,X30] :
      ( ( class_Int_Onumber(X30)
        & class_Rings_Oring(X30) )
     => c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),c_Groups_Ominus__class_Ominus(X30,X21,X33)) = c_Groups_Ominus__class_Ominus(X30,c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),X21),c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),X33)) ),
    c_0_107 ).

fof(c_0_1280,axiom,
    ! [X9,X21,X2,X30] :
      ( ( class_Int_Onumber(X30)
        & class_Rings_Osemiring(X30) )
     => c_Groups_Otimes__class_Otimes(X30,c_Groups_Oplus__class_Oplus(X30,X2,X21),c_Int_Onumber__class_Onumber__of(X30,X9)) = c_Groups_Oplus__class_Oplus(X30,c_Groups_Otimes__class_Otimes(X30,X2,c_Int_Onumber__class_Onumber__of(X30,X9)),c_Groups_Otimes__class_Otimes(X30,X21,c_Int_Onumber__class_Onumber__of(X30,X9))) ),
    c_0_108 ).

fof(c_0_1281,axiom,
    ! [X33,X21,X9,X30] :
      ( ( class_Int_Onumber(X30)
        & class_Rings_Osemiring(X30) )
     => c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),c_Groups_Oplus__class_Oplus(X30,X21,X33)) = c_Groups_Oplus__class_Oplus(X30,c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),X21),c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),X33)) ),
    c_0_109 ).

fof(c_0_1282,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))) ),
    c_0_110 ).

fof(c_0_1283,plain,
    ! [X7,X32,X9] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
       => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32),X7)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
       => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32),X7)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X32)),X7) ) ),
    inference(fof_simplification,[status(thm)],[c_0_111]) ).

fof(c_0_1284,axiom,
    ! [X20,X19,X53] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X19),c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X20))
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X53)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ) ),
    c_0_112 ).

fof(c_0_1285,axiom,
    ! [X14,X15,X46] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X46)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X46),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X14,X46))
      <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14) ) ),
    c_0_113 ).

fof(c_0_1286,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ),
    c_0_114 ).

fof(c_0_1287,axiom,
    ! [X17,X5,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X5),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X5))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ),
    c_0_115 ).

fof(c_0_1288,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ),
    c_0_116 ).

fof(c_0_1289,axiom,
    ! [X14,X15,X46] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X46)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X46,X15),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X46,X14))
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14) ) ),
    c_0_117 ).

fof(c_0_1290,axiom,
    ! [X14,X15,X46] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X46)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X46),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X14,X46))
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14) ) ),
    c_0_118 ).

fof(c_0_1291,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X19),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20))
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X20) ) ),
    c_0_119 ).

fof(c_0_1292,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,X17) ) ),
    c_0_120 ).

fof(c_0_1293,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ),
    c_0_121 ).

fof(c_0_1294,axiom,
    ! [X20,X19,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X19),c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X20))
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ) ),
    c_0_122 ).

fof(c_0_1295,axiom,
    ! [X2,X62,X20,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X62)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oone__class_Oone(X3))
           => c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X62),c_Power_Opower__class_Opower(X3,X2,X20)) ) ) ) ),
    c_0_123 ).

fof(c_0_1296,axiom,
    ! [X2,X62,X20,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X62)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Oone__class_Oone(X3))
           => c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X62),c_Power_Opower__class_Opower(X3,X2,X20)) ) ) ) ),
    c_0_124 ).

fof(c_0_1297,axiom,
    ! [X24,X42,X25,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X25,X42),c_Groups_Otimes__class_Otimes(X3,X24,X42))
      <=> ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X42)
            & c_Orderings_Oord__class_Oless(X3,X25,X24) )
          | ( c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Ozero__class_Ozero(X3))
            & c_Orderings_Oord__class_Oless(X3,X24,X25) ) ) ) ),
    c_0_125 ).

fof(c_0_1298,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
      <=> ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X42)
            & c_Orderings_Oord__class_Oless(X3,X25,X24) )
          | ( c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Ozero__class_Ozero(X3))
            & c_Orderings_Oord__class_Oless(X3,X24,X25) ) ) ) ),
    c_0_126 ).

fof(c_0_1299,axiom,
    ! [X20,X21,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
           => c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X21,X20)) ) ) ) ),
    c_0_127 ).

fof(c_0_1300,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) ),
    c_0_128 ).

fof(c_0_1301,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) ),
    c_0_129 ).

fof(c_0_1302,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
    c_0_130 ).

fof(c_0_1303,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Oring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
    c_0_131 ).

fof(c_0_1304,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Oring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) ),
    c_0_132 ).

fof(c_0_1305,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) ),
    c_0_133 ).

fof(c_0_1306,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) ),
    c_0_134 ).

fof(c_0_1307,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) ),
    c_0_135 ).

fof(c_0_1308,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
    c_0_136 ).

fof(c_0_1309,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Oplus__class_Oplus(X3,X33,X34)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ),
    c_0_137 ).

fof(c_0_1310,axiom,
    ! [X26,X27,X28,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X27),c_Groups_Otimes__class_Otimes(X3,X28,X26)) ),
    c_0_138 ).

fof(c_0_1311,axiom,
    ! [X33,X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Groups_Ominus__class_Ominus(X3,c_Int_Onumber__class_Onumber__of(X3,X8),X33)) = c_Groups_Ominus__class_Ominus(X3,c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)),X33) ),
    c_0_139 ).

fof(c_0_1312,axiom,
    ! [X10,X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X8),X10)) = c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)),X10) ),
    c_0_140 ).

fof(c_0_1313,axiom,
    ! [X10,X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,X8),X10)) = c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)),X10) ),
    c_0_141 ).

fof(c_0_1314,axiom,
    ! [X23,X20,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
       => c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X23) = c_Power_Opower__class_Opower(X3,X23,X20) ) ),
    c_0_142 ).

fof(c_0_1315,axiom,
    ! [X20,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,X23,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20)) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X23,X20)) ),
    c_0_143 ).

fof(c_0_1316,axiom,
    ! [X34,X33,X21,X2,X54,X3] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
     => ( X54 != c_Groups_Ozero__class_Ozero(X3)
       => ( ( X2 = X21
            & X33 != X34 )
         => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Otimes__class_Otimes(X3,X54,X33)) != c_Groups_Oplus__class_Oplus(X3,X21,c_Groups_Otimes__class_Otimes(X3,X54,X34)) ) ) ),
    c_0_144 ).

fof(c_0_1317,axiom,
    ! [X20,X23,X22,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X22,X23)
       => c_Power_Opower__class_Opower(X3,c_Divides_Odiv__class_Odiv(X3,X23,X22),X20) = c_Divides_Odiv__class_Odiv(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X20)) ) ),
    c_0_145 ).

fof(c_0_1318,axiom,
    ! [X21,X39,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X21)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X39)) ) ) ),
    c_0_146 ).

fof(c_0_1319,axiom,
    ! [X21,X39,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X21)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X39),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21)) ) ) ),
    c_0_147 ).

fof(c_0_1320,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X23)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
           => X23 = X22 ) ) ) ),
    c_0_148 ).

fof(c_0_1321,axiom,
    ! [X33,X21,X2] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X21),X33) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X33)),X33),
    c_0_149 ).

fof(c_0_1322,axiom,
    ! [X33,X21,X2] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X33)),X33) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X21),X33),
    c_0_150 ).

fof(c_0_1323,axiom,
    ! [X19,X22,X23] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X19)),X19) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,X22),X19),
    c_0_151 ).

fof(c_0_1324,axiom,
    ! [X22,X19,X23] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X19),X22),X19) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,X22),X19),
    c_0_152 ).

fof(c_0_1325,axiom,
    ! [X22,X19,X23] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X19),X22),X19) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X22),X19),
    c_0_153 ).

fof(c_0_1326,axiom,
    ! [X19,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7)),X19) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X51),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X19)) ),
    c_0_154 ).

fof(c_0_1327,axiom,
    ! [X19,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),c_Nat_OSuc(X51)) ),
    c_0_155 ).

fof(c_0_1328,axiom,
    ! [X19,X21,X20,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X2,X20),X21)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
         => c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X2,X19),X21) ) ) ),
    c_0_156 ).

fof(c_0_1329,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X17))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
    c_0_157 ).

fof(c_0_1330,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X17))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
    c_0_158 ).

fof(c_0_1331,axiom,
    ! [X20,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin) ),
    c_0_159 ).

fof(c_0_1332,axiom,
    ! [X24,X42,X25,X3] :
      ( class_Rings_Oidom(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X25,X42),c_Groups_Otimes__class_Otimes(X3,X24,X42))
      <=> ( X42 = c_Groups_Ozero__class_Ozero(X3)
          | c_Rings_Odvd__class_Odvd(X3,X25,X24) ) ) ),
    c_0_160 ).

fof(c_0_1333,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Rings_Oidom(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
      <=> ( X42 = c_Groups_Ozero__class_Ozero(X3)
          | c_Rings_Odvd__class_Odvd(X3,X25,X24) ) ) ),
    c_0_161 ).

fof(c_0_1334,axiom,
    ! [X66,X65,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X65)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X5))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X5),X65) ) ),
    c_0_162 ).

fof(c_0_1335,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
       => c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20))) ) ),
    c_0_163 ).

fof(c_0_1336,axiom,
    ! [X24,X42,X25,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X25,X42),c_Groups_Oplus__class_Oplus(X3,X24,X42))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X25,X24) ) ),
    c_0_164 ).

fof(c_0_1337,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X42,X25),c_Groups_Oplus__class_Oplus(X3,X42,X24))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X25,X24) ) ),
    c_0_165 ).

fof(c_0_1338,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X33))
       => c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ),
    c_0_166 ).

fof(c_0_1339,axiom,
    ! [X21,X2,X33,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X33,X2),c_Groups_Oplus__class_Oplus(X3,X33,X21))
       => c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ),
    c_0_167 ).

fof(c_0_1340,axiom,
    ! [X21,X2,X33,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X33,X2),c_Groups_Oplus__class_Oplus(X3,X33,X21))
       => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ),
    c_0_168 ).

fof(c_0_1341,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X33))
       => c_Orderings_Oord__class_Oless(X3,X2,X21) ) ),
    c_0_169 ).

fof(c_0_1342,axiom,
    ! [X24,X25,X42,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X42,X25),c_Groups_Oplus__class_Oplus(X3,X42,X24))
      <=> c_Orderings_Oord__class_Oless(X3,X25,X24) ) ),
    c_0_170 ).

fof(c_0_1343,axiom,
    ! [X24,X42,X25,X3] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X25,X42),c_Groups_Oplus__class_Oplus(X3,X24,X42))
      <=> c_Orderings_Oord__class_Oless(X3,X25,X24) ) ),
    c_0_171 ).

fof(c_0_1344,axiom,
    ! [X35,X54,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X35))
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    c_0_172 ).

fof(c_0_1345,axiom,
    ! [X20,X19,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X19)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20)
       => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X7),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20) ) ),
    c_0_173 ).

fof(c_0_1346,axiom,
    ! [X35,X54,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X35))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X2)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X35) ) ) ),
    c_0_174 ).

fof(c_0_1347,axiom,
    ! [X55,X17,X18] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
       => hBOOL(hAPP(hAPP(X55,X17),X18)) )
     => ( ( X18 = X17
         => hBOOL(hAPP(hAPP(X55,X17),X18)) )
       => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
           => hBOOL(hAPP(hAPP(X55,X17),X18)) )
         => hBOOL(hAPP(hAPP(X55,X17),X18)) ) ) ),
    c_0_175 ).

fof(c_0_1348,axiom,
    ! [X20,X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20)) = c_Power_Opower__class_Opower(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    c_0_176 ).

fof(c_0_1349,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20))
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X19)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
         => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X20) ) ) ),
    c_0_177 ).

fof(c_0_1350,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20))
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X20)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
         => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X19) ) ) ),
    c_0_178 ).

fof(c_0_1351,axiom,
    ! [X24,X25,X17] :
      ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X25,X17),c_Power_Opower__class_Opower(tc_Nat_Onat,X24,X17))
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24) ) ),
    c_0_179 ).

fof(c_0_1352,axiom,
    ! [X21,X20,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X20),c_Power_Opower__class_Opower(tc_Nat_Onat,X21,X20))
     => ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21) ) ),
    c_0_180 ).

fof(c_0_1353,axiom,
    ! [X21,X20,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X20),c_Power_Opower__class_Opower(tc_Int_Oint,X21,X20))
     => ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X21) ) ),
    c_0_181 ).

fof(c_0_1354,axiom,
    ! [X24,X25,X17] :
      ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X25,X17),c_Power_Opower__class_Opower(tc_Int_Oint,X24,X17))
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,X24) ) ),
    c_0_182 ).

fof(c_0_1355,axiom,
    ! [X23,X3] :
      ( class_Rings_Oring__1(X3)
     => c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X23),c_Groups_Oone__class_Oone(X3)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X23,c_Groups_Oone__class_Oone(X3)),c_Groups_Ominus__class_Ominus(X3,X23,c_Groups_Oone__class_Oone(X3))) ),
    c_0_183 ).

fof(c_0_1356,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X19),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X20))
     => ( X7 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X19,X20) ) ),
    c_0_184 ).

fof(c_0_1357,axiom,
    ! [X57,X18,X5] :
      ( X5 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X18,X57)
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X18),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X57)) ) ),
    c_0_185 ).

fof(c_0_1358,axiom,
    ! [X17,X18,X5] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
    <=> ( X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,X17) ) ),
    c_0_186 ).

fof(c_0_1359,axiom,
    ! [X17,X5,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X5),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X5))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ),
    c_0_187 ).

fof(c_0_1360,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ),
    c_0_188 ).

fof(c_0_1361,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X17))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
    c_0_189 ).

fof(c_0_1362,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X17))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
    c_0_190 ).

fof(c_0_1363,axiom,
    ! [X21,X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Power_Opower__class_Opower(X3,X2,X20) = c_Power_Opower__class_Opower(X3,X21,X20)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
           => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
             => X2 = X21 ) ) ) ) ),
    c_0_191 ).

fof(c_0_1364,axiom,
    ! [X20,X21,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X21,X20)) ) ) ),
    c_0_192 ).

fof(c_0_1365,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Oordered__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ) ),
    c_0_193 ).

fof(c_0_1366,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Oordered__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
    c_0_194 ).

fof(c_0_1367,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Oordered__comm__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
    c_0_195 ).

fof(c_0_1368,axiom,
    ! [X33,X2,X21,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X21,X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ) ),
    c_0_196 ).

fof(c_0_1369,axiom,
    ! [X33,X2,X21,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X21,X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
    c_0_197 ).

fof(c_0_1370,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ) ),
    c_0_198 ).

fof(c_0_1371,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
    c_0_199 ).

fof(c_0_1372,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Olinordered__comm__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
    c_0_200 ).

fof(c_0_1373,axiom,
    ! [X33,X2,X21,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X21,X2)
       => ( c_Orderings_Oord__class_Oless(X3,X33,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ) ),
    c_0_201 ).

fof(c_0_1374,axiom,
    ! [X33,X2,X21,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X21,X2)
       => ( c_Orderings_Oord__class_Oless(X3,X33,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
    c_0_202 ).

fof(c_0_1375,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X23)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
         => ( c_Orderings_Oord__class_Oless__eq(X3,X22,c_Groups_Oone__class_Oone(X3))
           => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),X23) ) ) ) ),
    c_0_203 ).

fof(c_0_1376,axiom,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X23)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
         => ( c_Orderings_Oord__class_Oless__eq(X3,X22,c_Groups_Oone__class_Oone(X3))
           => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X22,X23),X23) ) ) ) ),
    c_0_204 ).

fof(c_0_1377,axiom,
    ! [X2,X62,X20,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X62)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
         => c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X2,X62)) ) ) ),
    c_0_205 ).

fof(c_0_1378,axiom,
    ! [X2,X62,X20,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X62)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X2)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X2,X62)) ) ) ),
    c_0_206 ).

fof(c_0_1379,plain,
    ! [X16,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)))
      <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
            & X15 != c_Groups_Ozero__class_Ozero(X3) )
          | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
            & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_207]) ).

fof(c_0_1380,axiom,
    ! [X19,X20,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19),X7)) ),
    c_0_208 ).

fof(c_0_1381,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ) ) ),
    c_0_209 ).

fof(c_0_1382,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,X33,X34)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ) ) ),
    c_0_210 ).

fof(c_0_1383,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ) ) ),
    c_0_211 ).

fof(c_0_1384,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => ( c_Orderings_Oord__class_Oless(X3,X33,X34)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ) ) ),
    c_0_212 ).

fof(c_0_1385,axiom,
    ! [X34,X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
       => ( c_Rings_Odvd__class_Odvd(X3,X33,X34)
         => c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ),
    c_0_213 ).

fof(c_0_1386,axiom,
    ! [X19,X20,X3] :
      ( class_Power_Opower(X3)
     => ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X3,X19,X20) = c_Groups_Oone__class_Oone(X3) )
        & ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X3,X19,X20) = c_Groups_Otimes__class_Otimes(X3,X19,c_Power_Opower__class_Opower(X3,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    c_0_214 ).

fof(c_0_1387,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X21) ) ),
    c_0_215 ).

fof(c_0_1388,axiom,
    ! [X19,X20,X22,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X23,X22)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
         => c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X19)) ) ) ),
    c_0_216 ).

fof(c_0_1389,axiom,
    ! [X14,X15,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X15,X15),c_Groups_Otimes__class_Otimes(X3,X14,X14)) = c_Groups_Ozero__class_Ozero(X3)
      <=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
          & X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    c_0_217 ).

fof(c_0_1390,plain,
    ! [X16,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)),c_Groups_Ozero__class_Ozero(X3))
      <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
              & c_Orderings_Oord__class_Oless__eq(X3,X15,c_Groups_Ozero__class_Ozero(X3)) )
            | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
              & X15 = c_Groups_Ozero__class_Ozero(X3) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_218]) ).

fof(c_0_1391,plain,
    ! [X16,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)))
      <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
          | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
            & c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_219]) ).

fof(c_0_1392,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) = c_Groups_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X3,X2,X21),X33) ),
    c_0_220 ).

fof(c_0_1393,axiom,
    ! [X21,X2,X33,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) = c_Groups_Otimes__class_Otimes(X3,X33,c_Divides_Odiv__class_Omod(X3,X2,X21)) ),
    c_0_221 ).

fof(c_0_1394,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Otimes__class_Otimes(X3,X33,X21)),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
    c_0_222 ).

fof(c_0_1395,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X33)),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
    c_0_223 ).

fof(c_0_1396,axiom,
    ! [X44,X22,X23,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X22),X44) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X44),c_Groups_Otimes__class_Otimes(X3,X22,X44)) ),
    c_0_224 ).

fof(c_0_1397,axiom,
    ! [X21,X43,X2,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X2,X43),X21) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Otimes__class_Otimes(X3,X43,X21)) ),
    c_0_225 ).

fof(c_0_1398,axiom,
    ! [X22,X23,X40,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,X40,c_Groups_Ominus__class_Ominus(X3,X23,X22)) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X40,X23),c_Groups_Otimes__class_Otimes(X3,X40,X22)) ),
    c_0_226 ).

fof(c_0_1399,axiom,
    ! [X39,X21,X2,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ominus__class_Ominus(X3,X21,X39)) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Otimes__class_Otimes(X3,X2,X39)) ),
    c_0_227 ).

fof(c_0_1400,axiom,
    ! [X20,X21,X2,X3] :
      ( class_Groups_Ocomm__monoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X20) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X21,X20)) ),
    c_0_228 ).

fof(c_0_1401,axiom,
    ! [X21,X19,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X19),c_Groups_Otimes__class_Otimes(X3,X21,X19)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X19) ),
    c_0_229 ).

fof(c_0_1402,axiom,
    ! [X44,X22,X23,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X23,X22),X44) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X44),c_Groups_Otimes__class_Otimes(X3,X22,X44)) ),
    c_0_230 ).

fof(c_0_1403,axiom,
    ! [X21,X43,X2,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X43),X21) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Otimes__class_Otimes(X3,X43,X21)) ),
    c_0_231 ).

fof(c_0_1404,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ),
    c_0_232 ).

fof(c_0_1405,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ),
    c_0_233 ).

fof(c_0_1406,axiom,
    ! [X22,X23,X40,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,X40,c_Groups_Oplus__class_Oplus(X3,X23,X22)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X40,X23),c_Groups_Otimes__class_Otimes(X3,X40,X22)) ),
    c_0_234 ).

fof(c_0_1407,axiom,
    ! [X10,X22,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X23,c_Groups_Oplus__class_Oplus(X3,X22,X10)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),c_Groups_Otimes__class_Otimes(X3,X23,X10)) ),
    c_0_235 ).

fof(c_0_1408,axiom,
    ! [X39,X21,X2,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Oplus__class_Oplus(X3,X21,X39)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Otimes__class_Otimes(X3,X2,X39)) ),
    c_0_236 ).

fof(c_0_1409,axiom,
    ! [X35,X22,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),X35) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X35),c_Power_Opower__class_Opower(X3,X22,X35)) ),
    c_0_237 ).

fof(c_0_1410,axiom,
    ! [X20,X19,X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X2,X19),c_Power_Opower__class_Opower(X3,X2,X20)) ),
    c_0_238 ).

fof(c_0_1411,axiom,
    ! [X35,X38,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X38),c_Power_Opower__class_Opower(X3,X23,X35)) = c_Power_Opower__class_Opower(X3,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X35)) ),
    c_0_239 ).

fof(c_0_1412,axiom,
    ! [X21,X43,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X43)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X43,X21)) ) ),
    c_0_240 ).

fof(c_0_1413,axiom,
    ! [X21,X43,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X43)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X43,X21),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21)) ) ),
    c_0_241 ).

fof(c_0_1414,axiom,
    ! [X22,X23,X10] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X10)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,X22)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X10,X23),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X10,X22)) ) ),
    c_0_242 ).

fof(c_0_1415,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X53),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X51)) ) ),
    c_0_243 ).

fof(c_0_1416,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X7)) ) ),
    c_0_244 ).

fof(c_0_1417,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X53,X51)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X53),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X51)) ) ),
    c_0_245 ).

fof(c_0_1418,axiom,
    ! [X38,X19] :
      ( ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Power_Opower__class_Opower(tc_Nat_Onat,X38,X19) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Power_Opower__class_Opower(tc_Nat_Onat,X38,X19) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X38,c_Power_Opower__class_Opower(tc_Nat_Onat,X38,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
    c_0_246 ).

fof(c_0_1419,axiom,
    ! [X20,X19] :
      ( ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20)) ) ),
    c_0_247 ).

fof(c_0_1420,axiom,
    ! [X5,X17,X55] :
      ( hBOOL(hAPP(X55,c_Divides_Odiv__class_Omod(tc_Int_Oint,X17,X5)))
    <=> ( ( X5 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X55,X17)) )
        & epred1_3(X55,X17,X5) ) ),
    inference(apply_def,[status(thm)],[c_0_248,c_0_1170,theory(equality,[symmetry])]) ).

fof(c_0_1421,axiom,
    ! [X10,X70,X8,X71] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X71,X8)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X70,X10)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X71,X70),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X10)) ) ),
    c_0_249 ).

fof(c_0_1422,axiom,
    ! [X6,X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X6)) ) ),
    c_0_250 ).

fof(c_0_1423,axiom,
    ! [X6,X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X6)) ) ),
    c_0_251 ).

fof(c_0_1424,axiom,
    ! [X6,X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X6)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X19)) ) ),
    c_0_252 ).

fof(c_0_1425,axiom,
    ! [X33,X21,X2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X21)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X2)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X33),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X33)) ) ),
    c_0_253 ).

fof(c_0_1426,axiom,
    ! [X6,X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X6)) ) ),
    c_0_254 ).

fof(c_0_1427,axiom,
    ! [X25,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      <=> X25 != c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_255 ).

fof(c_0_1428,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21))
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21) ) ) ),
    c_0_256 ).

fof(c_0_1429,axiom,
    ! [X2,X21,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X21,X2))
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21) ) ) ),
    c_0_257 ).

fof(c_0_1430,plain,
    ! [X15] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
    <=> ? [X31] : X15 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X31),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(fof_simplification,[status(thm)],[c_0_258]) ).

fof(c_0_1431,axiom,
    ! [X24,X25] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X25,X24))
      <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,X25)
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24) ) ) ),
    c_0_259 ).

fof(c_0_1432,plain,
    ! [X2,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ~ c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_260]) ).

fof(c_0_1433,axiom,
    ! [X8,X9] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X9)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X8))) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))),
    c_0_261 ).

fof(c_0_1434,axiom,
    ! [X14,X15] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X15),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X14,X14)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> ( X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        & X14 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    c_0_262 ).

fof(c_0_1435,axiom,
    ! [X19,X20,X7] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20),X19),X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),
    c_0_263 ).

fof(c_0_1436,axiom,
    ! [X7,X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),X7) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X7)),
    c_0_264 ).

fof(c_0_1437,axiom,
    ! [X20,X19,X7] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X19),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20)),
    c_0_265 ).

fof(c_0_1438,axiom,
    ! [X8,X12,X13] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X12),X8) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X13,X8),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X12,X8)),
    c_0_266 ).

fof(c_0_1439,axiom,
    ! [X7,X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X7) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X7)),
    c_0_267 ).

fof(c_0_1440,axiom,
    ! [X20,X19,X7] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X19),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20)),
    c_0_268 ).

fof(c_0_1441,axiom,
    ! [X12,X13,X8] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X13,X12)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X13),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X12)),
    c_0_269 ).

fof(c_0_1442,axiom,
    ! [X8,X12,X13] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X13,X12),X8) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,X8),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12,X8)),
    c_0_270 ).

fof(c_0_1443,axiom,
    ! [X8,X12,X13] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,X12),X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,X8),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12,X8)),
    c_0_271 ).

fof(c_0_1444,axiom,
    ! [X12,X13,X8] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,X12)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X13),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X12)),
    c_0_272 ).

fof(c_0_1445,axiom,
    ! [X7,X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X7)),
    c_0_273 ).

fof(c_0_1446,axiom,
    ! [X20,X19,X7] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X19),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20)),
    c_0_274 ).

fof(c_0_1447,axiom,
    ! [X10,X22,X23] : c_Power_Opower__class_Opower(tc_Int_Oint,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X10)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X22),c_Power_Opower__class_Opower(tc_Int_Oint,X23,X10)),
    c_0_275 ).

fof(c_0_1448,axiom,
    ! [X5,X65,X66] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X66,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X5))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X5),X65) ),
    c_0_276 ).

fof(c_0_1449,axiom,
    ! [X66,X5,X65] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X5),X66)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X5)) ),
    c_0_277 ).

fof(c_0_1450,plain,
    ! [X16,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)),c_Groups_Ozero__class_Ozero(X3))
      <=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
          & c_Orderings_Oord__class_Oless(X3,X15,c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_278]) ).

fof(c_0_1451,axiom,
    ! [X20,X19,X7,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X7,c_Divides_Odiv__class_Omod(X3,X19,X20))
       => ( c_Rings_Odvd__class_Odvd(X3,X7,X20)
         => c_Rings_Odvd__class_Odvd(X3,X7,X19) ) ) ),
    c_0_279 ).

fof(c_0_1452,axiom,
    ! [X18,X17,X5,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X5,X17)
       => ( c_Rings_Odvd__class_Odvd(X3,X5,c_Divides_Odiv__class_Omod(X3,X18,X17))
        <=> c_Rings_Odvd__class_Odvd(X3,X5,X18) ) ) ),
    c_0_280 ).

fof(c_0_1453,axiom,
    ! [X21,X2,X33] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
     => c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X33)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),X33) ),
    c_0_281 ).

fof(c_0_1454,axiom,
    ! [X53,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),X51) ),
    c_0_282 ).

fof(c_0_1455,axiom,
    ! [X53,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X7) ),
    c_0_283 ).

fof(c_0_1456,axiom,
    ! [X53,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7)) ),
    c_0_284 ).

fof(c_0_1457,axiom,
    ! [X53,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7),X53) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X53),X7) ),
    c_0_285 ).

fof(c_0_1458,axiom,
    ! [X53,X51,X7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X53),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7),X53) ),
    c_0_286 ).

fof(c_0_1459,axiom,
    ! [X25,X24] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X25,X24))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25) ) ),
    c_0_287 ).

fof(c_0_1460,axiom,
    ! [X25,X24] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X25,X24))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    c_0_288 ).

fof(c_0_1461,axiom,
    ! [X16,X15] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)))
    <=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) ) ),
    c_0_289 ).

fof(c_0_1462,axiom,
    ! [X66,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X66,X5))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X66) ) ),
    c_0_290 ).

fof(c_0_1463,axiom,
    ! [X24,X25,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X25,X24))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X25)
            & c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X24) )
          | ( c_Orderings_Oord__class_Oless__eq(X3,X25,c_Groups_Ozero__class_Ozero(X3))
            & c_Orderings_Oord__class_Oless__eq(X3,X24,c_Groups_Ozero__class_Ozero(X3)) ) ) ) ),
    c_0_291 ).

fof(c_0_1464,axiom,
    ! [X24,X25,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X25,X24),c_Groups_Ozero__class_Ozero(X3))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X25)
            & c_Orderings_Oord__class_Oless__eq(X3,X24,c_Groups_Ozero__class_Ozero(X3)) )
          | ( c_Orderings_Oord__class_Oless__eq(X3,X25,c_Groups_Ozero__class_Ozero(X3))
            & c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X24) ) ) ) ),
    c_0_292 ).

fof(c_0_1465,axiom,
    ! [X21,X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)) = c_Power_Opower__class_Opower(X3,X21,c_Nat_OSuc(X20))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
         => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
           => X2 = X21 ) ) ) ),
    c_0_293 ).

fof(c_0_1466,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X20)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) ),
    c_0_294 ).

fof(c_0_1467,axiom,
    ! [X20,X19] :
      ( ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20) = X20 )
      & ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20)) ) ),
    c_0_295 ).

fof(c_0_1468,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X20))
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X20)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X19) ) ),
    c_0_296 ).

fof(c_0_1469,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X19,X20))
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X20)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X19) ) ),
    c_0_297 ).

fof(c_0_1470,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oone__class_Oone(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)),c_Groups_Oone__class_Oone(X3)) ) ) ),
    c_0_298 ).

fof(c_0_1471,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17))
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18)
        & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17) ) ),
    c_0_299 ).

fof(c_0_1472,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)) ) ),
    c_0_300 ).

fof(c_0_1473,plain,
    ! [X22,X23,X20,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X23,X22)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X20)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_301]) ).

fof(c_0_1474,axiom,
    ! [X20,X54,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X54)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X54,c_Groups_Oone__class_Oone(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X54,c_Nat_OSuc(X20)),X54) ) ) ),
    c_0_302 ).

fof(c_0_1475,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    c_0_303 ).

fof(c_0_1476,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    c_0_304 ).

fof(c_0_1477,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X2,X21)) ) ) ),
    c_0_305 ).

fof(c_0_1478,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X2,X21)) ) ) ),
    c_0_306 ).

fof(c_0_1479,axiom,
    ! [X20,X19,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X19)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X20)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Otimes__class_Otimes(X3,X19,X20)) ) ) ),
    c_0_307 ).

fof(c_0_1480,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    c_0_308 ).

fof(c_0_1481,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X2,X21)) ) ) ),
    c_0_309 ).

fof(c_0_1482,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__cancel__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ) ),
    c_0_310 ).

fof(c_0_1483,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__cancel__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    c_0_311 ).

fof(c_0_1484,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__cancel__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X21,X2),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    c_0_312 ).

fof(c_0_1485,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__cancel__semiring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    c_0_313 ).

fof(c_0_1486,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ) ),
    c_0_314 ).

fof(c_0_1487,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__ring(X3)
     => ( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
            & c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21) )
          | ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
            & c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3)) ) )
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ),
    c_0_315 ).

fof(c_0_1488,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Oordered__cancel__semiring(X3)
     => ( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
            & c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3)) )
          | ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
            & c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21) ) )
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ),
    c_0_316 ).

fof(c_0_1489,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X2,X21)) ) ) ),
    c_0_317 ).

fof(c_0_1490,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    c_0_318 ).

fof(c_0_1491,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ) ),
    c_0_319 ).

fof(c_0_1492,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    c_0_320 ).

fof(c_0_1493,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X21,X2),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    c_0_321 ).

fof(c_0_1494,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Olinordered__semiring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    c_0_322 ).

fof(c_0_1495,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Olinordered__ring__strict(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
       => ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ) ),
    c_0_323 ).

fof(c_0_1496,axiom,
    ! [X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X19))),
    c_0_324 ).

fof(c_0_1497,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) ) ),
    c_0_325 ).

fof(c_0_1498,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19)) ) ),
    c_0_326 ).

fof(c_0_1499,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)) ) ),
    c_0_327 ).

fof(c_0_1500,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X33)) ) ),
    c_0_328 ).

fof(c_0_1501,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X33,X2),c_Groups_Oplus__class_Oplus(X3,X33,X21)) ) ),
    c_0_329 ).

fof(c_0_1502,axiom,
    ! [X20,X22,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X23,X22)
       => c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X20)) ) ),
    c_0_330 ).

fof(c_0_1503,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X33,X2),c_Groups_Oplus__class_Oplus(X3,X33,X21)) ) ),
    c_0_331 ).

fof(c_0_1504,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X2,X21)
       => c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X33)) ) ),
    c_0_332 ).

fof(c_0_1505,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
       => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
         => c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X3,X2,X20)) ) ) ),
    c_0_333 ).

fof(c_0_1506,axiom,
    ! [X2,X20,X19,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
       => c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X2,X19),c_Power_Opower__class_Opower(X3,X2,X20)) ) ),
    c_0_334 ).

fof(c_0_1507,plain,
    ! [X10,X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X22) )
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X23) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_335]) ).

fof(c_0_1508,axiom,
    ! [X14,X17,X15] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,X17) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X17)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X15,X14)) ),
    c_0_336 ).

fof(c_0_1509,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X21,X33)
         => c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
    c_0_337 ).

fof(c_0_1510,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,X33)
         => c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
    c_0_338 ).

fof(c_0_1511,axiom,
    ! [X2,X21,X33,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,X2)
         => c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
    c_0_339 ).

fof(c_0_1512,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X21,X33)
         => c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
    c_0_340 ).

fof(c_0_1513,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => ( c_Orderings_Oord__class_Oless(X3,X21,X33)
         => c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
    c_0_341 ).

fof(c_0_1514,plain,
    ! [X16,X61,X3] :
      ( ( class_Int_Onumber(X3)
        & class_Orderings_Olinorder(X3) )
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X61),c_Int_Onumber__class_Onumber__of(X3,X16))
      <=> ~ c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X16),c_Int_Onumber__class_Onumber__of(X3,X61)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_342]) ).

fof(c_0_1515,plain,
    ! [X17,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,X17))
      <=> ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
            & X15 != c_Groups_Ozero__class_Ozero(X3) )
          | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
            & c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_343]) ).

fof(c_0_1516,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
       => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X19,X20)
         => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X20,X19)
           => X19 = X20 ) ) ) ),
    c_0_344 ).

fof(c_0_1517,plain,
    ! [X17,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X15,X17),c_Groups_Ozero__class_Ozero(X3))
      <=> ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
              & c_Orderings_Oord__class_Oless__eq(X3,X15,c_Groups_Ozero__class_Ozero(X3)) )
            | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
              & X15 = c_Groups_Ozero__class_Ozero(X3) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_345]) ).

fof(c_0_1518,plain,
    ! [X17,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,X17))
      <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
          | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
            & c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_346]) ).

fof(c_0_1519,axiom,
    ! [X17,X25,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X25,X17))
      <=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X25)
          | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ) ),
    c_0_347 ).

fof(c_0_1520,plain,
    ! [X15,X17,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,X17))
        <=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_348]) ).

fof(c_0_1521,axiom,
    ! [X6,X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X6),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X6)) ),
    c_0_349 ).

fof(c_0_1522,axiom,
    ! [X6,X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X19)) ),
    c_0_350 ).

fof(c_0_1523,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,X51)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X53),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X51)) ),
    c_0_351 ).

fof(c_0_1524,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X53),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X51)) ),
    c_0_352 ).

fof(c_0_1525,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X7)) ),
    c_0_353 ).

fof(c_0_1526,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X7)) ),
    c_0_354 ).

fof(c_0_1527,axiom,
    ! [X10,X22,X23] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X23),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X22)) ),
    c_0_355 ).

fof(c_0_1528,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X7)) ),
    c_0_356 ).

fof(c_0_1529,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X53,X51)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X53,X7),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X51,X7)) ),
    c_0_357 ).

fof(c_0_1530,axiom,
    ! [X19,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X19),X19) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oone__class_Oone(X3)),X19) ),
    c_0_358 ).

fof(c_0_1531,axiom,
    ! [X2,X19,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X19,c_Groups_Otimes__class_Otimes(X3,X2,X19)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oone__class_Oone(X3)),X19) ),
    c_0_359 ).

fof(c_0_1532,axiom,
    ! [X20,X19,X7,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X7,X19)
       => ( c_Rings_Odvd__class_Odvd(X3,X7,X20)
         => c_Rings_Odvd__class_Odvd(X3,X7,c_Divides_Odiv__class_Omod(X3,X19,X20)) ) ) ),
    c_0_360 ).

fof(c_0_1533,axiom,
    ! [X10,X22,X23,X3] :
      ( class_Rings_Ocomm__ring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X23,X22)
       => ( c_Rings_Odvd__class_Odvd(X3,X23,X10)
         => c_Rings_Odvd__class_Odvd(X3,X23,c_Groups_Ominus__class_Ominus(X3,X22,X10)) ) ) ),
    c_0_361 ).

fof(c_0_1534,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
       => ( c_Rings_Odvd__class_Odvd(X3,X2,X33)
         => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Oplus__class_Oplus(X3,X21,X33)) ) ) ),
    c_0_362 ).

fof(c_0_1535,plain,
    ! [X17] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
    <=> ? [X1] : X17 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) ),
    inference(fof_simplification,[status(thm)],[c_0_363]) ).

fof(c_0_1536,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X18),X18)
      <=> X17 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    c_0_364 ).

fof(c_0_1537,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17),X18)
      <=> X17 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    c_0_365 ).

fof(c_0_1538,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    c_0_366 ).

fof(c_0_1539,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    c_0_367 ).

fof(c_0_1540,axiom,
    ! [X22,X23] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X22)) ) ),
    c_0_368 ).

fof(c_0_1541,axiom,
    ! [X22,X23] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ) ),
    c_0_369 ).

fof(c_0_1542,axiom,
    ! [X22,X23] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
    c_0_370 ).

fof(c_0_1543,axiom,
    ! [X22,X23] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X23)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X22)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X23,X22)) ) ),
    c_0_371 ).

fof(c_0_1544,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) ) ),
    c_0_372 ).

fof(c_0_1545,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X18)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X17)
       => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X5) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X5)
        <=> X18 = X17 ) ) ),
    c_0_373 ).

fof(c_0_1546,axiom,
    ! [X7,X23] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X7)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X23,X7),X23) ) ),
    c_0_374 ).

fof(c_0_1547,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X19) ) ),
    c_0_375 ).

fof(c_0_1548,axiom,
    ! [X25,X3] :
      ( class_Groups_Olinordered__ab__group__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X25,X25),c_Groups_Ozero__class_Ozero(X3))
      <=> c_Orderings_Oord__class_Oless__eq(X3,X25,c_Groups_Ozero__class_Ozero(X3)) ) ),
    c_0_376 ).

fof(c_0_1549,axiom,
    ! [X25,X3] :
      ( class_Groups_Olinordered__ab__group__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X25,X25))
      <=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X25) ) ),
    c_0_377 ).

fof(c_0_1550,axiom,
    ! [X25,X3] :
      ( class_Groups_Olinordered__ab__group__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X25,X25),c_Groups_Ozero__class_Ozero(X3))
      <=> c_Orderings_Oord__class_Oless(X3,X25,c_Groups_Ozero__class_Ozero(X3)) ) ),
    c_0_378 ).

fof(c_0_1551,axiom,
    ! [X25,X3] :
      ( class_Groups_Olinordered__ab__group__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X25,X25))
      <=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X25) ) ),
    c_0_379 ).

fof(c_0_1552,plain,
    ! [X17,X15,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X15,X17),c_Groups_Ozero__class_Ozero(X3))
      <=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
          & c_Orderings_Oord__class_Oless(X3,X15,c_Groups_Ozero__class_Ozero(X3)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_380]) ).

fof(c_0_1553,axiom,
    ! [X25,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X25,X25),c_Groups_Ozero__class_Ozero(X3))
      <=> c_Orderings_Oord__class_Oless(X3,X25,c_Groups_Ozero__class_Ozero(X3)) ) ),
    c_0_381 ).

fof(c_0_1554,axiom,
    ! [X7,X20,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),X20),c_Nat_OSuc(X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X7),
    c_0_382 ).

fof(c_0_1555,axiom,
    ! [X20,X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X2,X20),X2) = c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20)) ),
    c_0_383 ).

fof(c_0_1556,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oab__semigroup__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X21,X33)) ),
    c_0_384 ).

fof(c_0_1557,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Oab__semigroup__mult(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X33)) ),
    c_0_385 ).

fof(c_0_1558,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),X21) ),
    c_0_386 ).

fof(c_0_1559,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X21,X33)) ),
    c_0_387 ).

fof(c_0_1560,axiom,
    ! [X34,X33,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X33,X34)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),X34) ),
    c_0_388 ).

fof(c_0_1561,axiom,
    ! [X34,X33,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X33,X34)) = c_Groups_Oplus__class_Oplus(X3,X33,c_Groups_Oplus__class_Oplus(X3,X2,X34)) ),
    c_0_389 ).

fof(c_0_1562,axiom,
    ! [X26,X27,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X29,c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,X27,c_Groups_Otimes__class_Otimes(X3,X29,X26)) ),
    c_0_390 ).

fof(c_0_1563,axiom,
    ! [X26,X27,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X29,c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X27),X26) ),
    c_0_391 ).

fof(c_0_1564,axiom,
    ! [X27,X28,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),X27) = c_Groups_Otimes__class_Otimes(X3,X29,c_Groups_Otimes__class_Otimes(X3,X28,X27)) ),
    c_0_392 ).

fof(c_0_1565,axiom,
    ! [X27,X28,X29,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),X27) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X27),X28) ),
    c_0_393 ).

fof(c_0_1566,axiom,
    ! [X20,X19,X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)) = c_Power_Opower__class_Opower(X3,c_Power_Opower__class_Opower(X3,X2,X19),X20) ),
    c_0_394 ).

fof(c_0_1567,axiom,
    ! [X35,X38,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,c_Power_Opower__class_Opower(X3,X23,X38),X35) = c_Power_Opower__class_Opower(X3,X23,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X38,X35)) ),
    c_0_395 ).

fof(c_0_1568,axiom,
    ! [X24,X25,X3] :
      ( class_Groups_Oordered__ab__group__add(X3)
     => ( c_Orderings_Oord__class_Oless(X3,X25,X24)
      <=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),c_Groups_Ozero__class_Ozero(X3)) ) ),
    c_0_396 ).

fof(c_0_1569,axiom,
    ! [X24,X25,X3] :
      ( class_Groups_Oordered__ab__group__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,X25,X24)
      <=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),c_Groups_Ozero__class_Ozero(X3)) ) ),
    c_0_397 ).

fof(c_0_1570,axiom,
    ! [X20,X19] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)),X20),
    c_0_398 ).

fof(c_0_1571,axiom,
    ! [X6,X7] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X7),X6) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X6)),X6),
    c_0_399 ).

fof(c_0_1572,axiom,
    ! [X20,X19,X75] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X75,X19)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X75,X20)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,X75,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X20)) ) ),
    c_0_400 ).

fof(c_0_1573,axiom,
    ! [X20,X19,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X19)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X20)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) ) ),
    c_0_401 ).

fof(c_0_1574,axiom,
    ! [X15] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    c_0_402 ).

fof(c_0_1575,axiom,
    ! [X41,X42,X24,X25,X3] :
      ( class_Groups_Oordered__ab__group__add(X3)
     => ( c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ominus__class_Ominus(X3,X42,X41)
       => ( c_Orderings_Oord__class_Oless(X3,X25,X24)
        <=> c_Orderings_Oord__class_Oless(X3,X42,X41) ) ) ),
    c_0_403 ).

fof(c_0_1576,axiom,
    ! [X41,X42,X24,X25,X3] :
      ( class_Groups_Oordered__ab__group__add(X3)
     => ( c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ominus__class_Ominus(X3,X42,X41)
       => ( c_Orderings_Oord__class_Oless__eq(X3,X25,X24)
        <=> c_Orderings_Oord__class_Oless__eq(X3,X42,X41) ) ) ),
    c_0_404 ).

fof(c_0_1577,plain,
    ! [X32,X9] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
       => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,c_Int_OPls)
           => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X32)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_405]) ).

fof(c_0_1578,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33)
       => c_Rings_Odvd__class_Odvd(X3,X21,X33) ) ),
    c_0_406 ).

fof(c_0_1579,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33)
       => c_Rings_Odvd__class_Odvd(X3,X2,X33) ) ),
    c_0_407 ).

fof(c_0_1580,axiom,
    ! [X7,X51,X53] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X51),X7) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X7),X51),
    c_0_408 ).

fof(c_0_1581,axiom,
    ! [X11,X12,X13] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X13,X12),X11) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X13,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X12,X11)),
    c_0_409 ).

fof(c_0_1582,axiom,
    ! [X20,X7,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),
    c_0_410 ).

fof(c_0_1583,axiom,
    ! [X20,X19,X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X19),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),
    c_0_411 ).

fof(c_0_1584,axiom,
    ! [X7,X51,X53] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X51),X7) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X7)),
    c_0_412 ).

fof(c_0_1585,axiom,
    ! [X11,X12,X13] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,X12),X11) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,X11)),
    c_0_413 ).

fof(c_0_1586,axiom,
    ! [X10,X22,X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X10)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X10)),
    c_0_414 ).

fof(c_0_1587,axiom,
    ! [X10,X22,X23] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X22),X10) = c_Power_Opower__class_Opower(tc_Int_Oint,X23,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X10)),
    c_0_415 ).

fof(c_0_1588,axiom,
    ! [X7,X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X7)),
    c_0_416 ).

fof(c_0_1589,axiom,
    ! [X10,X22,X23] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X10)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X10)),
    c_0_417 ).

fof(c_0_1590,axiom,
    ! [X7,X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20),X7) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X7)),
    c_0_418 ).

fof(c_0_1591,axiom,
    ! [X11,X12,X13] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,X12),X11) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12,X11)),
    c_0_419 ).

fof(c_0_1592,axiom,
    ! [X46,X16] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X46,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X46)
        | X16 = X46 ) ),
    c_0_420 ).

fof(c_0_1593,axiom,
    ! [X17,X15] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X17))
    <=> ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) ) ),
    c_0_421 ).

fof(c_0_1594,axiom,
    ! [X17,X15] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X17))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
        | X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    c_0_422 ).

fof(c_0_1595,axiom,
    ! [X46,X16] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X46,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,X46) ),
    c_0_423 ).

fof(c_0_1596,axiom,
    ! [X46,X16] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Groups_Oone__class_Oone(tc_Int_Oint)),X46)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X46) ),
    c_0_424 ).

fof(c_0_1597,axiom,
    ! [X46,X16] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X46,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X46) ),
    c_0_425 ).

fof(c_0_1598,axiom,
    ! [X2,X21,X33,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X33,X21)
       => c_Divides_Odiv__class_Omod(X3,c_Divides_Odiv__class_Omod(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,X2,X33) ) ),
    c_0_426 ).

fof(c_0_1599,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_427 ).

fof(c_0_1600,axiom,
    ! [X18,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X18))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
    c_0_428 ).

fof(c_0_1601,axiom,
    ! [X14,X15] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X15,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    c_0_429 ).

fof(c_0_1602,plain,
    ! [X10,X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X23) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_430]) ).

fof(c_0_1603,plain,
    ! [X10,X22,X23] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
     => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X22) )
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X23) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_431]) ).

fof(c_0_1604,axiom,
    ! [X20,X19,X6,X7] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X20)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ) ),
    c_0_432 ).

fof(c_0_1605,plain,
    ! [X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
     => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
      <=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(fof_simplification,[status(thm)],[c_0_433]) ).

fof(c_0_1606,plain,
    ! [X20,X7,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),X20)
     => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
         => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20) ) ),
    inference(fof_simplification,[status(thm)],[c_0_434]) ).

fof(c_0_1607,axiom,
    ! [X20,X7,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
    c_0_435 ).

fof(c_0_1608,axiom,
    ! [X20,X7,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20) ),
    c_0_436 ).

fof(c_0_1609,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X7)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X7) ),
    c_0_437 ).

fof(c_0_1610,axiom,
    ! [X17,X5] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X5))
    <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5,X17) ),
    c_0_438 ).

fof(c_0_1611,axiom,
    ! [X9] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9))
     => c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    c_0_439 ).

fof(c_0_1612,axiom,
    ! [X14,X15,X3] :
      ( class_Groups_Oordered__comm__monoid__add(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15)
       => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X14)
         => ( c_Groups_Oplus__class_Oplus(X3,X15,X14) = c_Groups_Ozero__class_Ozero(X3)
          <=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
              & X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ) ) ),
    c_0_440 ).

fof(c_0_1613,axiom,
    ! [X14,X15,X3] :
      ( ( class_Divides_Osemiring__div(X3)
        & class_Int_Onumber(X3) )
     => ( c_Rings_Odvd__class_Odvd(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Divides_Odiv__class_Omod(X3,c_Int_Onumber__class_Onumber__of(X3,X14),c_Int_Onumber__class_Onumber__of(X3,X15)) = c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_441 ).

fof(c_0_1614,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) ),
    c_0_442 ).

fof(c_0_1615,axiom,
    ! [X60,X61] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X60))
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X61,X60)
         => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X60) )
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,X61,X60) ) ),
    c_0_443 ).

fof(c_0_1616,plain,
    ! [X15] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
    <=> ? [X31] : X15 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31)) ),
    inference(fof_simplification,[status(thm)],[c_0_444]) ).

fof(c_0_1617,axiom,
    ! [X20,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20)) = c_Groups_Oone__class_Oone(X3) ),
    c_0_445 ).

fof(c_0_1618,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
       => c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20))) ) ),
    c_0_446 ).

fof(c_0_1619,axiom,
    ! [X8,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(X8)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X3,X8)),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
    c_0_447 ).

fof(c_0_1620,axiom,
    ! [X8,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(X8)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X3,X8)),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
    c_0_448 ).

fof(c_0_1621,axiom,
    ! [X17,X18,X25,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X25)
       => ( c_Power_Opower__class_Opower(X3,X25,X18) = c_Power_Opower__class_Opower(X3,X25,X17)
        <=> X18 = X17 ) ) ),
    c_0_449 ).

fof(c_0_1622,axiom,
    ! [X20,X19] :
      ( ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)) = X20
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)) != X20
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)) ) ),
    c_0_450 ).

fof(c_0_1623,plain,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ) ),
    inference(fof_simplification,[status(thm)],[c_0_451]) ).

fof(c_0_1624,plain,
    ! [X21,X2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2) )
     => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21) ) ),
    inference(fof_simplification,[status(thm)],[c_0_452]) ).

fof(c_0_1625,plain,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ) ),
    inference(fof_simplification,[status(thm)],[c_0_453]) ).

fof(c_0_1626,plain,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ) ),
    inference(fof_simplification,[status(thm)],[c_0_454]) ).

fof(c_0_1627,axiom,
    ! [X20,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X53)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X20)) ),
    c_0_455 ).

fof(c_0_1628,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,X20)) ) ),
    c_0_456 ).

fof(c_0_1629,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X2)
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X3,X2,X20)) ) ),
    c_0_457 ).

fof(c_0_1630,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,X20)) ) ),
    c_0_458 ).

fof(c_0_1631,plain,
    ! [X2,X3] :
      ( class_Rings_Olinordered__ring(X3)
     => ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X2),c_Groups_Ozero__class_Ozero(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_459]) ).

fof(c_0_1632,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X2,X2),X2) ),
    c_0_460 ).

fof(c_0_1633,plain,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,X14))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14)
        | ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
          & c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) )
        | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
          & ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_461]) ).

fof(c_0_1634,axiom,
    ! [X2,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    c_0_462 ).

fof(c_0_1635,axiom,
    ! [X19,X53] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X19))),
    c_0_463 ).

fof(c_0_1636,axiom,
    ! [X19,X53] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X53))),
    c_0_464 ).

fof(c_0_1637,plain,
    ! [X32,X9] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
       => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
       => c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X32)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_465]) ).

fof(c_0_1638,plain,
    ! [X20,X19] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = X19 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) ) ),
    inference(fof_simplification,[status(thm)],[c_0_466]) ).

fof(c_0_1639,plain,
    ! [X20,X19] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) ),
    inference(fof_simplification,[status(thm)],[c_0_467]) ).

fof(c_0_1640,plain,
    ! [X60,X61] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X60))
    <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,X60)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,c_Int_OPls) ) ),
    inference(fof_simplification,[status(thm)],[c_0_468]) ).

fof(c_0_1641,axiom,
    ! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10),X10) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_469 ).

fof(c_0_1642,axiom,
    ! [X14,X15] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X14))
    <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X14),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_470 ).

fof(c_0_1643,axiom,
    ! [X53,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Nat_OSuc(X53)),X20) ),
    c_0_471 ).

fof(c_0_1644,plain,
    ! [X15] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X15))
    <=> X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(fof_simplification,[status(thm)],[c_0_472]) ).

fof(c_0_1645,axiom,
    ! [X23,X20,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
          | X23 = c_Groups_Oone__class_Oone(X3) )
       => c_Rings_Odvd__class_Odvd(X3,X23,c_Power_Opower__class_Opower(X3,X23,X20)) ) ),
    c_0_473 ).

fof(c_0_1646,axiom,
    ! [X17,X18,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
     => ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17)
      <=> X18 = X17 ) ),
    c_0_474 ).

fof(c_0_1647,plain,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
       => ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,X19) ) ),
    inference(fof_simplification,[status(thm)],[c_0_475]) ).

fof(c_0_1648,plain,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X19,X20)
       => ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X20,X19) ) ),
    inference(fof_simplification,[status(thm)],[c_0_476]) ).

fof(c_0_1649,axiom,
    ! [X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
       => c_Groups_Otimes__class_Otimes(X3,X2,c_Divides_Odiv__class_Odiv(X3,X21,X2)) = X21 ) ),
    c_0_477 ).

fof(c_0_1650,axiom,
    ! [X21,X33,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X33)
       => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ),
    c_0_478 ).

fof(c_0_1651,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
       => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ),
    c_0_479 ).

fof(c_0_1652,axiom,
    ! [X10] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10)) ),
    c_0_480 ).

fof(c_0_1653,axiom,
    ! [X20] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20)),
    c_0_481 ).

fof(c_0_1654,axiom,
    ! [X23] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
       => ( X23 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | X23 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    c_0_482 ).

fof(c_0_1655,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) ),
    c_0_483 ).

fof(c_0_1656,axiom,
    ! [X2,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21)) ),
    c_0_484 ).

fof(c_0_1657,axiom,
    ! [X2,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21))
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),X21) ) ),
    c_0_485 ).

fof(c_0_1658,axiom,
    ! [X2,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_486 ).

fof(c_0_1659,axiom,
    ! [X2,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        & c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21)) ) ),
    c_0_487 ).

fof(c_0_1660,axiom,
    ! [X20,X23] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,X23,X20)) ),
    c_0_488 ).

fof(c_0_1661,axiom,
    ! [X8,X30] :
      ( ( class_Groups_Omonoid__mult(X30)
        & class_Int_Onumber(X30) )
     => c_Power_Opower__class_Opower(X30,c_Int_Onumber__class_Onumber__of(X30,X8),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X8),c_Int_Onumber__class_Onumber__of(X30,X8)) ),
    c_0_489 ).

fof(c_0_1662,axiom,
    ! [X19,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X19,X19) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3)),X19) ),
    c_0_490 ).

fof(c_0_1663,axiom,
    ! [X10,X8] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X8,X10)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Groups_Oone__class_Oone(tc_Int_Oint)),X10) ),
    c_0_491 ).

fof(c_0_1664,plain,
    ! [X51,X53] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X53),
    inference(fof_simplification,[status(thm)],[c_0_492]) ).

fof(c_0_1665,plain,
    ! [X53,X51] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X53),X53),
    inference(fof_simplification,[status(thm)],[c_0_493]) ).

fof(c_0_1666,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),X20) ),
    c_0_494 ).

fof(c_0_1667,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),X20) ),
    c_0_495 ).

fof(c_0_1668,axiom,
    ! [X2,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),X21) ),
    c_0_496 ).

fof(c_0_1669,axiom,
    ! [X2,X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21)) ),
    c_0_497 ).

fof(c_0_1670,axiom,
    ! [X7,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X7),X19) ),
    c_0_498 ).

fof(c_0_1671,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
    <=> ? [X59] : X17 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X59)) ),
    c_0_499 ).

fof(c_0_1672,axiom,
    ! [X20,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X20)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X53)) = X53 ),
    c_0_500 ).

fof(c_0_1673,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) = X19 ),
    c_0_501 ).

fof(c_0_1674,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) = X19 ),
    c_0_502 ).

fof(c_0_1675,axiom,
    ! [X19,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X51)) ),
    c_0_503 ).

fof(c_0_1676,axiom,
    ! [X19,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X19)) ),
    c_0_504 ).

fof(c_0_1677,axiom,
    ! [X20,X7,X51] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X51,X7)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X20),X7) ),
    c_0_505 ).

fof(c_0_1678,axiom,
    ! [X19,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X19)) ),
    c_0_506 ).

fof(c_0_1679,axiom,
    ! [X19,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X51)) ),
    c_0_507 ).

fof(c_0_1680,axiom,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X14))
    <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ) ),
    c_0_508 ).

fof(c_0_1681,axiom,
    ! [X8,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3)),c_Int_Onumber__class_Onumber__of(X3,X8)) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(X8)) ),
    c_0_509 ).

fof(c_0_1682,axiom,
    ! [X14,X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X14) ) ),
    c_0_510 ).

fof(c_0_1683,axiom,
    ! [X14,X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,X14) ) ),
    c_0_511 ).

fof(c_0_1684,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
       => ( c_Rings_Odvd__class_Odvd(X3,X21,X33)
         => c_Rings_Odvd__class_Odvd(X3,X2,X33) ) ) ),
    c_0_512 ).

fof(c_0_1685,axiom,
    ! [X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X8)) = c_Groups_Ominus__class_Ominus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
    c_0_513 ).

fof(c_0_1686,axiom,
    ! [X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)) = c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
    c_0_514 ).

fof(c_0_1687,axiom,
    ! [X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)) ),
    c_0_515 ).

fof(c_0_1688,axiom,
    ! [X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)) ),
    c_0_516 ).

fof(c_0_1689,axiom,
    ! [X8,X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)) = c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
    c_0_517 ).

fof(c_0_1690,axiom,
    ! [X20,X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X2,X20),X2) ),
    c_0_518 ).

fof(c_0_1691,axiom,
    ! [X20,X2,X3] :
      ( class_Power_Opower(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)) = c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20)) ),
    c_0_519 ).

fof(c_0_1692,axiom,
    ! [X35,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(X35)) = c_Groups_Otimes__class_Otimes(X3,X23,c_Power_Opower__class_Opower(X3,X23,X35)) ),
    c_0_520 ).

fof(c_0_1693,axiom,
    ! [X35,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X23,c_Power_Opower__class_Opower(X3,X23,X35)) = c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(X35)) ),
    c_0_521 ).

fof(c_0_1694,axiom,
    ! [X35,X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X35),X23) = c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(X35)) ),
    c_0_522 ).

fof(c_0_1695,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X20)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19) ) ),
    c_0_523 ).

fof(c_0_1696,axiom,
    ! [X5,X66] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X66,X5) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ( X5 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X66)
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X66,X5) )
        | ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X66,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          & c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X66) ) ) ),
    c_0_524 ).

fof(c_0_1697,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X21)
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    c_0_525 ).

fof(c_0_1698,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X2)
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    c_0_526 ).

fof(c_0_1699,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X51,X7)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X53),X7) ) ),
    c_0_527 ).

fof(c_0_1700,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X21)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21) = X2 ) ),
    c_0_528 ).

fof(c_0_1701,axiom,
    ! [X21,X2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X2)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21) = X2 ) ),
    c_0_529 ).

fof(c_0_1702,axiom,
    ! [X20,X10] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X10,X20)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X20) ) ),
    c_0_530 ).

fof(c_0_1703,axiom,
    ! [X20,X7] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X20)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20) ) ),
    c_0_531 ).

fof(c_0_1704,plain,
    ! [X33,X21,X2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2) )
     => ( X21 = X33
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X33)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X33,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_532]) ).

fof(c_0_1705,plain,
    ! [X33,X21,X2] :
      ( X2 = X21
     => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X33)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X33,X21) )
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X33)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X33,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_533]) ).

fof(c_0_1706,axiom,
    ! [X5,X65,X66] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
     => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66) = X5
      <=> X65 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X66) ) ),
    c_0_534 ).

fof(c_0_1707,axiom,
    ! [X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Divides_Odiv__class_Omod(X3,X2,X21),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
    c_0_535 ).

fof(c_0_1708,axiom,
    ! [X2,X21,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X21,X2),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
    c_0_536 ).

fof(c_0_1709,axiom,
    ! [X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
    c_0_537 ).

fof(c_0_1710,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X20 ),
    c_0_538 ).

fof(c_0_1711,axiom,
    ! [X20,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20),
    c_0_539 ).

fof(c_0_1712,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X7)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X7) ) ),
    c_0_540 ).

fof(c_0_1713,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X53,X51)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X51,X7)
       => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X53,X7) ) ),
    c_0_541 ).

fof(c_0_1714,axiom,
    ! [X7,X51,X53] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,X51)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X51,X7)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,X7) ) ),
    c_0_542 ).

fof(c_0_1715,axiom,
    ! [X10,X22,X23] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10) ) ),
    c_0_543 ).

fof(c_0_1716,axiom,
    ! [X9,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Groups_Oone__class_Oone(X3)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,c_Int_OBit1(c_Int_OPls))) ),
    c_0_544 ).

fof(c_0_1717,axiom,
    ! [X8,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X3,X8)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X8)) ),
    c_0_545 ).

fof(c_0_1718,axiom,
    ! [X21] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),X21) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X21,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    c_0_546 ).

fof(c_0_1719,plain,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X15,X14))
    <=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
          & c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) )
        | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
          & ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_547]) ).

fof(c_0_1720,plain,
    ! [X22,X23] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
       => ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_548]) ).

fof(c_0_1721,plain,
    ! [X22,X23] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
       => ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_549]) ).

fof(c_0_1722,plain,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X14))
    <=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
          & c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) )
        | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
          & ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_550]) ).

fof(c_0_1723,plain,
    ! [X17,X18] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))
    <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
      <=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ),
    inference(fof_simplification,[status(thm)],[c_0_551]) ).

fof(c_0_1724,axiom,
    ! [X17,X18] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))
    <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
      <=> c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ),
    c_0_552 ).

fof(c_0_1725,plain,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14))
    <=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
          & c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) )
        | ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
          & ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_553]) ).

fof(c_0_1726,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X20))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X20)))
        & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X20))) ) ),
    c_0_554 ).

fof(c_0_1727,axiom,
    ! [X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)),
    c_0_555 ).

fof(c_0_1728,axiom,
    ! [X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)),
    c_0_556 ).

fof(c_0_1729,axiom,
    ! [X8,X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)),
    c_0_557 ).

fof(c_0_1730,axiom,
    ! [X8,X9] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)),
    c_0_558 ).

fof(c_0_1731,plain,
    ! [X20,X19] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) = X19 ),
    inference(fof_simplification,[status(thm)],[c_0_559]) ).

fof(c_0_1732,axiom,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X15,X14))
    <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) ) ),
    c_0_560 ).

fof(c_0_1733,plain,
    ! [X22,X23] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
       => ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_561]) ).

fof(c_0_1734,axiom,
    ! [X14,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X15,X14))
    <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) ) ),
    c_0_562 ).

fof(c_0_1735,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X5),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
    c_0_563 ).

fof(c_0_1736,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X5),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
    c_0_564 ).

fof(c_0_1737,axiom,
    ! [X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Groups_Oone__class_Oone(X3))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,c_Int_OBit1(c_Int_OPls)) ) ),
    c_0_565 ).

fof(c_0_1738,axiom,
    ! [X14,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X14) ) ),
    c_0_566 ).

fof(c_0_1739,axiom,
    ! [X14,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X14) ) ),
    c_0_567 ).

fof(c_0_1740,axiom,
    ! [X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Groups_Oone__class_Oone(X3))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,c_Int_OBit1(c_Int_OPls)) ) ),
    c_0_568 ).

fof(c_0_1741,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => X20 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    c_0_569 ).

fof(c_0_1742,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
     => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X20 ),
    c_0_570 ).

fof(c_0_1743,axiom,
    ! [X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Groups_Ozero__class_Ozero(X3))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,c_Int_OPls) ) ),
    c_0_571 ).

fof(c_0_1744,axiom,
    ! [X14,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X14) ) ),
    c_0_572 ).

fof(c_0_1745,axiom,
    ! [X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Groups_Ozero__class_Ozero(X3))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,c_Int_OPls) ) ),
    c_0_573 ).

fof(c_0_1746,axiom,
    ! [X14,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Rings_Olinordered__idom(X3) )
     => ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X3,X14))
      <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X14) ) ),
    c_0_574 ).

fof(c_0_1747,axiom,
    ! [X23,X20,X3] :
      ( ( class_Groups_Omonoid__mult(X3)
        & class_Rings_Olinordered__ring(X3) )
     => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
       => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X23,X20)) ) ),
    c_0_575 ).

fof(c_0_1748,axiom,
    ! [X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3))) ),
    c_0_576 ).

fof(c_0_1749,axiom,
    ! [X17,X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X15,X17))
    <=> ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
        & X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    c_0_577 ).

fof(c_0_1750,plain,
    ! [X20,X23] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X20)) ),
    inference(fof_simplification,[status(thm)],[c_0_578]) ).

fof(c_0_1751,plain,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ),
    inference(fof_simplification,[status(thm)],[c_0_579]) ).

fof(c_0_1752,plain,
    ! [X14,X15] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15) )
    <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
        & X15 != X14 ) ),
    inference(fof_simplification,[status(thm)],[c_0_580]) ).

fof(c_0_1753,plain,
    ! [X14,X15] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
    <=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15) )
        | X15 = X14 ) ),
    inference(fof_simplification,[status(thm)],[c_0_581]) ).

fof(c_0_1754,axiom,
    ! [X17,X18,X5] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X18) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X17)
    <=> X18 = X17 ),
    c_0_582 ).

fof(c_0_1755,axiom,
    ! [X41,X42,X24,X25,X3] :
      ( class_Groups_Oab__group__add(X3)
     => ( c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ominus__class_Ominus(X3,X42,X41)
       => ( X25 = X24
        <=> X42 = X41 ) ) ),
    c_0_583 ).

fof(c_0_1756,axiom,
    ! [X2,X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oone__class_Oone(X3))) ),
    c_0_584 ).

fof(c_0_1757,axiom,
    ! [X16,X25,X3] :
      ( ( class_Power_Opower(X3)
        & class_Rings_Omult__zero(X3)
        & class_Rings_Ono__zero__divisors(X3)
        & class_Rings_Ozero__neq__one(X3) )
     => ( c_Power_Opower__class_Opower(X3,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)) = c_Groups_Ozero__class_Ozero(X3)
      <=> ( X25 = c_Groups_Ozero__class_Ozero(X3)
          & c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    c_0_585 ).

fof(c_0_1758,axiom,
    ! [X33,X2,X21,X3] :
      ( class_Groups_Ocancel__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X21,X2) = c_Groups_Oplus__class_Oplus(X3,X33,X2)
       => X21 = X33 ) ),
    c_0_586 ).

fof(c_0_1759,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Ocancel__ab__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X2,X21) = c_Groups_Oplus__class_Oplus(X3,X2,X33)
       => X21 = X33 ) ),
    c_0_587 ).

fof(c_0_1760,axiom,
    ! [X33,X21,X2,X3] :
      ( class_Groups_Ocancel__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X2,X21) = c_Groups_Oplus__class_Oplus(X3,X2,X33)
       => X21 = X33 ) ),
    c_0_588 ).

fof(c_0_1761,axiom,
    ! [X42,X25,X24,X3] :
      ( class_Groups_Ocancel__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X24,X25) = c_Groups_Oplus__class_Oplus(X3,X42,X25)
      <=> X24 = X42 ) ),
    c_0_589 ).

fof(c_0_1762,axiom,
    ! [X42,X24,X25,X3] :
      ( class_Groups_Ocancel__semigroup__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X25,X24) = c_Groups_Oplus__class_Oplus(X3,X25,X42)
      <=> X24 = X42 ) ),
    c_0_590 ).

fof(c_0_1763,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
     => ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X18,X17) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      <=> ( X18 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X17 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    c_0_591 ).

fof(c_0_1764,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18))
      <=> X17 = X18 ) ),
    c_0_592 ).

fof(c_0_1765,axiom,
    ! [X25,X3] :
      ( class_Rings_Oring__1__no__zero__divisors(X3)
     => ( c_Power_Opower__class_Opower(X3,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X3)
      <=> X25 = c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_593 ).

fof(c_0_1766,plain,
    ! [X17,X18] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X18) ),
    inference(fof_simplification,[status(thm)],[c_0_594]) ).

fof(c_0_1767,plain,
    ! [X17,X18] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18)) ),
    inference(fof_simplification,[status(thm)],[c_0_595]) ).

fof(c_0_1768,axiom,
    ! [X20,X19] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => X19 = X20 ) ),
    c_0_596 ).

fof(c_0_1769,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
    <=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [X58] :
            ( X18 = c_Nat_OSuc(X58)
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,X58,X17) ) ) ),
    c_0_597 ).

fof(c_0_1770,axiom,
    ! [X61] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X61) ),
    c_0_598 ).

fof(c_0_1771,axiom,
    ! [X2,X3] :
      ( class_Rings_Olinordered__ring(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X2)) ),
    c_0_599 ).

fof(c_0_1772,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
    <=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_600 ).

fof(c_0_1773,axiom,
    ! [X6,X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit1(X6)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X6)),
    c_0_601 ).

fof(c_0_1774,axiom,
    ! [X6,X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit0(X6)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X6)),
    c_0_602 ).

fof(c_0_1775,axiom,
    ! [X6,X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit0(X6)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X6)),
    c_0_603 ).

fof(c_0_1776,axiom,
    ! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit1(X6)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X6)),
    c_0_604 ).

fof(c_0_1777,axiom,
    ! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit0(X6)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X6)),
    c_0_605 ).

fof(c_0_1778,axiom,
    ! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit0(X6)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X6)),
    c_0_606 ).

fof(c_0_1779,axiom,
    ! [X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Odiv(X3,c_Divides_Odiv__class_Omod(X3,X2,X21),X21) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_607 ).

fof(c_0_1780,axiom,
    ! [X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X21) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_608 ).

fof(c_0_1781,axiom,
    ! [X2,X21,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X21,X2),X21) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_609 ).

fof(c_0_1782,axiom,
    ! [X24,X25,X42] :
      ( X42 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X42,X25) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X42,X24)
      <=> X25 = X24 ) ),
    c_0_610 ).

fof(c_0_1783,axiom,
    ! [X24,X25,X42] :
      ( X42 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X25,X42) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X24,X42)
      <=> X25 = X24 ) ),
    c_0_611 ).

fof(c_0_1784,axiom,
    ! [X17,X18,X5] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17)
    <=> ( X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18 = X17 ) ),
    c_0_612 ).

fof(c_0_1785,axiom,
    ! [X17,X18,X5] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17)
    <=> ( X18 = X17
        | X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    c_0_613 ).

fof(c_0_1786,axiom,
    ! [X17,X5,X18] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X5) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X5)
    <=> ( X18 = X17
        | X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    c_0_614 ).

fof(c_0_1787,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
    <=> ? [X31] : X15 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X31) ),
    c_0_615 ).

fof(c_0_1788,axiom,
    ! [X17] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
    <=> ? [X1] : X17 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
    c_0_616 ).

fof(c_0_1789,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X15) ),
    c_0_617 ).

fof(c_0_1790,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
    <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X15) ),
    c_0_618 ).

fof(c_0_1791,axiom,
    ! [X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
     => ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    c_0_619 ).

fof(c_0_1792,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
       => X19 = X20 ) ),
    c_0_620 ).

fof(c_0_1793,axiom,
    ! [X8,X10] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X8)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X10)
       => X10 = X8 ) ),
    c_0_621 ).

fof(c_0_1794,axiom,
    ! [X8,X10] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X8)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X10)
       => X10 = X8 ) ),
    c_0_622 ).

fof(c_0_1795,axiom,
    ! [X22,X23] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
       => X23 = X22 ) ),
    c_0_623 ).

fof(c_0_1796,axiom,
    ! [X20,X19] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X20)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,X19)
       => X19 = X20 ) ),
    c_0_624 ).

fof(c_0_1797,plain,
    ! [X21,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
     => ( X2 != X21
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_625]) ).

fof(c_0_1798,plain,
    ! [X22,X23] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
     => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
        | X23 = X22 ) ),
    inference(fof_simplification,[status(thm)],[c_0_626]) ).

fof(c_0_1799,axiom,
    ! [X15,X14] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
      <=> X15 = X14 ) ),
    c_0_627 ).

fof(c_0_1800,plain,
    ! [X21,X2] :
      ( X2 != X21
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
       => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
          & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_628]) ).

fof(c_0_1801,axiom,
    ! [X14,X15] :
      ( X15 = X14
    <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15) ) ),
    c_0_629 ).

fof(c_0_1802,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Ogroup__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X21) = X2 ),
    c_0_630 ).

fof(c_0_1803,axiom,
    ! [X21,X2,X3] :
      ( class_Groups_Ogroup__add(X3)
     => c_Groups_Ominus__class_Ominus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X21) = X2 ),
    c_0_631 ).

fof(c_0_1804,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X2)) ),
    c_0_632 ).

fof(c_0_1805,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Otimes__class_Otimes(X3,X2,X21)) ),
    c_0_633 ).

fof(c_0_1806,axiom,
    ! [X17,X5,X18] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X5)
    <=> X18 = X17 ),
    c_0_634 ).

fof(c_0_1807,axiom,
    ! [X17,X18,X5] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X17)
    <=> X18 = X17 ),
    c_0_635 ).

fof(c_0_1808,axiom,
    ! [X41,X18] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X18,X41) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ? [X76] : X18 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X41,X76) ),
    c_0_636 ).

fof(c_0_1809,axiom,
    ! [X41,X18] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X18,X41) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ? [X76] : X18 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X41,X76) ),
    c_0_637 ).

fof(c_0_1810,axiom,
    ! [X7] : c_Int_OBit1(X7) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X7),X7),
    c_0_638 ).

fof(c_0_1811,axiom,
    ! [X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)),
    c_0_639 ).

fof(c_0_1812,axiom,
    ! [X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)),
    c_0_640 ).

fof(c_0_1813,axiom,
    ! [X6,X7] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X7),X6) = c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X6)),
    c_0_641 ).

fof(c_0_1814,axiom,
    ! [X10,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X10) = c_Groups_Oplus__class_Oplus(X3,X10,X10) ),
    c_0_642 ).

fof(c_0_1815,axiom,
    ! [X10,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,X10,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X3,X10,X10) ),
    c_0_643 ).

fof(c_0_1816,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
    <=> ? [X59] : X17 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X59) ),
    c_0_644 ).

fof(c_0_1817,axiom,
    ! [X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X23,X23) = c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    c_0_645 ).

fof(c_0_1818,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X3,X2,X2) ),
    c_0_646 ).

fof(c_0_1819,axiom,
    ! [X20,X19] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),c_Nat_OSuc(X19)),
    c_0_647 ).

fof(c_0_1820,plain,
    ! [X15] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
    <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X15,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(fof_simplification,[status(thm)],[c_0_648]) ).

fof(c_0_1821,axiom,
    ! [X6] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X6)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X6)),
    c_0_649 ).

fof(c_0_1822,axiom,
    ! [X6] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X6)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X6)),
    c_0_650 ).

fof(c_0_1823,axiom,
    ! [X6] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X6)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X6)),
    c_0_651 ).

fof(c_0_1824,axiom,
    ! [X6] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X6)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X6)),
    c_0_652 ).

fof(c_0_1825,axiom,
    ! [X21,X2] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_653 ).

fof(c_0_1826,axiom,
    ! [X19,X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_654 ).

fof(c_0_1827,axiom,
    ! [X19,X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19),X20) = X19,
    c_0_655 ).

fof(c_0_1828,axiom,
    ! [X20,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20),X20) = X19,
    c_0_656 ).

fof(c_0_1829,axiom,
    ! [X22,X23] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
       => c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
    c_0_657 ).

fof(c_0_1830,axiom,
    ! [X20,X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),X19),
    c_0_658 ).

fof(c_0_1831,axiom,
    ! [X20,X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X19),
    c_0_659 ).

fof(c_0_1832,axiom,
    ! [X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X19)),
    c_0_660 ).

fof(c_0_1833,axiom,
    ! [X19,X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19)),
    c_0_661 ).

fof(c_0_1834,axiom,
    ! [X19,X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)),
    c_0_662 ).

fof(c_0_1835,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OBit0(X49))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
    c_0_663 ).

fof(c_0_1836,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit0(X4))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
    c_0_664 ).

fof(c_0_1837,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OBit1(X49))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
    c_0_665 ).

fof(c_0_1838,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit1(X4))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
    c_0_666 ).

fof(c_0_1839,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OBit1(X49))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
    c_0_667 ).

fof(c_0_1840,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit1(X4))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
    c_0_668 ).

fof(c_0_1841,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OBit0(X49))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
    c_0_669 ).

fof(c_0_1842,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit0(X4))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
    c_0_670 ).

fof(c_0_1843,axiom,
    ! [X18,X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),c_Nat_OSuc(X18))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X18) ),
    c_0_671 ).

fof(c_0_1844,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OBit1(X49))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
    c_0_672 ).

fof(c_0_1845,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit1(X4))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
    c_0_673 ).

fof(c_0_1846,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X18),c_Nat_OSuc(X17))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
    c_0_674 ).

fof(c_0_1847,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X20))
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ),
    c_0_675 ).

fof(c_0_1848,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OBit0(X49))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
    c_0_676 ).

fof(c_0_1849,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit0(X4))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
    c_0_677 ).

fof(c_0_1850,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OBit0(X49))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
    c_0_678 ).

fof(c_0_1851,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit0(X4))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
    c_0_679 ).

fof(c_0_1852,axiom,
    ! [X49,X50] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OBit1(X49))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
    c_0_680 ).

fof(c_0_1853,axiom,
    ! [X4,X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit1(X4))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
    c_0_681 ).

fof(c_0_1854,axiom,
    ! [X16] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X16),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_682 ).

fof(c_0_1855,axiom,
    ! [X16] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X16),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_683 ).

fof(c_0_1856,axiom,
    ! [X24,X25,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X25,X24)
      <=> c_Divides_Odiv__class_Omod(X3,X24,X25) = c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_684 ).

fof(c_0_1857,axiom,
    ! [X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X10),
    c_0_685 ).

fof(c_0_1858,axiom,
    ! [X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X10) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X10),
    c_0_686 ).

fof(c_0_1859,axiom,
    ! [X21,X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
       => c_Divides_Odiv__class_Omod(X3,X21,X2) = c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_687 ).

fof(c_0_1860,plain,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Nat_OSuc(X20))
     => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
       => X19 = c_Nat_OSuc(X20) ) ),
    inference(fof_simplification,[status(thm)],[c_0_688]) ).

fof(c_0_1861,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
        | X18 = c_Nat_OSuc(X17) ) ),
    c_0_689 ).

fof(c_0_1862,axiom,
    ! [X7,X21,X2,X3] :
      ( class_Rings_Odvd(X3)
     => ( X2 = c_Groups_Otimes__class_Otimes(X3,X21,X7)
       => c_Rings_Odvd__class_Odvd(X3,X21,X2) ) ),
    c_0_690 ).

fof(c_0_1863,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X20)) ),
    c_0_691 ).

fof(c_0_1864,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
        | X18 = X17 ) ),
    c_0_692 ).

fof(c_0_1865,plain,
    ! [X18,X17] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18))
      <=> X17 = X18 ) ),
    inference(fof_simplification,[status(thm)],[c_0_693]) ).

fof(c_0_1866,plain,
    ! [X19,X20] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(X19))
       => X19 = X20 ) ),
    inference(fof_simplification,[status(thm)],[c_0_694]) ).

fof(c_0_1867,plain,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20))
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
       => X19 = X20 ) ),
    inference(fof_simplification,[status(thm)],[c_0_695]) ).

fof(c_0_1868,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => ( c_Nat_OSuc(X19) != X20
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),X20) ) ),
    c_0_696 ).

fof(c_0_1869,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
    <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X15,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_697 ).

fof(c_0_1870,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ),
    c_0_698 ).

fof(c_0_1871,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X18),X17)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
    c_0_699 ).

fof(c_0_1872,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
    c_0_700 ).

fof(c_0_1873,axiom,
    ! [X18,X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X18) ),
    c_0_701 ).

fof(c_0_1874,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
    c_0_702 ).

fof(c_0_1875,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ),
    c_0_703 ).

fof(c_0_1876,axiom,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
    <=> ? [X31] : X15 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31) ),
    c_0_704 ).

fof(c_0_1877,axiom,
    ! [X46] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X46)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X46) ),
    c_0_705 ).

fof(c_0_1878,axiom,
    ! [X23] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
     => ( X23 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X23 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    c_0_706 ).

fof(c_0_1879,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X20) ),
    c_0_707 ).

fof(c_0_1880,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) ),
    c_0_708 ).

fof(c_0_1881,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) ),
    c_0_709 ).

fof(c_0_1882,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) ),
    c_0_710 ).

fof(c_0_1883,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Int_OPls) ),
    c_0_711 ).

fof(c_0_1884,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X5))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X5) ),
    c_0_712 ).

fof(c_0_1885,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Int_OPls) ),
    c_0_713 ).

fof(c_0_1886,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X5))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X5) ),
    c_0_714 ).

fof(c_0_1887,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X5))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X5) ),
    c_0_715 ).

fof(c_0_1888,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X5))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X5) ),
    c_0_716 ).

fof(c_0_1889,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X5))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X5) ),
    c_0_717 ).

fof(c_0_1890,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OMin)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Int_OMin) ),
    c_0_718 ).

fof(c_0_1891,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OMin)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Int_OMin) ),
    c_0_719 ).

fof(c_0_1892,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X5))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X5) ),
    c_0_720 ).

fof(c_0_1893,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OMin)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Int_OMin) ),
    c_0_721 ).

fof(c_0_1894,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X5))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X5) ),
    c_0_722 ).

fof(c_0_1895,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OMin)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Int_OMin) ),
    c_0_723 ).

fof(c_0_1896,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Int_OPls) ),
    c_0_724 ).

fof(c_0_1897,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X5))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X5) ),
    c_0_725 ).

fof(c_0_1898,axiom,
    ! [X5] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OPls)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Int_OPls) ),
    c_0_726 ).

fof(c_0_1899,plain,
    ! [X22,X23] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
       => c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_727]) ).

fof(c_0_1900,axiom,
    ! [X17,X18] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
    c_0_728 ).

fof(c_0_1901,plain,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => X22 != X23 ),
    inference(fof_simplification,[status(thm)],[c_0_729]) ).

fof(c_0_1902,plain,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => X23 != X22 ),
    inference(fof_simplification,[status(thm)],[c_0_730]) ).

fof(c_0_1903,plain,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
     => X23 != X22 ),
    inference(fof_simplification,[status(thm)],[c_0_731]) ).

fof(c_0_1904,axiom,
    ! [X33,X21,X2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
     => ( X21 = X33
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X33) ) ),
    c_0_732 ).

fof(c_0_1905,axiom,
    ! [X33,X21,X2] :
      ( X2 = X21
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X33)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X33) ) ),
    c_0_733 ).

fof(c_0_1906,axiom,
    ! [X16,X46] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,X16)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X46,X16)
        & X46 != X16 ) ),
    c_0_734 ).

fof(c_0_1907,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_735 ).

fof(c_0_1908,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
     => ( X19 != X20
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ) ),
    c_0_736 ).

fof(c_0_1909,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
        | X18 = X17 ) ),
    c_0_737 ).

fof(c_0_1910,axiom,
    ! [X17,X18] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
        & X18 != X17 ) ),
    c_0_738 ).

fof(c_0_1911,axiom,
    ! [X14,X15] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14)
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
        & X15 != X14 ) ),
    c_0_739 ).

fof(c_0_1912,axiom,
    ! [X14,X15] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
    <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14)
        | X15 = X14 ) ),
    c_0_740 ).

fof(c_0_1913,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = X19 ),
    c_0_741 ).

fof(c_0_1914,axiom,
    ! [X16,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Int_Oring__char__0(X3) )
     => ( c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(X16)))
      <=> c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,X16)) ) ),
    c_0_742 ).

fof(c_0_1915,axiom,
    ! [X20,X19] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
        | X19 = X20 )
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
    c_0_743 ).

fof(c_0_1916,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
    c_0_744 ).

fof(c_0_1917,axiom,
    ! [X22,X23] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
     => c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ),
    c_0_745 ).

fof(c_0_1918,axiom,
    ! [X23,X22] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
     => c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ),
    c_0_746 ).

fof(c_0_1919,axiom,
    ! [X17,X25,X3] :
      ( ( class_Power_Opower(X3)
        & class_Rings_Omult__zero(X3)
        & class_Rings_Ono__zero__divisors(X3)
        & class_Rings_Ozero__neq__one(X3) )
     => ( c_Power_Opower__class_Opower(X3,X25,X17) = c_Groups_Ozero__class_Ozero(X3)
      <=> ( X25 = c_Groups_Ozero__class_Ozero(X3)
          & X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    c_0_747 ).

fof(c_0_1920,axiom,
    ! [X8,X3] :
      ( ( class_Power_Opower(X3)
        & class_Rings_Osemiring__0(X3) )
     => ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X8) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X8)) = c_Groups_Oone__class_Oone(X3) )
        & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X8) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X8)) = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    c_0_748 ).

fof(c_0_1921,axiom,
    ! [X20] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X20))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X20),
    c_0_749 ).

fof(c_0_1922,axiom,
    ! [X3] :
      ( class_Rings_Osemiring__1(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X3) ),
    c_0_750 ).

fof(c_0_1923,axiom,
    ! [X3] :
      ( class_Rings_Osemiring__1(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_751 ).

fof(c_0_1924,plain,
    ! [X22,X23,X3] :
      ( class_Rings_Olinordered__idom(X3)
     => ( X23 != X22
       => ( ~ c_Orderings_Oord__class_Oless(X3,X23,X22)
         => c_Orderings_Oord__class_Oless(X3,X22,X23) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_752]) ).

fof(c_0_1925,axiom,
    ! [X20,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),
    c_0_753 ).

fof(c_0_1926,axiom,
    ! [X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Nat_OSuc(X20)),
    c_0_754 ).

fof(c_0_1927,axiom,
    ! [X33,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,X33) = c_Groups_Oplus__class_Oplus(X3,X33,X2) ),
    c_0_755 ).

fof(c_0_1928,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,X21) = c_Groups_Otimes__class_Otimes(X3,X21,X2) ),
    c_0_756 ).

fof(c_0_1929,plain,
    ! [X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Ozero__class_Ozero(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_757]) ).

fof(c_0_1930,plain,
    ! [X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Ozero__class_Ozero(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_758]) ).

fof(c_0_1931,axiom,
    ! [X17,X18] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X17 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    c_0_759 ).

fof(c_0_1932,axiom,
    ! [X17,X18] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17)
    <=> ( ( X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X17 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    c_0_760 ).

fof(c_0_1933,axiom,
    ! [X18] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_761 ).

fof(c_0_1934,axiom,
    ! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20) = c_Nat_OSuc(c_Nat_OSuc(X20)),
    c_0_762 ).

fof(c_0_1935,axiom,
    ! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X20)),
    c_0_763 ).

fof(c_0_1936,plain,
    ! [X23,X3] :
      ( class_Int_Onumber__ring(X3)
     => ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
       => c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin) ) ),
    inference(fof_simplification,[status(thm)],[c_0_764]) ).

fof(c_0_1937,plain,
    ! [X23,X3] :
      ( class_Int_Onumber__ring(X3)
     => ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
         => c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Groups_Oone__class_Oone(X3) )
        & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
         => c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_765]) ).

fof(c_0_1938,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Ono__zero__divisors(X3)
     => ( c_Groups_Otimes__class_Otimes(X3,X2,X21) = c_Groups_Ozero__class_Ozero(X3)
       => ( X2 = c_Groups_Ozero__class_Ozero(X3)
          | X21 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    c_0_766 ).

fof(c_0_1939,axiom,
    ! [X21,X2,X3] :
      ( class_Rings_Ono__zero__divisors(X3)
     => ( X2 != c_Groups_Ozero__class_Ozero(X3)
       => ( X21 != c_Groups_Ozero__class_Ozero(X3)
         => c_Groups_Otimes__class_Otimes(X3,X2,X21) != c_Groups_Ozero__class_Ozero(X3) ) ) ),
    c_0_767 ).

fof(c_0_1940,axiom,
    ! [X24,X25,X3] :
      ( class_Rings_Oring__no__zero__divisors(X3)
     => ( c_Groups_Otimes__class_Otimes(X3,X25,X24) = c_Groups_Ozero__class_Ozero(X3)
      <=> ( X25 = c_Groups_Ozero__class_Ozero(X3)
          | X24 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    c_0_768 ).

fof(c_0_1941,axiom,
    ! [X23,X3] :
      ( class_Int_Onumber__ring(X3)
     => ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
       => c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Groups_Oone__class_Oone(X3) ) ),
    c_0_769 ).

fof(c_0_1942,plain,
    ! [X22,X23] :
      ( X23 != X22
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X22)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X23) ) ),
    inference(fof_simplification,[status(thm)],[c_0_770]) ).

fof(c_0_1943,axiom,
    ! [X17,X18] :
      ( X18 != X17
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18) ) ),
    c_0_771 ).

fof(c_0_1944,axiom,
    ! [X22,X23] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,X22)
      | X23 = X22
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X23) ),
    c_0_772 ).

fof(c_0_1945,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Ozero__class_Ozero(X3),X2)
       => X2 = c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_773 ).

fof(c_0_1946,axiom,
    ! [X10] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X10,
    c_0_774 ).

fof(c_0_1947,axiom,
    ! [X18,X15] :
      ( c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X18) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X15 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    c_0_775 ).

fof(c_0_1948,axiom,
    ! [X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_776 ).

fof(c_0_1949,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19) ),
    c_0_777 ).

fof(c_0_1950,axiom,
    ! [X8,X10] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X8)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X10) ),
    c_0_778 ).

fof(c_0_1951,axiom,
    ! [X8,X10] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X8)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X10) ),
    c_0_779 ).

fof(c_0_1952,axiom,
    ! [X23] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_780 ).

fof(c_0_1953,axiom,
    ! [X8,X10] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X10,X8) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X8,X10),
    c_0_781 ).

fof(c_0_1954,axiom,
    ! [X8,X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X10),
    c_0_782 ).

fof(c_0_1955,axiom,
    ! [X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19),
    c_0_783 ).

fof(c_0_1956,axiom,
    ! [X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19),
    c_0_784 ).

fof(c_0_1957,axiom,
    ! [X8,X10] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X10,X8) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X10),
    c_0_785 ).

fof(c_0_1958,axiom,
    ! [X20,X2,X3] :
      ( class_Rings_Oring__1__no__zero__divisors(X3)
     => ( X2 != c_Groups_Ozero__class_Ozero(X3)
       => c_Power_Opower__class_Opower(X3,X2,X20) != c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_786 ).

fof(c_0_1959,axiom,
    ! [X25,X3] :
      ( class_Groups_Olinordered__ab__group__add(X3)
     => ( c_Groups_Ozero__class_Ozero(X3) = c_Groups_Oplus__class_Oplus(X3,X25,X25)
      <=> X25 = c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_787 ).

fof(c_0_1960,axiom,
    ! [X25,X3] :
      ( class_Groups_Olinordered__ab__group__add(X3)
     => ( c_Groups_Oplus__class_Oplus(X3,X25,X25) = c_Groups_Ozero__class_Ozero(X3)
      <=> X25 = c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_788 ).

fof(c_0_1961,plain,
    ! [X23] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(fof_simplification,[status(thm)],[c_0_789]) ).

fof(c_0_1962,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    c_0_790 ).

fof(c_0_1963,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    c_0_791 ).

fof(c_0_1964,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    c_0_792 ).

fof(c_0_1965,axiom,
    ! [X17,X18] :
      ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X18,X17) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    <=> ( ( X18 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X17 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | ( X18 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
          & X17 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ) ) ),
    c_0_793 ).

fof(c_0_1966,axiom,
    ! [X20,X19] :
      ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X19,X20) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => ( X19 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X19 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ) ),
    c_0_794 ).

fof(c_0_1967,axiom,
    ! [X17,X18] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        & X17 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    c_0_795 ).

fof(c_0_1968,axiom,
    ! [X24,X25,X3] :
      ( class_Groups_Oab__group__add(X3)
     => ( X25 = X24
      <=> c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_796 ).

fof(c_0_1969,axiom,
    ! [X24,X25,X3] :
      ( class_Groups_Ogroup__add(X3)
     => ( c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ozero__class_Ozero(X3)
      <=> X25 = X24 ) ),
    c_0_797 ).

fof(c_0_1970,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3)) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    c_0_798 ).

fof(c_0_1971,axiom,
    ! [X17] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
    <=> ? [X1] : X17 = c_Nat_OSuc(X1) ),
    c_0_799 ).

fof(c_0_1972,axiom,
    ! [X25,X24,X3] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
     => ( X24 = c_Groups_Oplus__class_Oplus(X3,X24,X25)
      <=> X25 = c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_800 ).

fof(c_0_1973,axiom,
    ? [X1] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),
    c_0_801 ).

fof(c_0_1974,plain,
    ! [X8,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Int_Oring__char__0(X3) )
     => ~ c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(X8))) ),
    inference(fof_simplification,[status(thm)],[c_0_802]) ).

fof(c_0_1975,axiom,
    ! [X61] :
      ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,c_Int_OPls) ),
    c_0_803 ).

fof(c_0_1976,axiom,
    ! [X61] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,c_Int_OPls) ),
    c_0_804 ).

fof(c_0_1977,axiom,
    ! [X17,X18] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    c_0_805 ).

fof(c_0_1978,axiom,
    ! [X2,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls)),X2) = X2 ),
    c_0_806 ).

fof(c_0_1979,axiom,
    ! [X2,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls))) = X2 ),
    c_0_807 ).

fof(c_0_1980,axiom,
    ! [X17] :
      ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) ),
    c_0_808 ).

fof(c_0_1981,plain,
    ! [X20] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X20),X20),
    inference(fof_simplification,[status(thm)],[c_0_809]) ).

fof(c_0_1982,axiom,
    ! [X20,X19] :
      ( X19 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)
     => ( X20 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    c_0_810 ).

fof(c_0_1983,axiom,
    ! [X18] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    <=> X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    c_0_811 ).

fof(c_0_1984,axiom,
    ! [X17] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_812 ).

fof(c_0_1985,axiom,
    ! [X17,X18] :
      ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    <=> ( X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X17 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    c_0_813 ).

fof(c_0_1986,axiom,
    ! [X17,X18] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17)
    <=> ( X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X17 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    c_0_814 ).

fof(c_0_1987,axiom,
    ! [X17,X18] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    c_0_815 ).

fof(c_0_1988,axiom,
    ! [X20,X19] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
     => X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_816 ).

fof(c_0_1989,axiom,
    ! [X20,X19] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20) = X19
     => X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_817 ).

fof(c_0_1990,plain,
    ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_simplification,[status(thm)],[c_0_818]) ).

fof(c_0_1991,plain,
    ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_simplification,[status(thm)],[c_0_819]) ).

fof(c_0_1992,plain,
    ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_simplification,[status(thm)],[c_0_820]) ).

fof(c_0_1993,axiom,
    ! [X63,X64] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X64,X63)
     => X64 != X63 ),
    c_0_821 ).

fof(c_0_1994,axiom,
    ! [X19,X20] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
     => X19 != X20 ),
    c_0_822 ).

fof(c_0_1995,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(fof_simplification,[status(thm)],[c_0_823]) ).

fof(c_0_1996,axiom,
    ! [X2,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls),X2) = X2 ),
    c_0_824 ).

fof(c_0_1997,axiom,
    ! [X2,X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls)) = X2 ),
    c_0_825 ).

fof(c_0_1998,axiom,
    ! [X20,X3] :
      ( ( class_Power_Opower(X3)
        & class_Rings_Osemiring__0(X3) )
     => c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),c_Nat_OSuc(X20)) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_826 ).

fof(c_0_1999,axiom,
    ! [X20,X3] :
      ( ( class_Power_Opower(X3)
        & class_Rings_Osemiring__0(X3) )
     => ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),X20) = c_Groups_Oone__class_Oone(X3) )
        & ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),X20) = c_Groups_Ozero__class_Ozero(X3) ) ) ),
    c_0_827 ).

fof(c_0_2000,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    c_0_828 ).

fof(c_0_2001,plain,
    ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X20),
    inference(fof_simplification,[status(thm)],[c_0_829]) ).

fof(c_0_2002,plain,
    ! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X20),
    inference(fof_simplification,[status(thm)],[c_0_830]) ).

fof(c_0_2003,plain,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => ~ c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls))) ),
    inference(fof_simplification,[status(thm)],[c_0_831]) ).

fof(c_0_2004,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
    inference(fof_simplification,[status(thm)],[c_0_832]) ).

fof(c_0_2005,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
    inference(fof_simplification,[status(thm)],[c_0_833]) ).

fof(c_0_2006,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
    inference(fof_simplification,[status(thm)],[c_0_834]) ).

fof(c_0_2007,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(fof_simplification,[status(thm)],[c_0_835]) ).

fof(c_0_2008,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    c_0_836 ).

fof(c_0_2009,axiom,
    ! [X2] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_837 ).

fof(c_0_2010,axiom,
    ! [X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oone__class_Oone(X3)) ),
    c_0_838 ).

fof(c_0_2011,axiom,
    ! [X3] :
      ( class_Rings_Olinordered__semidom(X3)
     => c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oone__class_Oone(X3)) ),
    c_0_839 ).

fof(c_0_2012,axiom,
    ! [X20] : c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_840 ).

fof(c_0_2013,axiom,
    ! [X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,X2,c_Groups_Oone__class_Oone(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_841 ).

fof(c_0_2014,axiom,
    ! [X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,c_Groups_Ozero__class_Ozero(X3),X2) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_842 ).

fof(c_0_2015,axiom,
    ! [X20,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,c_Groups_Oone__class_Oone(X3),X20) = c_Groups_Oone__class_Oone(X3) ),
    c_0_843 ).

fof(c_0_2016,axiom,
    ! [X23,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,X23,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_844 ).

fof(c_0_2017,axiom,
    ! [X2,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_845 ).

fof(c_0_2018,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_846 ).

fof(c_0_2019,axiom,
    ! [X2,X3] :
      ( class_Rings_Omult__zero(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_847 ).

fof(c_0_2020,axiom,
    ! [X22,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Ozero__class_Ozero(X3),X22) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_848 ).

fof(c_0_2021,axiom,
    ! [X21,X3] :
      ( class_RealVector_Oreal__normed__algebra(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Ozero__class_Ozero(X3),X21) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_849 ).

fof(c_0_2022,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Ozero__class_Ozero(X3),X2) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_850 ).

fof(c_0_2023,axiom,
    ! [X2,X3] :
      ( class_Rings_Omult__zero(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Ozero__class_Ozero(X3),X2) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_851 ).

fof(c_0_2024,axiom,
    ! [X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => ( X2 != c_Groups_Ozero__class_Ozero(X3)
       => c_Divides_Odiv__class_Odiv(X3,X2,X2) = c_Groups_Oone__class_Oone(X3) ) ),
    c_0_852 ).

fof(c_0_2025,plain,
    ! [X20] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) ),
    inference(fof_simplification,[status(thm)],[c_0_853]) ).

fof(c_0_2026,axiom,
    ! [X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Odiv(X3,X2,c_Groups_Oone__class_Oone(X3)) = X2 ),
    c_0_854 ).

fof(c_0_2027,axiom,
    ! [X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
    c_0_855 ).

fof(c_0_2028,axiom,
    ! [X2,X3] :
      ( class_Power_Opower(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X3) ),
    c_0_856 ).

fof(c_0_2029,axiom,
    ! [X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X3) ),
    c_0_857 ).

fof(c_0_2030,axiom,
    ! [X2,X3] :
      ( class_Groups_Ocomm__monoid__mult(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Oone__class_Oone(X3)) = X2 ),
    c_0_858 ).

fof(c_0_2031,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Oone__class_Oone(X3)) = X2 ),
    c_0_859 ).

fof(c_0_2032,axiom,
    ! [X2,X3] :
      ( class_Groups_Ocomm__monoid__mult(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oone__class_Oone(X3),X2) = X2 ),
    c_0_860 ).

fof(c_0_2033,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oone__class_Oone(X3),X2) = X2 ),
    c_0_861 ).

fof(c_0_2034,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Oone__class_Oone(X3)) = X2 ),
    c_0_862 ).

fof(c_0_2035,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Otimes__class_Otimes(X3,c_Groups_Oone__class_Oone(X3),X2) = X2 ),
    c_0_863 ).

fof(c_0_2036,axiom,
    ! [X2,X3] :
      ( class_Groups_Ogroup__add(X3)
     => c_Groups_Ominus__class_Ominus(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
    c_0_864 ).

fof(c_0_2037,axiom,
    ! [X2,X3] :
      ( class_Groups_Ocomm__monoid__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
    c_0_865 ).

fof(c_0_2038,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
    c_0_866 ).

fof(c_0_2039,axiom,
    ! [X2,X3] :
      ( class_Groups_Ocomm__monoid__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X2) = X2 ),
    c_0_867 ).

fof(c_0_2040,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__add(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X2) = X2 ),
    c_0_868 ).

fof(c_0_2041,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X2) = X2 ),
    c_0_869 ).

fof(c_0_2042,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
    c_0_870 ).

fof(c_0_2043,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Rings_Odvd__class_Odvd(X3,c_Groups_Oone__class_Oone(X3),X2) ),
    c_0_871 ).

fof(c_0_2044,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Ozero__class_Ozero(X3)) ),
    c_0_872 ).

fof(c_0_2045,axiom,
    ! [X19] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_873 ).

fof(c_0_2046,axiom,
    ! [X2,X3] :
      ( class_Divides_Osemiring__div(X3)
     => c_Divides_Odiv__class_Omod(X3,X2,X2) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_874 ).

fof(c_0_2047,axiom,
    ! [X2,X3] :
      ( class_Groups_Omonoid__mult(X3)
     => c_Power_Opower__class_Opower(X3,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2 ),
    c_0_875 ).

fof(c_0_2048,axiom,
    ! [X23,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Power_Opower__class_Opower(X3,X23,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X23 ),
    c_0_876 ).

fof(c_0_2049,plain,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => ~ c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin)) ),
    inference(fof_simplification,[status(thm)],[c_0_877]) ).

fof(c_0_2050,axiom,
    ! [X2,X3] :
      ( class_Groups_Ogroup__add(X3)
     => c_Groups_Ominus__class_Ominus(X3,X2,X2) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_878 ).

fof(c_0_2051,axiom,
    ! [X7] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7),
    c_0_879 ).

fof(c_0_2052,axiom,
    ! [X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20,
    c_0_880 ).

fof(c_0_2053,axiom,
    ! [X20] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X20)),
    c_0_881 ).

fof(c_0_2054,axiom,
    ! [X2,X3] :
      ( class_Rings_Ocomm__semiring__1(X3)
     => c_Rings_Odvd__class_Odvd(X3,X2,X2) ),
    c_0_882 ).

fof(c_0_2055,axiom,
    ! [X14,X15,X3] :
      ( ( class_Int_Onumber__ring(X3)
        & class_Int_Oring__char__0(X3) )
     => ( c_Int_Onumber__class_Onumber__of(X3,X15) = c_Int_Onumber__class_Onumber__of(X3,X14)
      <=> X15 = X14 ) ),
    c_0_883 ).

fof(c_0_2056,axiom,
    ! [X20] : c_Nat_OSuc(X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X20),
    c_0_884 ).

fof(c_0_2057,axiom,
    ! [X20] : c_Nat_OSuc(X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    c_0_885 ).

fof(c_0_2058,axiom,
    ! [X20] :
      ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) ),
    c_0_886 ).

fof(c_0_2059,axiom,
    ! [X2] :
      ( X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    c_0_887 ).

fof(c_0_2060,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    c_0_888 ).

fof(c_0_2061,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    c_0_889 ).

fof(c_0_2062,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    c_0_890 ).

fof(c_0_2063,axiom,
    ! [X20] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(X20)),
    c_0_891 ).

fof(c_0_2064,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    c_0_892 ).

fof(c_0_2065,axiom,
    ! [X2] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      & c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X2 ),
    c_0_893 ).

fof(c_0_2066,axiom,
    ! [X21] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_894 ).

fof(c_0_2067,axiom,
    ! [X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_895 ).

fof(c_0_2068,axiom,
    ! [X20] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_896 ).

fof(c_0_2069,axiom,
    ! [X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_897 ).

fof(c_0_2070,axiom,
    ! [X20] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20,
    c_0_898 ).

fof(c_0_2071,axiom,
    ! [X20] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X20) = X20,
    c_0_899 ).

fof(c_0_2072,axiom,
    ! [X10] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X10) = X10,
    c_0_900 ).

fof(c_0_2073,axiom,
    ! [X10] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10) = X10,
    c_0_901 ).

fof(c_0_2074,axiom,
    ! [X10] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X10,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X10,
    c_0_902 ).

fof(c_0_2075,axiom,
    ! [X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
    c_0_903 ).

fof(c_0_2076,axiom,
    ! [X7] : c_Int_OBit0(X7) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X7),
    c_0_904 ).

fof(c_0_2077,axiom,
    ! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X10,
    c_0_905 ).

fof(c_0_2078,axiom,
    ! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10) = X10,
    c_0_906 ).

fof(c_0_2079,axiom,
    ! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) = X20,
    c_0_907 ).

fof(c_0_2080,axiom,
    ! [X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
    c_0_908 ).

fof(c_0_2081,axiom,
    ! [X20,X19] :
      ( X19 = X20
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
    c_0_909 ).

fof(c_0_2082,axiom,
    ! [X22,X23] :
      ( X23 = X22
     => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ),
    c_0_910 ).

fof(c_0_2083,axiom,
    ! [X23] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X23),
    c_0_911 ).

fof(c_0_2084,axiom,
    ! [X23] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_912 ).

fof(c_0_2085,axiom,
    ! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20),
    c_0_913 ).

fof(c_0_2086,axiom,
    ! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20),
    c_0_914 ).

fof(c_0_2087,axiom,
    ! [X2] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_915 ).

fof(c_0_2088,axiom,
    ! [X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_916 ).

fof(c_0_2089,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    c_0_917 ).

fof(c_0_2090,axiom,
    ! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X20),
    c_0_918 ).

fof(c_0_2091,axiom,
    ! [X8] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X8),
    c_0_919 ).

fof(c_0_2092,axiom,
    ! [X8] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X8),
    c_0_920 ).

fof(c_0_2093,axiom,
    ! [X23] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X23),
    c_0_921 ).

fof(c_0_2094,axiom,
    ! [X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,c_Int_OPls) = X7,
    c_0_922 ).

fof(c_0_2095,axiom,
    ! [X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X7) = X7,
    c_0_923 ).

fof(c_0_2096,axiom,
    ! [X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,c_Int_OPls) = X7,
    c_0_924 ).

fof(c_0_2097,axiom,
    ! [X8] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,X8) = c_Int_OPls,
    c_0_925 ).

fof(c_0_2098,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
    c_0_926 ).

fof(c_0_2099,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    c_0_927 ).

fof(c_0_2100,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
    c_0_928 ).

fof(c_0_2101,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
    c_0_929 ).

fof(c_0_2102,plain,
    ! [X15] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X15))
    <=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15) ),
    inference(fof_simplification,[status(thm)],[c_0_930]) ).

fof(c_0_2103,axiom,
    ! [X15,X16,X3] :
      ( class_Int_Onumber(X3)
     => ( c_Int_Onumber__class_Onumber__of(X3,X16) = X15
      <=> X15 = c_Int_Onumber__class_Onumber__of(X3,X16) ) ),
    c_0_931 ).

fof(c_0_2104,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls)) ),
    c_0_932 ).

fof(c_0_2105,axiom,
    c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    c_0_933 ).

fof(c_0_2106,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    c_0_934 ).

fof(c_0_2107,plain,
    ! [X3] :
      ( class_Rings_Osemiring__1(X3)
     => ~ c_Int_Oiszero(X3,c_Groups_Oone__class_Oone(X3)) ),
    inference(fof_simplification,[status(thm)],[c_0_935]) ).

fof(c_0_2108,axiom,
    ! [X46,X3] :
      ( class_Rings_Osemiring__1(X3)
     => ( c_Int_Oiszero(X3,X46)
      <=> X46 = c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_936 ).

fof(c_0_2109,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),
    c_0_937 ).

fof(c_0_2110,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X3) ),
    c_0_938 ).

fof(c_0_2111,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Oone__class_Oone(X3) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls)) ),
    c_0_939 ).

fof(c_0_2112,axiom,
    ! [X3] :
      ( class_Rings_Osemiring__1(X3)
     => c_Int_Oiszero(X3,c_Groups_Ozero__class_Ozero(X3)) ),
    c_0_940 ).

fof(c_0_2113,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_simplification,[status(thm)],[c_0_941]) ).

fof(c_0_2114,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_simplification,[status(thm)],[c_0_942]) ).

fof(c_0_2115,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Groups_Ozero__class_Ozero(X3) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls) ),
    c_0_943 ).

fof(c_0_2116,axiom,
    ! [X3] :
      ( class_Int_Onumber__ring(X3)
     => c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X3) ),
    c_0_944 ).

fof(c_0_2117,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_945 ).

fof(c_0_2118,axiom,
    ! [X15,X3] :
      ( class_Groups_Oone(X3)
     => ( c_Groups_Oone__class_Oone(X3) = X15
      <=> X15 = c_Groups_Oone__class_Oone(X3) ) ),
    c_0_946 ).

fof(c_0_2119,axiom,
    ! [X15,X3] :
      ( class_Groups_Ozero(X3)
     => ( c_Groups_Ozero__class_Ozero(X3) = X15
      <=> X15 = c_Groups_Ozero__class_Ozero(X3) ) ),
    c_0_947 ).

fof(c_0_2120,axiom,
    ! [X3] :
      ( class_Rings_Ozero__neq__one(X3)
     => c_Groups_Oone__class_Oone(X3) != c_Groups_Ozero__class_Ozero(X3) ),
    c_0_948 ).

fof(c_0_2121,axiom,
    ! [X3] :
      ( class_Rings_Ozero__neq__one(X3)
     => c_Groups_Ozero__class_Ozero(X3) != c_Groups_Oone__class_Oone(X3) ),
    c_0_949 ).

fof(c_0_2122,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
    c_0_950 ).

fof(c_0_2123,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    c_0_951 ).

fof(c_0_2124,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
    c_0_952 ).

fof(c_0_2125,axiom,
    c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    c_0_953 ).

fof(c_0_2126,axiom,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_954 ).

fof(c_0_2127,axiom,
    ! [X22,X23] :
      ( c_Nat_OSuc(X23) = c_Nat_OSuc(X22)
     => X23 = X22 ),
    c_0_955 ).

fof(c_0_2128,axiom,
    ! [X36,X37] :
      ( c_Nat_OSuc(X37) = c_Nat_OSuc(X36)
    <=> X37 = X36 ),
    c_0_956 ).

fof(c_0_2129,axiom,
    ! [X4,X5] :
      ( c_Int_OBit0(X5) = c_Int_OBit0(X4)
    <=> X5 = X4 ),
    c_0_957 ).

fof(c_0_2130,axiom,
    ! [X4,X5] :
      ( c_Int_OBit1(X5) = c_Int_OBit1(X4)
    <=> X5 = X4 ),
    c_0_958 ).

fof(c_0_2131,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
    c_0_959 ).

fof(c_0_2132,axiom,
    ! [X7] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X7) = X7,
    c_0_960 ).

fof(c_0_2133,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
    c_0_961 ).

fof(c_0_2134,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_962 ).

fof(c_0_2135,axiom,
    ! [X6,X7] : c_Int_OBit1(X7) != c_Int_OBit0(X6),
    c_0_963 ).

fof(c_0_2136,axiom,
    ! [X6,X7] : c_Int_OBit0(X7) != c_Int_OBit1(X6),
    c_0_964 ).

fof(c_0_2137,axiom,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    c_0_965 ).

fof(c_0_2138,axiom,
    ! [X19] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X19),
    c_0_966 ).

fof(c_0_2139,axiom,
    ! [X48] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X48),
    c_0_967 ).

fof(c_0_2140,axiom,
    ! [X19] : c_Nat_OSuc(X19) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_968 ).

fof(c_0_2141,axiom,
    ! [X47] : c_Nat_OSuc(X47) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_969 ).

fof(c_0_2142,axiom,
    ! [X19] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X19),
    c_0_970 ).

fof(c_0_2143,axiom,
    ! [X19] : c_Nat_OSuc(X19) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_971 ).

fof(c_0_2144,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_972 ).

fof(c_0_2145,axiom,
    ! [X5] :
      ( c_Int_OBit1(X5) = c_Int_OMin
    <=> X5 = c_Int_OMin ),
    c_0_973 ).

fof(c_0_2146,axiom,
    ! [X4] :
      ( c_Int_OMin = c_Int_OBit1(X4)
    <=> c_Int_OMin = X4 ),
    c_0_974 ).

fof(c_0_2147,axiom,
    ! [X5] :
      ( c_Int_OBit0(X5) = c_Int_OPls
    <=> X5 = c_Int_OPls ),
    c_0_975 ).

fof(c_0_2148,axiom,
    ! [X4] :
      ( c_Int_OPls = c_Int_OBit0(X4)
    <=> c_Int_OPls = X4 ),
    c_0_976 ).

fof(c_0_2149,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    c_0_977 ).

fof(c_0_2150,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    c_0_978 ).

fof(c_0_2151,axiom,
    ! [X20] : c_Nat_OSuc(X20) != X20,
    c_0_979 ).

fof(c_0_2152,axiom,
    ! [X20] : X20 != c_Nat_OSuc(X20),
    c_0_980 ).

fof(c_0_2153,axiom,
    ! [X7] : c_Int_OBit0(X7) != c_Int_OMin,
    c_0_981 ).

fof(c_0_2154,axiom,
    ! [X6] : c_Int_OMin != c_Int_OBit0(X6),
    c_0_982 ).

fof(c_0_2155,axiom,
    ! [X7] : c_Int_OBit1(X7) != c_Int_OPls,
    c_0_983 ).

fof(c_0_2156,axiom,
    ! [X6] : c_Int_OPls != c_Int_OBit1(X6),
    c_0_984 ).

fof(c_0_2157,axiom,
    v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_985 ).

fof(c_0_2158,axiom,
    v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_986 ).

fof(c_0_2159,axiom,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    c_0_987 ).

fof(c_0_2160,axiom,
    class_Groups_Oone(tc_Complex_Ocomplex),
    c_0_988 ).

fof(c_0_2161,axiom,
    class_Int_Onumber(tc_Complex_Ocomplex),
    c_0_989 ).

fof(c_0_2162,axiom,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    c_0_990 ).

fof(c_0_2163,axiom,
    class_Rings_Oring(tc_Complex_Ocomplex),
    c_0_991 ).

fof(c_0_2164,axiom,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    c_0_992 ).

fof(c_0_2165,axiom,
    class_Power_Opower(tc_Complex_Ocomplex),
    c_0_993 ).

fof(c_0_2166,axiom,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    c_0_994 ).

fof(c_0_2167,axiom,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    c_0_995 ).

fof(c_0_2168,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    c_0_996 ).

fof(c_0_2169,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    c_0_997 ).

fof(c_0_2170,axiom,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    c_0_998 ).

fof(c_0_2171,axiom,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    c_0_999 ).

fof(c_0_2172,axiom,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    c_0_1000 ).

fof(c_0_2173,axiom,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    c_0_1001 ).

fof(c_0_2174,axiom,
    class_Rings_Osemiring__1(tc_Complex_Ocomplex),
    c_0_1002 ).

fof(c_0_2175,axiom,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    c_0_1003 ).

fof(c_0_2176,axiom,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    c_0_1004 ).

fof(c_0_2177,axiom,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    c_0_1005 ).

fof(c_0_2178,axiom,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    c_0_1006 ).

fof(c_0_2179,axiom,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    c_0_1007 ).

fof(c_0_2180,axiom,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    c_0_1008 ).

fof(c_0_2181,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    c_0_1009 ).

fof(c_0_2182,axiom,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    c_0_1010 ).

fof(c_0_2183,axiom,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    c_0_1011 ).

fof(c_0_2184,axiom,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    c_0_1012 ).

fof(c_0_2185,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    c_0_1013 ).

fof(c_0_2186,axiom,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    c_0_1014 ).

fof(c_0_2187,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    c_0_1015 ).

fof(c_0_2188,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    c_0_1016 ).

fof(c_0_2189,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    c_0_1017 ).

fof(c_0_2190,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    c_0_1018 ).

fof(c_0_2191,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    c_0_1019 ).

fof(c_0_2192,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    c_0_1020 ).

fof(c_0_2193,axiom,
    class_Rings_Odvd(tc_RealDef_Oreal),
    c_0_1021 ).

fof(c_0_2194,axiom,
    class_Groups_Oone(tc_RealDef_Oreal),
    c_0_1022 ).

fof(c_0_2195,axiom,
    class_Int_Onumber(tc_RealDef_Oreal),
    c_0_1023 ).

fof(c_0_2196,axiom,
    class_Rings_Oidom(tc_RealDef_Oreal),
    c_0_1024 ).

fof(c_0_2197,axiom,
    class_Rings_Oring(tc_RealDef_Oreal),
    c_0_1025 ).

fof(c_0_2198,axiom,
    class_Groups_Ozero(tc_RealDef_Oreal),
    c_0_1026 ).

fof(c_0_2199,axiom,
    class_Power_Opower(tc_RealDef_Oreal),
    c_0_1027 ).

fof(c_0_2200,axiom,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    c_0_1028 ).

fof(c_0_2201,axiom,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    c_0_1029 ).

fof(c_0_2202,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    c_0_1030 ).

fof(c_0_2203,axiom,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    c_0_1031 ).

fof(c_0_2204,axiom,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    c_0_1032 ).

fof(c_0_2205,axiom,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    c_0_1033 ).

fof(c_0_2206,axiom,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    c_0_1034 ).

fof(c_0_2207,axiom,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    c_0_1035 ).

fof(c_0_2208,axiom,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    c_0_1036 ).

fof(c_0_2209,axiom,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    c_0_1037 ).

fof(c_0_2210,axiom,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    c_0_1038 ).

fof(c_0_2211,axiom,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    c_0_1039 ).

fof(c_0_2212,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    c_0_1040 ).

fof(c_0_2213,axiom,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    c_0_1041 ).

fof(c_0_2214,axiom,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    c_0_1042 ).

fof(c_0_2215,axiom,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    c_0_1043 ).

fof(c_0_2216,axiom,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    c_0_1044 ).

fof(c_0_2217,axiom,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    c_0_1045 ).

fof(c_0_2218,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    c_0_1046 ).

fof(c_0_2219,axiom,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    c_0_1047 ).

fof(c_0_2220,axiom,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    c_0_1048 ).

fof(c_0_2221,axiom,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    c_0_1049 ).

fof(c_0_2222,axiom,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    c_0_1050 ).

fof(c_0_2223,axiom,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    c_0_1051 ).

fof(c_0_2224,axiom,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    c_0_1052 ).

fof(c_0_2225,axiom,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    c_0_1053 ).

fof(c_0_2226,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    c_0_1054 ).

fof(c_0_2227,axiom,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    c_0_1055 ).

fof(c_0_2228,axiom,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    c_0_1056 ).

fof(c_0_2229,axiom,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    c_0_1057 ).

fof(c_0_2230,axiom,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    c_0_1058 ).

fof(c_0_2231,axiom,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    c_0_1059 ).

fof(c_0_2232,axiom,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    c_0_1060 ).

fof(c_0_2233,axiom,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    c_0_1061 ).

fof(c_0_2234,axiom,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    c_0_1062 ).

fof(c_0_2235,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    c_0_1063 ).

fof(c_0_2236,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    c_0_1064 ).

fof(c_0_2237,axiom,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    c_0_1065 ).

fof(c_0_2238,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    c_0_1066 ).

fof(c_0_2239,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    c_0_1067 ).

fof(c_0_2240,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    c_0_1068 ).

fof(c_0_2241,axiom,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    c_0_1069 ).

fof(c_0_2242,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    c_0_1070 ).

fof(c_0_2243,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    c_0_1071 ).

fof(c_0_2244,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    c_0_1072 ).

fof(c_0_2245,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    c_0_1073 ).

fof(c_0_2246,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    c_0_1074 ).

fof(c_0_2247,axiom,
    class_Rings_Odvd(tc_Nat_Onat),
    c_0_1075 ).

fof(c_0_2248,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    c_0_1076 ).

fof(c_0_2249,axiom,
    class_Int_Onumber(tc_Nat_Onat),
    c_0_1077 ).

fof(c_0_2250,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    c_0_1078 ).

fof(c_0_2251,axiom,
    class_Power_Opower(tc_Nat_Onat),
    c_0_1079 ).

fof(c_0_2252,axiom,
    class_Rings_Osemiring(tc_Nat_Onat),
    c_0_1080 ).

fof(c_0_2253,axiom,
    class_Rings_Omult__zero(tc_Nat_Onat),
    c_0_1081 ).

fof(c_0_2254,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    c_0_1082 ).

fof(c_0_2255,axiom,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    c_0_1083 ).

fof(c_0_2256,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    c_0_1084 ).

fof(c_0_2257,axiom,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    c_0_1085 ).

fof(c_0_2258,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    c_0_1086 ).

fof(c_0_2259,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    c_0_1087 ).

fof(c_0_2260,axiom,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    c_0_1088 ).

fof(c_0_2261,axiom,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    c_0_1089 ).

fof(c_0_2262,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    c_0_1090 ).

fof(c_0_2263,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    c_0_1091 ).

fof(c_0_2264,axiom,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    c_0_1092 ).

fof(c_0_2265,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    c_0_1093 ).

fof(c_0_2266,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    c_0_1094 ).

fof(c_0_2267,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    c_0_1095 ).

fof(c_0_2268,axiom,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    c_0_1096 ).

fof(c_0_2269,axiom,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    c_0_1097 ).

fof(c_0_2270,axiom,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    c_0_1098 ).

fof(c_0_2271,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    c_0_1099 ).

fof(c_0_2272,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    c_0_1100 ).

fof(c_0_2273,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    c_0_1101 ).

fof(c_0_2274,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    c_0_1102 ).

fof(c_0_2275,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    c_0_1103 ).

fof(c_0_2276,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    c_0_1104 ).

fof(c_0_2277,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    c_0_1105 ).

fof(c_0_2278,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    c_0_1106 ).

fof(c_0_2279,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    c_0_1107 ).

fof(c_0_2280,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    c_0_1108 ).

fof(c_0_2281,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    c_0_1109 ).

fof(c_0_2282,axiom,
    class_Rings_Odvd(tc_Int_Oint),
    c_0_1110 ).

fof(c_0_2283,axiom,
    class_Groups_Oone(tc_Int_Oint),
    c_0_1111 ).

fof(c_0_2284,axiom,
    class_Int_Onumber(tc_Int_Oint),
    c_0_1112 ).

fof(c_0_2285,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    c_0_1113 ).

fof(c_0_2286,axiom,
    class_Rings_Oring(tc_Int_Oint),
    c_0_1114 ).

fof(c_0_2287,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    c_0_1115 ).

fof(c_0_2288,axiom,
    class_Power_Opower(tc_Int_Oint),
    c_0_1116 ).

fof(c_0_2289,axiom,
    class_Rings_Oring__1(tc_Int_Oint),
    c_0_1117 ).

fof(c_0_2290,axiom,
    class_Rings_Osemiring(tc_Int_Oint),
    c_0_1118 ).

fof(c_0_2291,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    c_0_1119 ).

fof(c_0_2292,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    c_0_1120 ).

fof(c_0_2293,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    c_0_1121 ).

fof(c_0_2294,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    c_0_1122 ).

fof(c_0_2295,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    c_0_1123 ).

fof(c_0_2296,axiom,
    class_Groups_Ogroup__add(tc_Int_Oint),
    c_0_1124 ).

fof(c_0_2297,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    c_0_1125 ).

fof(c_0_2298,axiom,
    class_Rings_Osemiring__1(tc_Int_Oint),
    c_0_1126 ).

fof(c_0_2299,axiom,
    class_Groups_Omonoid__add(tc_Int_Oint),
    c_0_1127 ).

fof(c_0_2300,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    c_0_1128 ).

fof(c_0_2301,axiom,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    c_0_1129 ).

fof(c_0_2302,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    c_0_1130 ).

fof(c_0_2303,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    c_0_1131 ).

fof(c_0_2304,axiom,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    c_0_1132 ).

fof(c_0_2305,axiom,
    class_Groups_Oab__group__add(tc_Int_Oint),
    c_0_1133 ).

fof(c_0_2306,axiom,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    c_0_1134 ).

fof(c_0_2307,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    c_0_1135 ).

fof(c_0_2308,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    c_0_1136 ).

fof(c_0_2309,axiom,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    c_0_1137 ).

fof(c_0_2310,axiom,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    c_0_1138 ).

fof(c_0_2311,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    c_0_1139 ).

fof(c_0_2312,axiom,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    c_0_1140 ).

fof(c_0_2313,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    c_0_1141 ).

fof(c_0_2314,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    c_0_1142 ).

fof(c_0_2315,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    c_0_1143 ).

fof(c_0_2316,axiom,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    c_0_1144 ).

fof(c_0_2317,axiom,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    c_0_1145 ).

fof(c_0_2318,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    c_0_1146 ).

fof(c_0_2319,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    c_0_1147 ).

fof(c_0_2320,axiom,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    c_0_1148 ).

fof(c_0_2321,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    c_0_1149 ).

fof(c_0_2322,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    c_0_1150 ).

fof(c_0_2323,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    c_0_1151 ).

fof(c_0_2324,axiom,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    c_0_1152 ).

fof(c_0_2325,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    c_0_1153 ).

fof(c_0_2326,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    c_0_1154 ).

fof(c_0_2327,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    c_0_1155 ).

fof(c_0_2328,axiom,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    c_0_1156 ).

fof(c_0_2329,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    c_0_1157 ).

fof(c_0_2330,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    c_0_1158 ).

fof(c_0_2331,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    c_0_1159 ).

fof(c_0_2332,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    c_0_1160 ).

fof(c_0_2333,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    c_0_1161 ).

fof(c_0_2334,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    c_0_1162 ).

fof(c_0_2335,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    c_0_1163 ).

fof(c_0_2336,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    c_0_1164 ).

fof(c_0_2337,axiom,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    c_0_1165 ).

fof(c_0_2338,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_1166 ).

fof(c_0_2339,axiom,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    c_0_1167 ).

fof(c_0_2340,axiom,
    c_Int_OPls != c_Int_OMin,
    c_0_1168 ).

fof(c_0_2341,axiom,
    c_Int_OMin != c_Int_OPls,
    c_0_1169 ).

fof(c_0_2342,plain,
    ! [X24,X25,X26,X27,X28] :
      ( ~ class_RealVector_Oreal__normed__algebra(X28)
      | c_Groups_Ominus__class_Ominus(X28,c_Groups_Otimes__class_Otimes(X28,X27,X26),c_Groups_Otimes__class_Otimes(X28,X25,X24)) = c_Groups_Oplus__class_Oplus(X28,c_Groups_Oplus__class_Oplus(X28,c_Groups_Otimes__class_Otimes(X28,c_Groups_Ominus__class_Ominus(X28,X27,X25),c_Groups_Ominus__class_Ominus(X28,X26,X24)),c_Groups_Otimes__class_Otimes(X28,c_Groups_Ominus__class_Ominus(X28,X27,X25),X24)),c_Groups_Otimes__class_Otimes(X28,X25,c_Groups_Ominus__class_Ominus(X28,X26,X24))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1171])]) ).

fof(c_0_2343,plain,
    ! [X69,X70,X71,X72,X73] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X73,X71),X70),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X72,X71),X69))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X70,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X73),X71),X69))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X70,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X73),X71),X69))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X73,X71),X70),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X72,X71),X69))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1172])])]) ).

fof(c_0_2344,plain,
    ! [X69,X70,X71,X72,X73] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X72,X71),X70),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X73,X71),X69))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X73),X71),X70),X69)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X73),X71),X70),X69)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X72,X71),X70),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X73,X71),X69))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1173])])]) ).

fof(c_0_2345,plain,
    ! [X69,X70,X71,X72,X73] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X73,X71),X70),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X72,X71),X69))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X70,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X73),X71),X69))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X70,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X73),X71),X69))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X73,X71),X70),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X72,X71),X69))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1174])])]) ).

fof(c_0_2346,plain,
    ! [X69,X70,X71,X72,X73] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X72,X71),X70),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X73,X71),X69))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X73),X71),X70),X69)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X73),X71),X70),X69)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X72,X71),X70),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X73,X71),X69))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1175])])]) ).

fof(c_0_2347,plain,
    ! [X68,X69,X70,X71,X72,X73] :
      ( ( ~ c_Orderings_Oord__class_Oless(X73,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X72,X71),X70),c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X69,X71),X68))
        | c_Orderings_Oord__class_Oless(X73,X70,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,c_Groups_Ominus__class_Ominus(X73,X69,X72),X71),X68))
        | ~ class_Rings_Oordered__ring(X73) )
      & ( ~ c_Orderings_Oord__class_Oless(X73,X70,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,c_Groups_Ominus__class_Ominus(X73,X69,X72),X71),X68))
        | c_Orderings_Oord__class_Oless(X73,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X72,X71),X70),c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X69,X71),X68))
        | ~ class_Rings_Oordered__ring(X73) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1176])])]) ).

fof(c_0_2348,plain,
    ! [X68,X69,X70,X71,X72,X73] :
      ( ( ~ c_Orderings_Oord__class_Oless(X73,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X72,X71),X70),c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X69,X71),X68))
        | c_Orderings_Oord__class_Oless(X73,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,c_Groups_Ominus__class_Ominus(X73,X72,X69),X71),X70),X68)
        | ~ class_Rings_Oordered__ring(X73) )
      & ( ~ c_Orderings_Oord__class_Oless(X73,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,c_Groups_Ominus__class_Ominus(X73,X72,X69),X71),X70),X68)
        | c_Orderings_Oord__class_Oless(X73,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X72,X71),X70),c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X69,X71),X68))
        | ~ class_Rings_Oordered__ring(X73) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1177])])]) ).

fof(c_0_2349,plain,
    ! [X68,X69,X70,X71,X72,X73] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X73,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X72,X71),X70),c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X69,X71),X68))
        | c_Orderings_Oord__class_Oless__eq(X73,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,c_Groups_Ominus__class_Ominus(X73,X72,X69),X71),X70),X68)
        | ~ class_Rings_Oordered__ring(X73) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X73,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,c_Groups_Ominus__class_Ominus(X73,X72,X69),X71),X70),X68)
        | c_Orderings_Oord__class_Oless__eq(X73,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X72,X71),X70),c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X69,X71),X68))
        | ~ class_Rings_Oordered__ring(X73) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1178])])]) ).

fof(c_0_2350,plain,
    ! [X68,X69,X70,X71,X72,X73] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X73,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X72,X71),X70),c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X69,X71),X68))
        | c_Orderings_Oord__class_Oless__eq(X73,X70,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,c_Groups_Ominus__class_Ominus(X73,X69,X72),X71),X68))
        | ~ class_Rings_Oordered__ring(X73) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X73,X70,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,c_Groups_Ominus__class_Ominus(X73,X69,X72),X71),X68))
        | c_Orderings_Oord__class_Oless__eq(X73,c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X72,X71),X70),c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X69,X71),X68))
        | ~ class_Rings_Oordered__ring(X73) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1179])])]) ).

fof(c_0_2351,plain,
    ! [X34,X35,X36] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X36,X35),X34) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X36,X34),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X35,X34)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X36,X34),c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X34)),X34)),
    inference(variable_rename,[status(thm)],[c_0_1180]) ).

fof(c_0_2352,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X22)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,c_Groups_Oone__class_Oone(tc_Int_Oint)),X23)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1181])]) ).

fof(c_0_2353,plain,
    ! [X24,X25,X26] :
      ( ~ class_Int_Onumber__ring(X26)
      | c_Power_Opower__class_Opower(X26,c_Groups_Ominus__class_Ominus(X26,X25,X24),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(X26,c_Groups_Oplus__class_Oplus(X26,c_Power_Opower__class_Opower(X26,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X26,X24,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X26,c_Groups_Otimes__class_Otimes(X26,c_Int_Onumber__class_Onumber__of(X26,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X25),X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1182])]) ).

fof(c_0_2354,plain,
    ! [X24,X25,X26] :
      ( ~ class_Int_Onumber__ring(X26)
      | c_Power_Opower__class_Opower(X26,c_Groups_Oplus__class_Oplus(X26,X25,X24),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X26,c_Groups_Oplus__class_Oplus(X26,c_Power_Opower__class_Opower(X26,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X26,X24,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X26,c_Groups_Otimes__class_Otimes(X26,c_Int_Onumber__class_Onumber__of(X26,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X25),X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1183])]) ).

fof(c_0_2355,plain,
    ! [X24,X25] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X25,X24),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X24,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X25),X24)),
    inference(variable_rename,[status(thm)],[c_0_1184]) ).

fof(c_0_2356,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__idom(X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Ozero__class_Ozero(X23),c_Power_Opower__class_Opower(X23,X22,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21))))
      | c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Ozero__class_Ozero(X23),X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1185])]) ).

fof(c_0_2357,plain,
    ! [X16,X17,X18] :
      ( ( ~ c_Orderings_Oord__class_Oless(X18,c_Groups_Ozero__class_Ozero(X18),c_Groups_Oplus__class_Oplus(X18,c_Power_Opower__class_Opower(X18,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X18,X16,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | X17 != c_Groups_Ozero__class_Ozero(X18)
        | X16 != c_Groups_Ozero__class_Ozero(X18)
        | ~ class_Rings_Olinordered__idom(X18) )
      & ( X17 = c_Groups_Ozero__class_Ozero(X18)
        | c_Orderings_Oord__class_Oless(X18,c_Groups_Ozero__class_Ozero(X18),c_Groups_Oplus__class_Oplus(X18,c_Power_Opower__class_Opower(X18,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X18,X16,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ class_Rings_Olinordered__idom(X18) )
      & ( X16 = c_Groups_Ozero__class_Ozero(X18)
        | c_Orderings_Oord__class_Oless(X18,c_Groups_Ozero__class_Ozero(X18),c_Groups_Oplus__class_Oplus(X18,c_Power_Opower__class_Opower(X18,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X18,X16,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ class_Rings_Olinordered__idom(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1186])])]) ).

fof(c_0_2358,plain,
    ! [X16,X17,X18] :
      ( ( X17 = c_Groups_Ozero__class_Ozero(X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X18,c_Groups_Oplus__class_Oplus(X18,c_Power_Opower__class_Opower(X18,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X18,X16,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X18))
        | ~ class_Rings_Olinordered__idom(X18) )
      & ( X16 = c_Groups_Ozero__class_Ozero(X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X18,c_Groups_Oplus__class_Oplus(X18,c_Power_Opower__class_Opower(X18,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X18,X16,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X18))
        | ~ class_Rings_Olinordered__idom(X18) )
      & ( X17 != c_Groups_Ozero__class_Ozero(X18)
        | X16 != c_Groups_Ozero__class_Ozero(X18)
        | c_Orderings_Oord__class_Oless__eq(X18,c_Groups_Oplus__class_Oplus(X18,c_Power_Opower__class_Opower(X18,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X18,X16,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X18))
        | ~ class_Rings_Olinordered__idom(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1187])])]) ).

fof(c_0_2359,plain,
    ! [X54,X55,X56,X57,X58] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X58,X57)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X58,X56),X55),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X57,X56),X54)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X57,X58),X56),X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1188])]) ).

fof(c_0_2360,plain,
    ! [X54,X55,X56,X57,X58] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X58,X57)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X57,X56),X55),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X58,X56),X54)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X57,X58),X56),X55),X54) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1189])]) ).

fof(c_0_2361,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Olinordered__idom(X26)
      | ~ c_Orderings_Oord__class_Oless(X26,c_Groups_Oplus__class_Oplus(X26,c_Power_Opower__class_Opower(X26,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X26,X24,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X26)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1190])]) ).

fof(c_0_2362,plain,
    ! [X73,X74,X75,X76,X77,X78,X79,X80] :
      ( ( ~ c_Rings_Odvd__class_Odvd(X76,X75,c_Groups_Oplus__class_Oplus(X76,X77,X73))
        | c_Rings_Odvd__class_Odvd(X76,X75,c_Groups_Oplus__class_Oplus(X76,c_Groups_Ominus__class_Ominus(X76,X77,c_Groups_Otimes__class_Otimes(X76,X78,X74)),X73))
        | ~ c_Rings_Odvd__class_Odvd(X76,X75,X74)
        | ~ class_Rings_Ocomm__ring(X76)
        | ~ class_Rings_Odvd(X76) )
      & ( ~ c_Rings_Odvd__class_Odvd(X76,X75,c_Groups_Oplus__class_Oplus(X76,c_Groups_Ominus__class_Ominus(X76,X79,c_Groups_Otimes__class_Otimes(X76,X80,X74)),X73))
        | c_Rings_Odvd__class_Odvd(X76,X75,c_Groups_Oplus__class_Oplus(X76,X79,X73))
        | ~ c_Rings_Odvd__class_Odvd(X76,X75,X74)
        | ~ class_Rings_Ocomm__ring(X76)
        | ~ class_Rings_Odvd(X76) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1191])])])])]) ).

fof(c_0_2363,plain,
    ! [X73,X74,X75,X76,X77,X78,X79,X80] :
      ( ( ~ c_Rings_Odvd__class_Odvd(X76,X75,c_Groups_Oplus__class_Oplus(X76,X77,X73))
        | c_Rings_Odvd__class_Odvd(X76,X75,c_Groups_Oplus__class_Oplus(X76,c_Groups_Ominus__class_Ominus(X76,X77,c_Groups_Otimes__class_Otimes(X76,X78,X74)),X73))
        | ~ c_Rings_Odvd__class_Odvd(X76,X75,X74)
        | ~ class_Rings_Ocomm__ring(X76)
        | ~ class_Rings_Odvd(X76) )
      & ( ~ c_Rings_Odvd__class_Odvd(X76,X75,c_Groups_Oplus__class_Oplus(X76,c_Groups_Ominus__class_Ominus(X76,X79,c_Groups_Otimes__class_Otimes(X76,X80,X74)),X73))
        | c_Rings_Odvd__class_Odvd(X76,X75,c_Groups_Oplus__class_Oplus(X76,X79,X73))
        | ~ c_Rings_Odvd__class_Odvd(X76,X75,X74)
        | ~ class_Rings_Ocomm__ring(X76)
        | ~ class_Rings_Odvd(X76) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1192])])])])]) ).

fof(c_0_2364,plain,
    ! [X75,X76,X77,X78,X79,X80] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X80,X79),X78) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X77,X76),X75)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X77,X76),X75))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X75,X77)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X78)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X77)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X77,X80)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X79,X76) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1193])]) ).

fof(c_0_2365,plain,
    ! [X75,X76,X77,X78,X79,X80] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X80,X79),X78) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X77,X76),X75)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X77,X76),X75),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,X80)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X75)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X77)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X77,X80)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X76,X79) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1194])]) ).

fof(c_0_2366,plain,
    ! [X58,X59,X60,X61,X62] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X62,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X60,X59))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X62,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X60,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X58,X61)),X59))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X62,X61) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X62,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X60,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X58,X61)),X59))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X62,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X60,X59))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X62,X61) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1195])])]) ).

fof(c_0_2367,plain,
    ! [X10,X11,X12,X13] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X11))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X10)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X11))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X10),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X11))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X13))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X12)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X13))) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X12),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X13))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1196])])])]) ).

fof(c_0_2368,plain,
    ! [X75,X76,X77,X78,X79] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X79,X78),X77),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X79,X76),X75))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X77)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X77,X79)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X75,X79)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X78,X76) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1197])]) ).

fof(c_0_2369,plain,
    ! [X75,X76,X77,X78,X79] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X79,X78),X77),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X79,X76),X75))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X75,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X75)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X77)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X76,X78) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1198])]) ).

fof(c_0_2370,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X22)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X23))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1199])]) ).

fof(c_0_2371,plain,
    ! [X55,X56,X57,X58] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X58)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,X56)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X56,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X57,X58),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X57,c_Divides_Odiv__class_Omod(tc_Int_Oint,X55,X58)),X56)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1200])]) ).

fof(c_0_2372,plain,
    ! [X55,X56,X57,X58] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X58)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X57)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,X56)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X56,c_Divides_Odiv__class_Omod(tc_Int_Oint,X55,X58)),X57),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X56,X58)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1201])]) ).

fof(c_0_2373,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__idom(X23)
      | ~ c_Orderings_Oord__class_Oless(X23,X22,c_Groups_Ozero__class_Ozero(X23))
      | c_Orderings_Oord__class_Oless(X23,c_Power_Opower__class_Opower(X23,X22,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21))),c_Groups_Ozero__class_Ozero(X23)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1202])]) ).

fof(c_0_2374,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Ocomm__semiring__1(X26)
      | c_Power_Opower__class_Opower(X26,X25,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X24))) = c_Groups_Otimes__class_Otimes(X26,X25,c_Groups_Otimes__class_Otimes(X26,c_Power_Opower__class_Opower(X26,X25,X24),c_Power_Opower__class_Opower(X26,X25,X24))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1203])]) ).

fof(c_0_2375,plain,
    ! [X53,X54,X55,X56,X57,X58] :
      ( ~ class_Rings_Olinordered__semiring__1__strict(X58)
      | ~ c_Orderings_Oord__class_Oless(X58,X57,X56)
      | ~ c_Orderings_Oord__class_Oless(X58,X55,X56)
      | ~ c_Orderings_Oord__class_Oless__eq(X58,c_Groups_Ozero__class_Ozero(X58),X54)
      | ~ c_Orderings_Oord__class_Oless__eq(X58,c_Groups_Ozero__class_Ozero(X58),X53)
      | c_Groups_Oplus__class_Oplus(X58,X54,X53) != c_Groups_Oone__class_Oone(X58)
      | c_Orderings_Oord__class_Oless(X58,c_Groups_Oplus__class_Oplus(X58,c_Groups_Otimes__class_Otimes(X58,X54,X57),c_Groups_Otimes__class_Otimes(X58,X53,X55)),X56) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1204])]) ).

fof(c_0_2376,plain,
    ! [X53,X54,X55,X56,X57,X58] :
      ( ~ class_Rings_Olinordered__semiring__1(X58)
      | ~ c_Orderings_Oord__class_Oless__eq(X58,X57,X56)
      | ~ c_Orderings_Oord__class_Oless__eq(X58,X55,X56)
      | ~ c_Orderings_Oord__class_Oless__eq(X58,c_Groups_Ozero__class_Ozero(X58),X54)
      | ~ c_Orderings_Oord__class_Oless__eq(X58,c_Groups_Ozero__class_Ozero(X58),X53)
      | c_Groups_Oplus__class_Oplus(X58,X54,X53) != c_Groups_Oone__class_Oone(X58)
      | c_Orderings_Oord__class_Oless__eq(X58,c_Groups_Oplus__class_Oplus(X58,c_Groups_Otimes__class_Otimes(X58,X54,X57),c_Groups_Otimes__class_Otimes(X58,X53,X55)),X56) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1205])]) ).

fof(c_0_2377,plain,
    ! [X55,X56,X57,X58] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X58)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,X56)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X56,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X57,c_Divides_Odiv__class_Omod(tc_Int_Oint,X55,X58)),X56),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1206])]) ).

fof(c_0_2378,plain,
    ! [X55,X56,X57,X58] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X58)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X57)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,X56)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X56,c_Divides_Odiv__class_Omod(tc_Int_Oint,X55,X58)),X57)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1207])]) ).

fof(c_0_2379,plain,
    ! [X78,X79,X80,X81,X82,X83,X84,X85,X86,X87] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X78)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X82)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X82,X78)
        | X79 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X78,X81),X82)
        | hBOOL(hAPP(X80,X82))
        | ~ epred1_3(X80,X79,X78) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X78,X84)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X84,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | X79 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X78,X83),X84)
        | hBOOL(hAPP(X80,X84))
        | ~ epred1_3(X80,X79,X78) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X85,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X85)
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X85,esk21_3(X85,X86,X87))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X85)
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X85,X86,X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X85)
        | epred1_3(X87,X86,X85) )
      & ( X86 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X85,esk20_3(X85,X86,X87)),esk21_3(X85,X86,X87))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X85)
        | epred1_3(X87,X86,X85) )
      & ( ~ hBOOL(hAPP(X87,esk21_3(X85,X86,X87)))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X85)
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X85,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X85,X86,X87))
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X85,esk21_3(X85,X86,X87))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X85,X86,X87))
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X85,X86,X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X85,X86,X87))
        | epred1_3(X87,X86,X85) )
      & ( X86 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X85,esk20_3(X85,X86,X87)),esk21_3(X85,X86,X87))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X85,X86,X87))
        | epred1_3(X87,X86,X85) )
      & ( ~ hBOOL(hAPP(X87,esk21_3(X85,X86,X87)))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X85,X86,X87))
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X85,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X85,X86,X87),X85)
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X85,esk21_3(X85,X86,X87))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X85,X86,X87),X85)
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X85,X86,X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X85,X86,X87),X85)
        | epred1_3(X87,X86,X85) )
      & ( X86 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X85,esk20_3(X85,X86,X87)),esk21_3(X85,X86,X87))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X85,X86,X87),X85)
        | epred1_3(X87,X86,X85) )
      & ( ~ hBOOL(hAPP(X87,esk21_3(X85,X86,X87)))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X85,X86,X87),X85)
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X85,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | X86 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X85,esk18_3(X85,X86,X87)),esk19_3(X85,X86,X87))
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X85,esk21_3(X85,X86,X87))
        | X86 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X85,esk18_3(X85,X86,X87)),esk19_3(X85,X86,X87))
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X85,X86,X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | X86 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X85,esk18_3(X85,X86,X87)),esk19_3(X85,X86,X87))
        | epred1_3(X87,X86,X85) )
      & ( X86 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X85,esk20_3(X85,X86,X87)),esk21_3(X85,X86,X87))
        | X86 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X85,esk18_3(X85,X86,X87)),esk19_3(X85,X86,X87))
        | epred1_3(X87,X86,X85) )
      & ( ~ hBOOL(hAPP(X87,esk21_3(X85,X86,X87)))
        | X86 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X85,esk18_3(X85,X86,X87)),esk19_3(X85,X86,X87))
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X85,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ hBOOL(hAPP(X87,esk19_3(X85,X86,X87)))
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X85,esk21_3(X85,X86,X87))
        | ~ hBOOL(hAPP(X87,esk19_3(X85,X86,X87)))
        | epred1_3(X87,X86,X85) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X85,X86,X87),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ hBOOL(hAPP(X87,esk19_3(X85,X86,X87)))
        | epred1_3(X87,X86,X85) )
      & ( X86 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X85,esk20_3(X85,X86,X87)),esk21_3(X85,X86,X87))
        | ~ hBOOL(hAPP(X87,esk19_3(X85,X86,X87)))
        | epred1_3(X87,X86,X85) )
      & ( ~ hBOOL(hAPP(X87,esk21_3(X85,X86,X87)))
        | ~ hBOOL(hAPP(X87,esk19_3(X85,X86,X87)))
        | epred1_3(X87,X86,X85) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1208])])])])])]) ).

fof(c_0_2380,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X22)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,c_Groups_Oone__class_Oone(tc_Int_Oint)),X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1209])]) ).

fof(c_0_2381,plain,
    ! [X57,X58,X59,X60,X62] :
      ( ( c_Rings_Odvd__class_Odvd(X59,X57,c_Groups_Oplus__class_Oplus(X59,esk7_3(X57,X58,X59),c_Groups_Ozero__class_Ozero(X59)))
        | ~ hBOOL(hAPP(X58,c_Groups_Otimes__class_Otimes(X59,X57,X60)))
        | ~ class_Rings_Odvd(X59)
        | ~ class_Rings_Osemiring__0(X59) )
      & ( hBOOL(hAPP(X58,esk7_3(X57,X58,X59)))
        | ~ hBOOL(hAPP(X58,c_Groups_Otimes__class_Otimes(X59,X57,X60)))
        | ~ class_Rings_Odvd(X59)
        | ~ class_Rings_Osemiring__0(X59) )
      & ( ~ c_Rings_Odvd__class_Odvd(X59,X57,c_Groups_Oplus__class_Oplus(X59,X62,c_Groups_Ozero__class_Ozero(X59)))
        | ~ hBOOL(hAPP(X58,X62))
        | hBOOL(hAPP(X58,c_Groups_Otimes__class_Otimes(X59,X57,esk8_3(X57,X58,X59))))
        | ~ class_Rings_Odvd(X59)
        | ~ class_Rings_Osemiring__0(X59) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1210])])])])]) ).

fof(c_0_2382,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Olinordered__idom(X26)
      | c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Ozero__class_Ozero(X26),c_Groups_Oplus__class_Oplus(X26,c_Power_Opower__class_Opower(X26,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X26,X24,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1211])]) ).

fof(c_0_2383,plain,
    ! [X69,X70,X71,X72,X73] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X73,X71),X70) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X72,X71),X69)
        | X70 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X73),X71),X69)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72) )
      & ( X70 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X73),X71),X69)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X73,X71),X70) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X72,X71),X69)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1212])])]) ).

fof(c_0_2384,plain,
    ! [X69,X70,X71,X72,X73] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X72,X71),X70) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X73,X71),X69)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X73),X71),X70) = X69
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72) )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X73),X71),X70) != X69
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X72,X71),X70) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X73,X71),X69)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X73,X72) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1213])])]) ).

fof(c_0_2385,plain,
    ! [X24,X25,X26,X27,X28] :
      ( ~ class_Rings_Oring(X28)
      | c_Groups_Ominus__class_Ominus(X28,c_Groups_Otimes__class_Otimes(X28,X27,X26),c_Groups_Otimes__class_Otimes(X28,X25,X24)) = c_Groups_Oplus__class_Oplus(X28,c_Groups_Otimes__class_Otimes(X28,X27,c_Groups_Ominus__class_Ominus(X28,X26,X24)),c_Groups_Otimes__class_Otimes(X28,c_Groups_Ominus__class_Ominus(X28,X27,X25),X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1214])]) ).

fof(c_0_2386,plain,
    ! [X16,X17,X18] :
      ( ( ~ c_Orderings_Oord__class_Oless(X18,c_Groups_Ozero__class_Ozero(X18),c_Groups_Oplus__class_Oplus(X18,c_Groups_Otimes__class_Otimes(X18,X17,X17),c_Groups_Otimes__class_Otimes(X18,X16,X16)))
        | X17 != c_Groups_Ozero__class_Ozero(X18)
        | X16 != c_Groups_Ozero__class_Ozero(X18)
        | ~ class_Rings_Olinordered__ring__strict(X18) )
      & ( X17 = c_Groups_Ozero__class_Ozero(X18)
        | c_Orderings_Oord__class_Oless(X18,c_Groups_Ozero__class_Ozero(X18),c_Groups_Oplus__class_Oplus(X18,c_Groups_Otimes__class_Otimes(X18,X17,X17),c_Groups_Otimes__class_Otimes(X18,X16,X16)))
        | ~ class_Rings_Olinordered__ring__strict(X18) )
      & ( X16 = c_Groups_Ozero__class_Ozero(X18)
        | c_Orderings_Oord__class_Oless(X18,c_Groups_Ozero__class_Ozero(X18),c_Groups_Oplus__class_Oplus(X18,c_Groups_Otimes__class_Otimes(X18,X17,X17),c_Groups_Otimes__class_Otimes(X18,X16,X16)))
        | ~ class_Rings_Olinordered__ring__strict(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1215])])]) ).

fof(c_0_2387,plain,
    ! [X16,X17,X18] :
      ( ( X17 = c_Groups_Ozero__class_Ozero(X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X18,c_Groups_Oplus__class_Oplus(X18,c_Groups_Otimes__class_Otimes(X18,X17,X17),c_Groups_Otimes__class_Otimes(X18,X16,X16)),c_Groups_Ozero__class_Ozero(X18))
        | ~ class_Rings_Olinordered__ring__strict(X18) )
      & ( X16 = c_Groups_Ozero__class_Ozero(X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X18,c_Groups_Oplus__class_Oplus(X18,c_Groups_Otimes__class_Otimes(X18,X17,X17),c_Groups_Otimes__class_Otimes(X18,X16,X16)),c_Groups_Ozero__class_Ozero(X18))
        | ~ class_Rings_Olinordered__ring__strict(X18) )
      & ( X17 != c_Groups_Ozero__class_Ozero(X18)
        | X16 != c_Groups_Ozero__class_Ozero(X18)
        | c_Orderings_Oord__class_Oless__eq(X18,c_Groups_Oplus__class_Oplus(X18,c_Groups_Otimes__class_Otimes(X18,X17,X17),c_Groups_Otimes__class_Otimes(X18,X16,X16)),c_Groups_Ozero__class_Ozero(X18))
        | ~ class_Rings_Olinordered__ring__strict(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1216])])]) ).

fof(c_0_2388,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Olinordered__ring(X26)
      | ~ c_Orderings_Oord__class_Oless(X26,c_Groups_Oplus__class_Oplus(X26,c_Groups_Otimes__class_Otimes(X26,X25,X25),c_Groups_Otimes__class_Otimes(X26,X24,X24)),c_Groups_Ozero__class_Ozero(X26)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1217])]) ).

fof(c_0_2389,plain,
    ! [X21,X22,X23] :
      ( ~ class_Groups_Omonoid__mult(X23)
      | c_Power_Opower__class_Opower(X23,X22,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21))) = c_Groups_Otimes__class_Otimes(X23,X22,c_Power_Opower__class_Opower(X23,c_Power_Opower__class_Opower(X23,X22,X21),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1218])]) ).

fof(c_0_2390,plain,
    ! [X68,X69,X70,X71,X72,X73] :
      ( ( c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X72,X71),X70) != c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X69,X71),X68)
        | X70 = c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,c_Groups_Ominus__class_Ominus(X73,X69,X72),X71),X68)
        | ~ class_Rings_Oring(X73) )
      & ( X70 != c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,c_Groups_Ominus__class_Ominus(X73,X69,X72),X71),X68)
        | c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X72,X71),X70) = c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X69,X71),X68)
        | ~ class_Rings_Oring(X73) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1219])])]) ).

fof(c_0_2391,plain,
    ! [X68,X69,X70,X71,X72,X73] :
      ( ( c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X72,X71),X70) != c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X69,X71),X68)
        | c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,c_Groups_Ominus__class_Ominus(X73,X72,X69),X71),X70) = X68
        | ~ class_Rings_Oring(X73) )
      & ( c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,c_Groups_Ominus__class_Ominus(X73,X72,X69),X71),X70) != X68
        | c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X72,X71),X70) = c_Groups_Oplus__class_Oplus(X73,c_Groups_Otimes__class_Otimes(X73,X69,X71),X68)
        | ~ class_Rings_Oring(X73) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1220])])]) ).

fof(c_0_2392,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
      | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X22)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X22,X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1221])]) ).

fof(c_0_2393,plain,
    ! [X8,X9,X10] :
      ( ~ class_Rings_Olinordered__idom(X10)
      | ~ c_Orderings_Oord__class_Oless__eq(X10,c_Power_Opower__class_Opower(X10,X9,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X8)),c_Groups_Ozero__class_Ozero(X10))
      | X9 = c_Groups_Ozero__class_Ozero(X10) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1222])]) ).

fof(c_0_2394,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Olinordered__semidom(X26)
      | ~ c_Orderings_Oord__class_Oless(X26,c_Power_Opower__class_Opower(X26,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X26,X24,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Ozero__class_Ozero(X26),X24)
      | c_Orderings_Oord__class_Oless(X26,X25,X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1223])]) ).

fof(c_0_2395,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Olinordered__semidom(X26)
      | ~ c_Orderings_Oord__class_Oless__eq(X26,c_Power_Opower__class_Opower(X26,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X26,X24,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Ozero__class_Ozero(X26),X24)
      | c_Orderings_Oord__class_Oless__eq(X26,X25,X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1224])]) ).

fof(c_0_2396,plain,
    ! [X46,X47,X48,X49,X50] :
      ( ~ class_Rings_Osemiring(X50)
      | c_Groups_Oplus__class_Oplus(X50,c_Groups_Otimes__class_Otimes(X50,X49,X48),c_Groups_Oplus__class_Oplus(X50,c_Groups_Otimes__class_Otimes(X50,X47,X48),X46)) = c_Groups_Oplus__class_Oplus(X50,c_Groups_Otimes__class_Otimes(X50,c_Groups_Oplus__class_Oplus(X50,X49,X47),X48),X46) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1225])]) ).

fof(c_0_2397,plain,
    ! [X47,X48,X49,X50,X51] :
      ( ( c_Groups_Oplus__class_Oplus(X51,c_Groups_Otimes__class_Otimes(X51,X50,X49),c_Groups_Otimes__class_Otimes(X51,X48,X47)) != c_Groups_Oplus__class_Oplus(X51,c_Groups_Otimes__class_Otimes(X51,X50,X47),c_Groups_Otimes__class_Otimes(X51,X48,X49))
        | X50 = X48
        | X49 = X47
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X51) )
      & ( X50 != X48
        | c_Groups_Oplus__class_Oplus(X51,c_Groups_Otimes__class_Otimes(X51,X50,X49),c_Groups_Otimes__class_Otimes(X51,X48,X47)) = c_Groups_Oplus__class_Oplus(X51,c_Groups_Otimes__class_Otimes(X51,X50,X47),c_Groups_Otimes__class_Otimes(X51,X48,X49))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X51) )
      & ( X49 != X47
        | c_Groups_Oplus__class_Oplus(X51,c_Groups_Otimes__class_Otimes(X51,X50,X49),c_Groups_Otimes__class_Otimes(X51,X48,X47)) = c_Groups_Oplus__class_Oplus(X51,c_Groups_Otimes__class_Otimes(X51,X50,X47),c_Groups_Otimes__class_Otimes(X51,X48,X49))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X51) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1226])])]) ).

fof(c_0_2398,plain,
    ! [X43,X44,X45,X46,X47] :
      ( ( X46 = X45
        | X44 = X43
        | c_Groups_Oplus__class_Oplus(X47,c_Groups_Otimes__class_Otimes(X47,X46,X44),c_Groups_Otimes__class_Otimes(X47,X45,X43)) != c_Groups_Oplus__class_Oplus(X47,c_Groups_Otimes__class_Otimes(X47,X46,X43),c_Groups_Otimes__class_Otimes(X47,X45,X44))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X47) )
      & ( X46 != X45
        | c_Groups_Oplus__class_Oplus(X47,c_Groups_Otimes__class_Otimes(X47,X46,X44),c_Groups_Otimes__class_Otimes(X47,X45,X43)) = c_Groups_Oplus__class_Oplus(X47,c_Groups_Otimes__class_Otimes(X47,X46,X43),c_Groups_Otimes__class_Otimes(X47,X45,X44))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X47) )
      & ( X44 != X43
        | c_Groups_Oplus__class_Oplus(X47,c_Groups_Otimes__class_Otimes(X47,X46,X44),c_Groups_Otimes__class_Otimes(X47,X45,X43)) = c_Groups_Oplus__class_Oplus(X47,c_Groups_Otimes__class_Otimes(X47,X46,X43),c_Groups_Otimes__class_Otimes(X47,X45,X44))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X47) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1227])])]) ).

fof(c_0_2399,plain,
    ! [X54,X55,X56,X57] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X57,X56),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X55,X56),X54)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X55),X56),X54),
    inference(variable_rename,[status(thm)],[c_0_1228]) ).

fof(c_0_2400,plain,
    ! [X75,X76,X77] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X77,X76),X75),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X75)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X77)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X76,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1229])]) ).

fof(c_0_2401,plain,
    ! [X75,X76,X77] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X77,X76),X75))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X75,X77)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X77)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X76) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1230])]) ).

fof(c_0_2402,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),X34) = c_Divides_Odiv__class_Omod(X37,c_Groups_Otimes__class_Otimes(X37,c_Divides_Odiv__class_Omod(X37,X36,X34),c_Divides_Odiv__class_Omod(X37,X35,X34)),X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1231])]) ).

fof(c_0_2403,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Oring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Ominus__class_Ominus(X37,X36,X35),X34) = c_Divides_Odiv__class_Omod(X37,c_Groups_Ominus__class_Ominus(X37,c_Divides_Odiv__class_Omod(X37,X36,X34),c_Divides_Odiv__class_Omod(X37,X35,X34)),X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1232])]) ).

fof(c_0_2404,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),X34) = c_Divides_Odiv__class_Omod(X37,c_Groups_Oplus__class_Oplus(X37,c_Divides_Odiv__class_Omod(X37,X36,X34),c_Divides_Odiv__class_Omod(X37,X35,X34)),X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1233])]) ).

fof(c_0_2405,plain,
    ! [X21,X22,X23] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X22),X21)),X22) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X21),X22),
    inference(variable_rename,[status(thm)],[c_0_1234]) ).

fof(c_0_2406,plain,
    ! [X16,X17,X18] :
      ( ( X17 = c_Groups_Ozero__class_Ozero(X18)
        | c_Groups_Oplus__class_Oplus(X18,c_Power_Opower__class_Opower(X18,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X18,X16,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X18)
        | ~ class_Rings_Olinordered__idom(X18) )
      & ( X16 = c_Groups_Ozero__class_Ozero(X18)
        | c_Groups_Oplus__class_Oplus(X18,c_Power_Opower__class_Opower(X18,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X18,X16,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X18)
        | ~ class_Rings_Olinordered__idom(X18) )
      & ( X17 != c_Groups_Ozero__class_Ozero(X18)
        | X16 != c_Groups_Ozero__class_Ozero(X18)
        | c_Groups_Oplus__class_Oplus(X18,c_Power_Opower__class_Opower(X18,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X18,X16,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X18)
        | ~ class_Rings_Olinordered__idom(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1235])])]) ).

fof(c_0_2407,plain,
    ! [X16,X17,X18,X19] :
      ( ( X17 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X16,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X16 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X16,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X19 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X18 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X19,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1236])])])])]) ).

fof(c_0_2408,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__semidom(X23)
      | ~ c_Orderings_Oord__class_Oless(X23,c_Groups_Ozero__class_Ozero(X23),X22)
      | ~ c_Orderings_Oord__class_Oless(X23,X22,c_Groups_Oone__class_Oone(X23))
      | c_Orderings_Oord__class_Oless(X23,c_Groups_Otimes__class_Otimes(X23,X22,c_Power_Opower__class_Opower(X23,X22,X21)),c_Power_Opower__class_Opower(X23,X22,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1237])]) ).

fof(c_0_2409,plain,
    ! [X70,X71,X72,X73,X74,X75,X76] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X71,X70)
        | hBOOL(hAPP(X72,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X72,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X71,X70))) )
      & ( X71 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X70,X73)
        | hBOOL(hAPP(X72,X73))
        | ~ hBOOL(hAPP(X72,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X71,X70))) )
      & ( X75 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X74,esk15_3(X74,X75,X76))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X75,X74)
        | hBOOL(hAPP(X76,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X75,X74))) )
      & ( ~ hBOOL(hAPP(X76,esk15_3(X74,X75,X76)))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X75,X74)
        | hBOOL(hAPP(X76,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X75,X74))) )
      & ( X75 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X74,esk15_3(X74,X75,X76))
        | ~ hBOOL(hAPP(X76,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X76,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X75,X74))) )
      & ( ~ hBOOL(hAPP(X76,esk15_3(X74,X75,X76)))
        | ~ hBOOL(hAPP(X76,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X76,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X75,X74))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1238])])])])])]) ).

fof(c_0_2410,plain,
    ! [X70,X71,X72,X73,X74,X75,X76] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X71,X70)
        | hBOOL(hAPP(X72,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X72,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X71,X70))) )
      & ( X71 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X70,X73)
        | hBOOL(hAPP(X72,X73))
        | ~ hBOOL(hAPP(X72,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X71,X70))) )
      & ( X75 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X74,esk14_3(X74,X75,X76))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X75,X74)
        | hBOOL(hAPP(X76,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X75,X74))) )
      & ( ~ hBOOL(hAPP(X76,esk14_3(X74,X75,X76)))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X75,X74)
        | hBOOL(hAPP(X76,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X75,X74))) )
      & ( X75 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X74,esk14_3(X74,X75,X76))
        | ~ hBOOL(hAPP(X76,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X76,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X75,X74))) )
      & ( ~ hBOOL(hAPP(X76,esk14_3(X74,X75,X76)))
        | ~ hBOOL(hAPP(X76,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X76,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X75,X74))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1239])])])])])]) ).

fof(c_0_2411,plain,
    ! [X44,X45,X46,X47,X48,X49] :
      ( ~ class_Divides_Osemiring__div(X49)
      | c_Divides_Odiv__class_Omod(X49,X48,X47) != c_Divides_Odiv__class_Omod(X49,X46,X47)
      | c_Divides_Odiv__class_Omod(X49,X45,X47) != c_Divides_Odiv__class_Omod(X49,X44,X47)
      | c_Divides_Odiv__class_Omod(X49,c_Groups_Otimes__class_Otimes(X49,X48,X45),X47) = c_Divides_Odiv__class_Omod(X49,c_Groups_Otimes__class_Otimes(X49,X46,X44),X47) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1240])]) ).

fof(c_0_2412,plain,
    ! [X44,X45,X46,X47,X48,X49] :
      ( ~ class_Divides_Oring__div(X49)
      | c_Divides_Odiv__class_Omod(X49,X48,X47) != c_Divides_Odiv__class_Omod(X49,X46,X47)
      | c_Divides_Odiv__class_Omod(X49,X45,X47) != c_Divides_Odiv__class_Omod(X49,X44,X47)
      | c_Divides_Odiv__class_Omod(X49,c_Groups_Ominus__class_Ominus(X49,X48,X45),X47) = c_Divides_Odiv__class_Omod(X49,c_Groups_Ominus__class_Ominus(X49,X46,X44),X47) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1241])]) ).

fof(c_0_2413,plain,
    ! [X44,X45,X46,X47,X48,X49] :
      ( ~ class_Divides_Osemiring__div(X49)
      | c_Divides_Odiv__class_Omod(X49,X48,X47) != c_Divides_Odiv__class_Omod(X49,X46,X47)
      | c_Divides_Odiv__class_Omod(X49,X45,X47) != c_Divides_Odiv__class_Omod(X49,X44,X47)
      | c_Divides_Odiv__class_Omod(X49,c_Groups_Oplus__class_Oplus(X49,X48,X45),X47) = c_Divides_Odiv__class_Omod(X49,c_Groups_Oplus__class_Oplus(X49,X46,X44),X47) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1242])]) ).

fof(c_0_2414,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Ocomm__ring__1(X26)
      | c_Groups_Ominus__class_Ominus(X26,c_Power_Opower__class_Opower(X26,X25,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(X26,X24,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Otimes__class_Otimes(X26,c_Groups_Ominus__class_Ominus(X26,X25,X24),c_Groups_Oplus__class_Oplus(X26,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1243])]) ).

fof(c_0_2415,plain,
    ! [X47,X48] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X47),X47),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X48),X48),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1244])])])]) ).

fof(c_0_2416,plain,
    ! [X81,X82,X83,X84] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X83)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X83)
        | X83 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X83) = X81
        | X84 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X83,X82),X81) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X83,X81)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X83)
        | X83 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X83) = X81
        | X84 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X83,X82),X81) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X83)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X81)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X81,X83)
        | X83 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X83) = X81
        | X84 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X83,X82),X81) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X83,X81)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X81,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X81)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X81,X83)
        | X83 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X84,X83) = X81
        | X84 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X83,X82),X81) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1245])])]) ).

fof(c_0_2417,plain,
    ! [X30,X31,X32,X33,X34] :
      ( ~ class_Rings_Ocomm__semiring__1(X34)
      | c_Groups_Otimes__class_Otimes(X34,c_Groups_Otimes__class_Otimes(X34,X33,X32),c_Groups_Otimes__class_Otimes(X34,X31,X30)) = c_Groups_Otimes__class_Otimes(X34,X33,c_Groups_Otimes__class_Otimes(X34,X32,c_Groups_Otimes__class_Otimes(X34,X31,X30))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1246])]) ).

fof(c_0_2418,plain,
    ! [X30,X31,X32,X33,X34] :
      ( ~ class_Rings_Ocomm__semiring__1(X34)
      | c_Groups_Otimes__class_Otimes(X34,c_Groups_Otimes__class_Otimes(X34,X33,X32),c_Groups_Otimes__class_Otimes(X34,X31,X30)) = c_Groups_Otimes__class_Otimes(X34,X31,c_Groups_Otimes__class_Otimes(X34,c_Groups_Otimes__class_Otimes(X34,X33,X32),X30)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1247])]) ).

fof(c_0_2419,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ class_Rings_Olinordered__semiring__strict(X39)
      | ~ c_Orderings_Oord__class_Oless(X39,X38,X37)
      | ~ c_Orderings_Oord__class_Oless(X39,X36,X35)
      | ~ c_Orderings_Oord__class_Oless(X39,c_Groups_Ozero__class_Ozero(X39),X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,c_Groups_Ozero__class_Ozero(X39),X36)
      | c_Orderings_Oord__class_Oless(X39,c_Groups_Otimes__class_Otimes(X39,X38,X36),c_Groups_Otimes__class_Otimes(X39,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1248])]) ).

fof(c_0_2420,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ class_Rings_Olinordered__semiring__strict(X39)
      | ~ c_Orderings_Oord__class_Oless(X39,X38,X37)
      | ~ c_Orderings_Oord__class_Oless(X39,X36,X35)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,c_Groups_Ozero__class_Ozero(X39),X38)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,c_Groups_Ozero__class_Ozero(X39),X36)
      | c_Orderings_Oord__class_Oless(X39,c_Groups_Otimes__class_Otimes(X39,X38,X36),c_Groups_Otimes__class_Otimes(X39,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1249])]) ).

fof(c_0_2421,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ class_Rings_Olinordered__semiring__strict(X39)
      | ~ c_Orderings_Oord__class_Oless(X39,X38,X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,X36,X35)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,c_Groups_Ozero__class_Ozero(X39),X38)
      | ~ c_Orderings_Oord__class_Oless(X39,c_Groups_Ozero__class_Ozero(X39),X36)
      | c_Orderings_Oord__class_Oless(X39,c_Groups_Otimes__class_Otimes(X39,X38,X36),c_Groups_Otimes__class_Otimes(X39,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1250])]) ).

fof(c_0_2422,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ class_Rings_Olinordered__semiring__strict(X39)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,X38,X37)
      | ~ c_Orderings_Oord__class_Oless(X39,X36,X35)
      | ~ c_Orderings_Oord__class_Oless(X39,c_Groups_Ozero__class_Ozero(X39),X38)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,c_Groups_Ozero__class_Ozero(X39),X36)
      | c_Orderings_Oord__class_Oless(X39,c_Groups_Otimes__class_Otimes(X39,X38,X36),c_Groups_Otimes__class_Otimes(X39,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1251])]) ).

fof(c_0_2423,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ class_Rings_Oordered__semiring(X39)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,X38,X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,X36,X35)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,c_Groups_Ozero__class_Ozero(X39),X38)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,c_Groups_Ozero__class_Ozero(X39),X36)
      | c_Orderings_Oord__class_Oless__eq(X39,c_Groups_Otimes__class_Otimes(X39,X38,X36),c_Groups_Otimes__class_Otimes(X39,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1252])]) ).

fof(c_0_2424,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ class_Rings_Oordered__semiring(X39)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,X38,X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,X36,X35)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,c_Groups_Ozero__class_Ozero(X39),X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,c_Groups_Ozero__class_Ozero(X39),X36)
      | c_Orderings_Oord__class_Oless__eq(X39,c_Groups_Otimes__class_Otimes(X39,X38,X36),c_Groups_Otimes__class_Otimes(X39,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1253])]) ).

fof(c_0_2425,plain,
    ! [X24] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X24,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X24),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(variable_rename,[status(thm)],[c_0_1254]) ).

fof(c_0_2426,plain,
    ! [X19,X20,X21] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X21),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X21))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X19)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X21),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X21))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X19)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1255])])]) ).

fof(c_0_2427,plain,
    ! [X19,X20,X21] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X21),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X21))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X19)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X21),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X21))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X19)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1256])])]) ).

fof(c_0_2428,plain,
    ! [X39,X40,X41,X42] :
      ( ~ class_Groups_Omonoid__mult(X42)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X40)
      | c_Power_Opower__class_Opower(X42,X39,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X40),X41)) = c_Groups_Otimes__class_Otimes(X42,c_Power_Opower__class_Opower(X42,X39,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,X41)),X39) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1257])]) ).

fof(c_0_2429,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X21,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X20,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X19)))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X21,X20) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X24,X23)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X24,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X24,X22))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1258])])])]) ).

fof(c_0_2430,plain,
    ! [X22,X23,X24,X25] :
      ( ~ class_Rings_Olinordered__semidom(X25)
      | ~ c_Orderings_Oord__class_Oless__eq(X25,c_Power_Opower__class_Opower(X25,X24,c_Nat_OSuc(X23)),c_Power_Opower__class_Opower(X25,X22,c_Nat_OSuc(X23)))
      | ~ c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25),X22)
      | c_Orderings_Oord__class_Oless__eq(X25,X24,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1259])]) ).

fof(c_0_2431,plain,
    ! [X24,X25,X26,X27] :
      ( ~ class_Divides_Osemiring__div(X27)
      | ~ c_Rings_Odvd__class_Odvd(X27,X26,X25)
      | ~ c_Rings_Odvd__class_Odvd(X27,X26,X24)
      | c_Divides_Odiv__class_Odiv(X27,c_Groups_Oplus__class_Oplus(X27,X25,X24),X26) = c_Groups_Oplus__class_Oplus(X27,c_Divides_Odiv__class_Odiv(X27,X25,X26),c_Divides_Odiv__class_Odiv(X27,X24,X26)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1260])]) ).

fof(c_0_2432,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Olinordered__ring(X26)
      | c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Ozero__class_Ozero(X26),c_Groups_Oplus__class_Oplus(X26,c_Groups_Otimes__class_Otimes(X26,X25,X25),c_Groups_Otimes__class_Otimes(X26,X24,X24))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1261])]) ).

fof(c_0_2433,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__semidom(X23)
      | ~ c_Orderings_Oord__class_Oless(X23,c_Groups_Oone__class_Oone(X23),X22)
      | c_Orderings_Oord__class_Oless(X23,c_Power_Opower__class_Opower(X23,X22,X21),c_Groups_Otimes__class_Otimes(X23,X22,c_Power_Opower__class_Opower(X23,X22,X21))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1262])]) ).

fof(c_0_2434,plain,
    ! [X22,X23,X24,X25] :
      ( ~ class_Rings_Olinordered__semidom(X25)
      | ~ c_Orderings_Oord__class_Oless(X25,c_Power_Opower__class_Opower(X25,X24,X23),c_Power_Opower__class_Opower(X25,X22,X23))
      | ~ c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25),X22)
      | c_Orderings_Oord__class_Oless(X25,X24,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1263])]) ).

fof(c_0_2435,plain,
    ! [X43,X44,X45,X46] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | c_Orderings_Oord__class_Oless__eq(X46,X44,X43)
        | ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Ozero__class_Ozero(X46),X45)
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X46,X44,X43)
        | c_Orderings_Oord__class_Oless__eq(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Ozero__class_Ozero(X46),X45)
        | ~ class_Rings_Olinordered__ring__strict(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1264])])]) ).

fof(c_0_2436,plain,
    ! [X43,X44,X45,X46] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | c_Orderings_Oord__class_Oless__eq(X46,X43,X44)
        | ~ c_Orderings_Oord__class_Oless(X46,X45,c_Groups_Ozero__class_Ozero(X46))
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X46,X43,X44)
        | c_Orderings_Oord__class_Oless__eq(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | ~ c_Orderings_Oord__class_Oless(X46,X45,c_Groups_Ozero__class_Ozero(X46))
        | ~ class_Rings_Olinordered__ring__strict(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1265])])]) ).

fof(c_0_2437,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Olinordered__semiring(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),c_Groups_Otimes__class_Otimes(X37,X34,X35))
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Ozero__class_Ozero(X37),X35)
      | c_Orderings_Oord__class_Oless(X37,X36,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1266])]) ).

fof(c_0_2438,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Olinordered__semiring__strict(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),c_Groups_Otimes__class_Otimes(X37,X34,X35))
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Ozero__class_Ozero(X37),X35)
      | c_Orderings_Oord__class_Oless(X37,X36,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1267])]) ).

fof(c_0_2439,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Olinordered__semiring(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),c_Groups_Otimes__class_Otimes(X37,X36,X34))
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Ozero__class_Ozero(X37),X36)
      | c_Orderings_Oord__class_Oless(X37,X35,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1268])]) ).

fof(c_0_2440,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Olinordered__semiring__strict(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),c_Groups_Otimes__class_Otimes(X37,X36,X34))
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Ozero__class_Ozero(X37),X36)
      | c_Orderings_Oord__class_Oless(X37,X35,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1269])]) ).

fof(c_0_2441,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Olinordered__semiring__strict(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),c_Groups_Otimes__class_Otimes(X37,X34,X35))
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X35)
      | c_Orderings_Oord__class_Oless__eq(X37,X36,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1270])]) ).

fof(c_0_2442,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Olinordered__semiring__strict(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),c_Groups_Otimes__class_Otimes(X37,X36,X34))
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X36)
      | c_Orderings_Oord__class_Oless__eq(X37,X35,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1271])]) ).

fof(c_0_2443,plain,
    ! [X43,X44,X45,X46] :
      ( ( ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | c_Orderings_Oord__class_Oless(X46,X44,X43)
        | ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Ozero__class_Ozero(X46),X45)
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( ~ c_Orderings_Oord__class_Oless(X46,X44,X43)
        | c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Ozero__class_Ozero(X46),X45)
        | ~ class_Rings_Olinordered__ring__strict(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1272])])]) ).

fof(c_0_2444,plain,
    ! [X43,X44,X45,X46] :
      ( ( ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | c_Orderings_Oord__class_Oless(X46,X43,X44)
        | ~ c_Orderings_Oord__class_Oless(X46,X45,c_Groups_Ozero__class_Ozero(X46))
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( ~ c_Orderings_Oord__class_Oless(X46,X43,X44)
        | c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | ~ c_Orderings_Oord__class_Oless(X46,X45,c_Groups_Ozero__class_Ozero(X46))
        | ~ class_Rings_Olinordered__ring__strict(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1273])])]) ).

fof(c_0_2445,plain,
    ! [X25,X26,X27,X28] :
      ( ( ~ c_Orderings_Oord__class_Oless(X28,c_Power_Opower__class_Opower(X28,X27,X26),c_Power_Opower__class_Opower(X28,X27,X25))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
        | ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Oone__class_Oone(X28),X27)
        | ~ class_Rings_Olinordered__semidom(X28) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X26,X25)
        | c_Orderings_Oord__class_Oless(X28,c_Power_Opower__class_Opower(X28,X27,X26),c_Power_Opower__class_Opower(X28,X27,X25))
        | ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Oone__class_Oone(X28),X27)
        | ~ class_Rings_Olinordered__semidom(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1274])])]) ).

fof(c_0_2446,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Rings_Olinordered__semidom(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Oone__class_Oone(X24),X23)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Power_Opower__class_Opower(X24,X23,X22),c_Power_Opower__class_Opower(X24,X23,X21))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1275])]) ).

fof(c_0_2447,plain,
    ! [X25,X26,X27,X28] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Power_Opower__class_Opower(X28,X27,X26),c_Power_Opower__class_Opower(X28,X27,X25))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
        | ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Oone__class_Oone(X28),X27)
        | ~ class_Rings_Olinordered__semidom(X28) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X25)
        | c_Orderings_Oord__class_Oless__eq(X28,c_Power_Opower__class_Opower(X28,X27,X26),c_Power_Opower__class_Opower(X28,X27,X25))
        | ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Oone__class_Oone(X28),X27)
        | ~ class_Rings_Olinordered__semidom(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1276])])]) ).

fof(c_0_2448,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Rings_Olinordered__semidom(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Oone__class_Oone(X24),X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,c_Power_Opower__class_Opower(X24,X23,X22),c_Power_Opower__class_Opower(X24,X23,X21))
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1277])]) ).

fof(c_0_2449,plain,
    ! [X31,X32,X33,X34] :
      ( ~ class_Int_Onumber(X34)
      | ~ class_Rings_Oring(X34)
      | c_Groups_Otimes__class_Otimes(X34,c_Groups_Ominus__class_Ominus(X34,X33,X32),c_Int_Onumber__class_Onumber__of(X34,X31)) = c_Groups_Ominus__class_Ominus(X34,c_Groups_Otimes__class_Otimes(X34,X33,c_Int_Onumber__class_Onumber__of(X34,X31)),c_Groups_Otimes__class_Otimes(X34,X32,c_Int_Onumber__class_Onumber__of(X34,X31))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1278])]) ).

fof(c_0_2450,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Int_Onumber(X37)
      | ~ class_Rings_Oring(X37)
      | c_Groups_Otimes__class_Otimes(X37,c_Int_Onumber__class_Onumber__of(X37,X36),c_Groups_Ominus__class_Ominus(X37,X35,X34)) = c_Groups_Ominus__class_Ominus(X37,c_Groups_Otimes__class_Otimes(X37,c_Int_Onumber__class_Onumber__of(X37,X36),X35),c_Groups_Otimes__class_Otimes(X37,c_Int_Onumber__class_Onumber__of(X37,X36),X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1279])]) ).

fof(c_0_2451,plain,
    ! [X31,X32,X33,X34] :
      ( ~ class_Int_Onumber(X34)
      | ~ class_Rings_Osemiring(X34)
      | c_Groups_Otimes__class_Otimes(X34,c_Groups_Oplus__class_Oplus(X34,X33,X32),c_Int_Onumber__class_Onumber__of(X34,X31)) = c_Groups_Oplus__class_Oplus(X34,c_Groups_Otimes__class_Otimes(X34,X33,c_Int_Onumber__class_Onumber__of(X34,X31)),c_Groups_Otimes__class_Otimes(X34,X32,c_Int_Onumber__class_Onumber__of(X34,X31))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1280])]) ).

fof(c_0_2452,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Int_Onumber(X37)
      | ~ class_Rings_Osemiring(X37)
      | c_Groups_Otimes__class_Otimes(X37,c_Int_Onumber__class_Onumber__of(X37,X36),c_Groups_Oplus__class_Oplus(X37,X35,X34)) = c_Groups_Oplus__class_Oplus(X37,c_Groups_Otimes__class_Otimes(X37,c_Int_Onumber__class_Onumber__of(X37,X36),X35),c_Groups_Otimes__class_Otimes(X37,c_Int_Onumber__class_Onumber__of(X37,X36),X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1281])]) ).

fof(c_0_2453,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__idom(X23)
      | c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Ozero__class_Ozero(X23),c_Power_Opower__class_Opower(X23,X22,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1282])]) ).

fof(c_0_2454,plain,
    ! [X33,X34,X35,X36,X37,X38] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X35,c_Int_OPls)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X35),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X34),X33)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X38,c_Int_OPls)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X38),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X37),X36)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X38,X37)),X36) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1283])])])]) ).

fof(c_0_2455,plain,
    ! [X54,X55,X56] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X56,X55),c_Power_Opower__class_Opower(tc_Nat_Onat,X56,X54))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X56)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X55,X54) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1284])]) ).

fof(c_0_2456,plain,
    ! [X47,X48,X49] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X48,X49),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X47,X49))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X48,X47)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X49) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X48,X47)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X48,X49),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X47,X49))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X49) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1285])])]) ).

fof(c_0_2457,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X22)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X22)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X22)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1286])])])])]) ).

fof(c_0_2458,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X19) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X23)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X24,X22)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X23)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1287])])])])]) ).

fof(c_0_2459,plain,
    ! [X19,X20,X21] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1288])])]) ).

fof(c_0_2460,plain,
    ! [X47,X48,X49] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X49,X48),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X49,X47))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X48,X47)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X49) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X48,X47)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X49,X48),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X49,X47))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X49) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1289])])]) ).

fof(c_0_2461,plain,
    ! [X47,X48,X49] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X48,X49),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X47,X49))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X48,X47)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X49) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X48,X47)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X48,X49),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X47,X49))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X49) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1290])])]) ).

fof(c_0_2462,plain,
    ! [X21,X22,X23] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X22),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X21))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1291])]) ).

fof(c_0_2463,plain,
    ! [X19,X20,X21] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19))
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,X19)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,X19)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1292])])]) ).

fof(c_0_2464,plain,
    ! [X19,X20,X21] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1293])])]) ).

fof(c_0_2465,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X56)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X56,X55),c_Power_Opower__class_Opower(tc_Nat_Onat,X56,X54))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X54) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1294])]) ).

fof(c_0_2466,plain,
    ! [X63,X64,X65,X66] :
      ( ~ class_Rings_Olinordered__semidom(X66)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X65,X64)
      | ~ c_Orderings_Oord__class_Oless(X66,c_Groups_Ozero__class_Ozero(X66),X63)
      | ~ c_Orderings_Oord__class_Oless(X66,X63,c_Groups_Oone__class_Oone(X66))
      | c_Orderings_Oord__class_Oless(X66,c_Power_Opower__class_Opower(X66,X63,X64),c_Power_Opower__class_Opower(X66,X63,X65)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1295])]) ).

fof(c_0_2467,plain,
    ! [X63,X64,X65,X66] :
      ( ~ class_Rings_Olinordered__semidom(X66)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X64)
      | ~ c_Orderings_Oord__class_Oless__eq(X66,c_Groups_Ozero__class_Ozero(X66),X63)
      | ~ c_Orderings_Oord__class_Oless__eq(X66,X63,c_Groups_Oone__class_Oone(X66))
      | c_Orderings_Oord__class_Oless__eq(X66,c_Power_Opower__class_Opower(X66,X63,X64),c_Power_Opower__class_Opower(X66,X63,X65)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1296])]) ).

fof(c_0_2468,plain,
    ! [X43,X44,X45,X46] :
      ( ( c_Orderings_Oord__class_Oless(X46,X44,c_Groups_Ozero__class_Ozero(X46))
        | c_Orderings_Oord__class_Oless(X46,c_Groups_Ozero__class_Ozero(X46),X44)
        | ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X43,X44))
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( c_Orderings_Oord__class_Oless(X46,X43,X45)
        | c_Orderings_Oord__class_Oless(X46,c_Groups_Ozero__class_Ozero(X46),X44)
        | ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X43,X44))
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( c_Orderings_Oord__class_Oless(X46,X44,c_Groups_Ozero__class_Ozero(X46))
        | c_Orderings_Oord__class_Oless(X46,X45,X43)
        | ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X43,X44))
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( c_Orderings_Oord__class_Oless(X46,X43,X45)
        | c_Orderings_Oord__class_Oless(X46,X45,X43)
        | ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X43,X44))
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Ozero__class_Ozero(X46),X44)
        | ~ c_Orderings_Oord__class_Oless(X46,X45,X43)
        | c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X43,X44))
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( ~ c_Orderings_Oord__class_Oless(X46,X44,c_Groups_Ozero__class_Ozero(X46))
        | ~ c_Orderings_Oord__class_Oless(X46,X43,X45)
        | c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X43,X44))
        | ~ class_Rings_Olinordered__ring__strict(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1297])])]) ).

fof(c_0_2469,plain,
    ! [X43,X44,X45,X46] :
      ( ( c_Orderings_Oord__class_Oless(X46,X45,c_Groups_Ozero__class_Ozero(X46))
        | c_Orderings_Oord__class_Oless(X46,c_Groups_Ozero__class_Ozero(X46),X45)
        | ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( c_Orderings_Oord__class_Oless(X46,X43,X44)
        | c_Orderings_Oord__class_Oless(X46,c_Groups_Ozero__class_Ozero(X46),X45)
        | ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( c_Orderings_Oord__class_Oless(X46,X45,c_Groups_Ozero__class_Ozero(X46))
        | c_Orderings_Oord__class_Oless(X46,X44,X43)
        | ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( c_Orderings_Oord__class_Oless(X46,X43,X44)
        | c_Orderings_Oord__class_Oless(X46,X44,X43)
        | ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Ozero__class_Ozero(X46),X45)
        | ~ c_Orderings_Oord__class_Oless(X46,X44,X43)
        | c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | ~ class_Rings_Olinordered__ring__strict(X46) )
      & ( ~ c_Orderings_Oord__class_Oless(X46,X45,c_Groups_Ozero__class_Ozero(X46))
        | ~ c_Orderings_Oord__class_Oless(X46,X43,X44)
        | c_Orderings_Oord__class_Oless(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | ~ class_Rings_Olinordered__ring__strict(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1298])])]) ).

fof(c_0_2470,plain,
    ! [X22,X23,X24,X25] :
      ( ~ class_Rings_Olinordered__semidom(X25)
      | ~ c_Orderings_Oord__class_Oless(X25,X24,X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25),X24)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X22)
      | c_Orderings_Oord__class_Oless(X25,c_Power_Opower__class_Opower(X25,X24,X22),c_Power_Opower__class_Opower(X25,X23,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1299])]) ).

fof(c_0_2471,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Otimes__class_Otimes(X37,c_Divides_Odiv__class_Omod(X37,X36,X35),X34),X35) = c_Divides_Odiv__class_Omod(X37,c_Groups_Otimes__class_Otimes(X37,X36,X34),X35) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1300])]) ).

fof(c_0_2472,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),X34) = c_Divides_Odiv__class_Omod(X37,c_Groups_Otimes__class_Otimes(X37,c_Divides_Odiv__class_Omod(X37,X36,X34),X35),X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1301])]) ).

fof(c_0_2473,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),X34) = c_Divides_Odiv__class_Omod(X37,c_Groups_Otimes__class_Otimes(X37,X36,c_Divides_Odiv__class_Omod(X37,X35,X34)),X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1302])]) ).

fof(c_0_2474,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Oring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Ominus__class_Ominus(X37,X36,X35),X34) = c_Divides_Odiv__class_Omod(X37,c_Groups_Ominus__class_Ominus(X37,X36,c_Divides_Odiv__class_Omod(X37,X35,X34)),X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1303])]) ).

fof(c_0_2475,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Oring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Ominus__class_Ominus(X37,X36,X35),X34) = c_Divides_Odiv__class_Omod(X37,c_Groups_Ominus__class_Ominus(X37,c_Divides_Odiv__class_Omod(X37,X36,X34),X35),X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1304])]) ).

fof(c_0_2476,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Oplus__class_Oplus(X37,c_Divides_Odiv__class_Omod(X37,X36,X35),X34),X35) = c_Divides_Odiv__class_Omod(X37,c_Groups_Oplus__class_Oplus(X37,X36,X34),X35) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1305])]) ).

fof(c_0_2477,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Oplus__class_Oplus(X37,X36,c_Divides_Odiv__class_Omod(X37,X35,X34)),X34) = c_Divides_Odiv__class_Omod(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1306])]) ).

fof(c_0_2478,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),X34) = c_Divides_Odiv__class_Omod(X37,c_Groups_Oplus__class_Oplus(X37,c_Divides_Odiv__class_Omod(X37,X36,X34),X35),X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1307])]) ).

fof(c_0_2479,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),X34) = c_Divides_Odiv__class_Omod(X37,c_Groups_Oplus__class_Oplus(X37,X36,c_Divides_Odiv__class_Omod(X37,X35,X34)),X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1308])]) ).

fof(c_0_2480,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ class_Rings_Ocomm__semiring__1(X39)
      | c_Groups_Oplus__class_Oplus(X39,c_Groups_Oplus__class_Oplus(X39,X38,X37),c_Groups_Oplus__class_Oplus(X39,X36,X35)) = c_Groups_Oplus__class_Oplus(X39,c_Groups_Oplus__class_Oplus(X39,X38,X36),c_Groups_Oplus__class_Oplus(X39,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1309])]) ).

fof(c_0_2481,plain,
    ! [X30,X31,X32,X33,X34] :
      ( ~ class_Rings_Ocomm__semiring__1(X34)
      | c_Groups_Otimes__class_Otimes(X34,c_Groups_Otimes__class_Otimes(X34,X33,X32),c_Groups_Otimes__class_Otimes(X34,X31,X30)) = c_Groups_Otimes__class_Otimes(X34,c_Groups_Otimes__class_Otimes(X34,X33,X31),c_Groups_Otimes__class_Otimes(X34,X32,X30)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1310])]) ).

fof(c_0_2482,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Int_Onumber__ring(X37)
      | c_Groups_Oplus__class_Oplus(X37,c_Int_Onumber__class_Onumber__of(X37,X36),c_Groups_Ominus__class_Ominus(X37,c_Int_Onumber__class_Onumber__of(X37,X35),X34)) = c_Groups_Ominus__class_Ominus(X37,c_Int_Onumber__class_Onumber__of(X37,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X36,X35)),X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1311])]) ).

fof(c_0_2483,plain,
    ! [X11,X12,X13,X14] :
      ( ~ class_Int_Onumber__ring(X14)
      | c_Groups_Oplus__class_Oplus(X14,c_Int_Onumber__class_Onumber__of(X14,X13),c_Groups_Oplus__class_Oplus(X14,c_Int_Onumber__class_Onumber__of(X14,X12),X11)) = c_Groups_Oplus__class_Oplus(X14,c_Int_Onumber__class_Onumber__of(X14,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,X12)),X11) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1312])]) ).

fof(c_0_2484,plain,
    ! [X11,X12,X13,X14] :
      ( ~ class_Int_Onumber__ring(X14)
      | c_Groups_Otimes__class_Otimes(X14,c_Int_Onumber__class_Onumber__of(X14,X13),c_Groups_Otimes__class_Otimes(X14,c_Int_Onumber__class_Onumber__of(X14,X12),X11)) = c_Groups_Otimes__class_Otimes(X14,c_Int_Onumber__class_Onumber__of(X14,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,X12)),X11) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1313])]) ).

fof(c_0_2485,plain,
    ! [X24,X25,X26] :
      ( ~ class_Groups_Omonoid__mult(X26)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25)
      | c_Groups_Otimes__class_Otimes(X26,c_Power_Opower__class_Opower(X26,X24,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X24) = c_Power_Opower__class_Opower(X26,X24,X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1314])]) ).

fof(c_0_2486,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Ocomm__semiring__1(X26)
      | c_Power_Opower__class_Opower(X26,X25,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X24)) = c_Groups_Otimes__class_Otimes(X26,c_Power_Opower__class_Opower(X26,X25,X24),c_Power_Opower__class_Opower(X26,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1315])]) ).

fof(c_0_2487,plain,
    ! [X55,X56,X57,X58,X59,X60] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X60)
      | X59 = c_Groups_Ozero__class_Ozero(X60)
      | X58 != X57
      | X56 = X55
      | c_Groups_Oplus__class_Oplus(X60,X58,c_Groups_Otimes__class_Otimes(X60,X59,X56)) != c_Groups_Oplus__class_Oplus(X60,X57,c_Groups_Otimes__class_Otimes(X60,X59,X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1316])]) ).

fof(c_0_2488,plain,
    ! [X24,X25,X26,X27] :
      ( ~ class_Divides_Osemiring__div(X27)
      | ~ c_Rings_Odvd__class_Odvd(X27,X26,X25)
      | c_Power_Opower__class_Opower(X27,c_Divides_Odiv__class_Odiv(X27,X25,X26),X24) = c_Divides_Odiv__class_Odiv(X27,c_Power_Opower__class_Opower(X27,X25,X24),c_Power_Opower__class_Opower(X27,X26,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1317])]) ).

fof(c_0_2489,plain,
    ! [X40,X41,X42] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X42)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X41)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X41,X40)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X42,X40),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X42,X41)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1318])]) ).

fof(c_0_2490,plain,
    ! [X40,X41,X42] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X42,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X41)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X41,X40)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X42,X41),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X42,X40)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1319])]) ).

fof(c_0_2491,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Olinordered__semidom(X26)
      | c_Power_Opower__class_Opower(X26,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(X26,X24,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Ozero__class_Ozero(X26),X25)
      | ~ c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Ozero__class_Ozero(X26),X24)
      | X25 = X24 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1320])]) ).

fof(c_0_2492,plain,
    ! [X34,X35,X36] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X36,X35),X34) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X36,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X34)),X34),
    inference(variable_rename,[status(thm)],[c_0_1321]) ).

fof(c_0_2493,plain,
    ! [X34,X35,X36] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X36,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X34)),X34) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X36,X35),X34),
    inference(variable_rename,[status(thm)],[c_0_1322]) ).

fof(c_0_2494,plain,
    ! [X24,X25,X26] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X26,c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X24)),X24) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X26,X25),X24),
    inference(variable_rename,[status(thm)],[c_0_1323]) ).

fof(c_0_2495,plain,
    ! [X24,X25,X26] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,X25),X24),X25) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X26,X24),X25),
    inference(variable_rename,[status(thm)],[c_0_1324]) ).

fof(c_0_2496,plain,
    ! [X24,X25,X26] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,X25),X24),X25) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X26,X24),X25),
    inference(variable_rename,[status(thm)],[c_0_1325]) ).

fof(c_0_2497,plain,
    ! [X52,X53,X54] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54,X53)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X54)),X52) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X53),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X54,X52)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1326])]) ).

fof(c_0_2498,plain,
    ! [X52,X53,X54] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X54,X53)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X52,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X54))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X52,X54),c_Nat_OSuc(X53)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1327])]) ).

fof(c_0_2499,plain,
    ! [X22,X23,X24,X25,X26] :
      ( ~ class_Rings_Ocomm__semiring__1(X26)
      | ~ c_Rings_Odvd__class_Odvd(X26,c_Power_Opower__class_Opower(X26,X25,X24),X23)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X24)
      | c_Rings_Odvd__class_Odvd(X26,c_Power_Opower__class_Opower(X26,X25,X22),X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1328])]) ).

fof(c_0_2500,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X21),X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X21),X19))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X22)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X24),X23),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X24),X22)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1329])])])]) ).

fof(c_0_2501,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X21),X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X21),X19))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X22)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X24),X23),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X24),X22)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1330])])])]) ).

fof(c_0_2502,plain,
    ! [X21,X22] :
      ( ~ class_Int_Onumber__ring(X22)
      | c_Power_Opower__class_Opower(X22,c_Int_Onumber__class_Onumber__of(X22,c_Int_OMin),c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21))) = c_Int_Onumber__class_Onumber__of(X22,c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1331])]) ).

fof(c_0_2503,plain,
    ! [X43,X44,X45,X46] :
      ( ( ~ c_Rings_Odvd__class_Odvd(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X43,X44))
        | X44 = c_Groups_Ozero__class_Ozero(X46)
        | c_Rings_Odvd__class_Odvd(X46,X45,X43)
        | ~ class_Rings_Oidom(X46) )
      & ( X44 != c_Groups_Ozero__class_Ozero(X46)
        | c_Rings_Odvd__class_Odvd(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X43,X44))
        | ~ class_Rings_Oidom(X46) )
      & ( ~ c_Rings_Odvd__class_Odvd(X46,X45,X43)
        | c_Rings_Odvd__class_Odvd(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X43,X44))
        | ~ class_Rings_Oidom(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1332])])]) ).

fof(c_0_2504,plain,
    ! [X43,X44,X45,X46] :
      ( ( ~ c_Rings_Odvd__class_Odvd(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | X45 = c_Groups_Ozero__class_Ozero(X46)
        | c_Rings_Odvd__class_Odvd(X46,X44,X43)
        | ~ class_Rings_Oidom(X46) )
      & ( X45 != c_Groups_Ozero__class_Ozero(X46)
        | c_Rings_Odvd__class_Odvd(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | ~ class_Rings_Oidom(X46) )
      & ( ~ c_Rings_Odvd__class_Odvd(X46,X44,X43)
        | c_Rings_Odvd__class_Odvd(X46,c_Groups_Otimes__class_Otimes(X46,X45,X44),c_Groups_Otimes__class_Otimes(X46,X45,X43))
        | ~ class_Rings_Oidom(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1333])])]) ).

fof(c_0_2505,plain,
    ! [X67,X68,X69] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X67,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X68,X69))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X67,X69),X68)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X69,X68) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X67,X69),X68)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X67,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X68,X69))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X69,X68) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1334])])]) ).

fof(c_0_2506,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__semidom(X23)
      | ~ c_Orderings_Oord__class_Oless(X23,c_Groups_Oone__class_Oone(X23),X22)
      | c_Orderings_Oord__class_Oless(X23,c_Groups_Oone__class_Oone(X23),c_Groups_Otimes__class_Otimes(X23,X22,c_Power_Opower__class_Opower(X23,X22,X21))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1335])]) ).

fof(c_0_2507,plain,
    ! [X43,X44,X45,X46] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X46,c_Groups_Oplus__class_Oplus(X46,X45,X44),c_Groups_Oplus__class_Oplus(X46,X43,X44))
        | c_Orderings_Oord__class_Oless__eq(X46,X45,X43)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X46) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X46,X45,X43)
        | c_Orderings_Oord__class_Oless__eq(X46,c_Groups_Oplus__class_Oplus(X46,X45,X44),c_Groups_Oplus__class_Oplus(X46,X43,X44))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1336])])]) ).

fof(c_0_2508,plain,
    ! [X43,X44,X45,X46] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X46,c_Groups_Oplus__class_Oplus(X46,X45,X44),c_Groups_Oplus__class_Oplus(X46,X45,X43))
        | c_Orderings_Oord__class_Oless__eq(X46,X44,X43)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X46) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X46,X44,X43)
        | c_Orderings_Oord__class_Oless__eq(X46,c_Groups_Oplus__class_Oplus(X46,X45,X44),c_Groups_Oplus__class_Oplus(X46,X45,X43))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1337])])]) ).

fof(c_0_2509,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),c_Groups_Oplus__class_Oplus(X37,X34,X35))
      | c_Orderings_Oord__class_Oless__eq(X37,X36,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1338])]) ).

fof(c_0_2510,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),c_Groups_Oplus__class_Oplus(X37,X36,X34))
      | c_Orderings_Oord__class_Oless__eq(X37,X35,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1339])]) ).

fof(c_0_2511,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),c_Groups_Oplus__class_Oplus(X37,X36,X34))
      | c_Orderings_Oord__class_Oless(X37,X35,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1340])]) ).

fof(c_0_2512,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),c_Groups_Oplus__class_Oplus(X37,X34,X35))
      | c_Orderings_Oord__class_Oless(X37,X36,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1341])]) ).

fof(c_0_2513,plain,
    ! [X43,X44,X45,X46] :
      ( ( ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Oplus__class_Oplus(X46,X45,X44),c_Groups_Oplus__class_Oplus(X46,X45,X43))
        | c_Orderings_Oord__class_Oless(X46,X44,X43)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X46) )
      & ( ~ c_Orderings_Oord__class_Oless(X46,X44,X43)
        | c_Orderings_Oord__class_Oless(X46,c_Groups_Oplus__class_Oplus(X46,X45,X44),c_Groups_Oplus__class_Oplus(X46,X45,X43))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1342])])]) ).

fof(c_0_2514,plain,
    ! [X43,X44,X45,X46] :
      ( ( ~ c_Orderings_Oord__class_Oless(X46,c_Groups_Oplus__class_Oplus(X46,X45,X44),c_Groups_Oplus__class_Oplus(X46,X43,X44))
        | c_Orderings_Oord__class_Oless(X46,X45,X43)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X46) )
      & ( ~ c_Orderings_Oord__class_Oless(X46,X45,X43)
        | c_Orderings_Oord__class_Oless(X46,c_Groups_Oplus__class_Oplus(X46,X45,X44),c_Groups_Oplus__class_Oplus(X46,X43,X44))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1343])])]) ).

fof(c_0_2515,plain,
    ! [X55,X56,X57] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X57)
      | X57 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X56,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X57,X55))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X56)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X55,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1344])]) ).

fof(c_0_2516,plain,
    ! [X21,X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X22)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X21)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X23),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X23)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1345])]) ).

fof(c_0_2517,plain,
    ! [X55,X56,X57] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X57)
      | X57 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X56,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X57,X55))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X56,X57)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X55) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1346])]) ).

fof(c_0_2518,plain,
    ! [X56,X57,X58] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X57,X58)
        | hBOOL(hAPP(hAPP(X56,X57),X58))
        | X58 = X57
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X58,X57) )
      & ( ~ hBOOL(hAPP(hAPP(X56,X57),X58))
        | hBOOL(hAPP(hAPP(X56,X57),X58))
        | X58 = X57
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X58,X57) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X57,X58)
        | hBOOL(hAPP(hAPP(X56,X57),X58))
        | ~ hBOOL(hAPP(hAPP(X56,X57),X58))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X58,X57) )
      & ( ~ hBOOL(hAPP(hAPP(X56,X57),X58))
        | hBOOL(hAPP(hAPP(X56,X57),X58))
        | ~ hBOOL(hAPP(hAPP(X56,X57),X58))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X58,X57) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X57,X58)
        | hBOOL(hAPP(hAPP(X56,X57),X58))
        | X58 = X57
        | ~ hBOOL(hAPP(hAPP(X56,X57),X58)) )
      & ( ~ hBOOL(hAPP(hAPP(X56,X57),X58))
        | hBOOL(hAPP(hAPP(X56,X57),X58))
        | X58 = X57
        | ~ hBOOL(hAPP(hAPP(X56,X57),X58)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X57,X58)
        | hBOOL(hAPP(hAPP(X56,X57),X58))
        | ~ hBOOL(hAPP(hAPP(X56,X57),X58))
        | ~ hBOOL(hAPP(hAPP(X56,X57),X58)) )
      & ( ~ hBOOL(hAPP(hAPP(X56,X57),X58))
        | hBOOL(hAPP(hAPP(X56,X57),X58))
        | ~ hBOOL(hAPP(hAPP(X56,X57),X58))
        | ~ hBOOL(hAPP(hAPP(X56,X57),X58)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1347])])]) ).

fof(c_0_2519,plain,
    ! [X21,X22,X23] :
      ( ~ class_Groups_Omonoid__mult(X23)
      | c_Power_Opower__class_Opower(X23,X22,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)) = c_Power_Opower__class_Opower(X23,c_Power_Opower__class_Opower(X23,X22,X21),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1348])]) ).

fof(c_0_2520,plain,
    ! [X21,X22,X23] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X22)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1349])]) ).

fof(c_0_2521,plain,
    ! [X21,X22,X23] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X21)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X22)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1350])]) ).

fof(c_0_2522,plain,
    ! [X26,X27,X28] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X27,X28),c_Power_Opower__class_Opower(tc_Nat_Onat,X26,X28))
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X27,X26)
        | X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X27,X26)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X27,X28),c_Power_Opower__class_Opower(tc_Nat_Onat,X26,X28))
        | X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1351])])]) ).

fof(c_0_2523,plain,
    ! [X22,X23,X24] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X24,X23),c_Power_Opower__class_Opower(tc_Nat_Onat,X22,X23))
      | X23 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1352])]) ).

fof(c_0_2524,plain,
    ! [X22,X23,X24] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X24,X23),c_Power_Opower__class_Opower(tc_Int_Oint,X22,X23))
      | X23 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X24,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1353])]) ).

fof(c_0_2525,plain,
    ! [X26,X27,X28] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X27,X28),c_Power_Opower__class_Opower(tc_Int_Oint,X26,X28))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X27,X26)
        | X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X27,X26)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X27,X28),c_Power_Opower__class_Opower(tc_Int_Oint,X26,X28))
        | X28 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1354])])]) ).

fof(c_0_2526,plain,
    ! [X24,X25] :
      ( ~ class_Rings_Oring__1(X25)
      | c_Groups_Ominus__class_Ominus(X25,c_Groups_Otimes__class_Otimes(X25,X24,X24),c_Groups_Oone__class_Oone(X25)) = c_Groups_Otimes__class_Otimes(X25,c_Groups_Oplus__class_Oplus(X25,X24,c_Groups_Oone__class_Oone(X25)),c_Groups_Ominus__class_Ominus(X25,X24,c_Groups_Oone__class_Oone(X25))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1355])]) ).

fof(c_0_2527,plain,
    ! [X21,X22,X23] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X21))
      | X23 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1356])]) ).

fof(c_0_2528,plain,
    ! [X58,X59,X60] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X59,X58)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X60,X59),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X60,X58))
        | X60 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X60,X59),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X60,X58))
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X59,X58)
        | X60 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1357])])]) ).

fof(c_0_2529,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19))
        | X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,X19) )
      & ( X24 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X22)) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X22)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1358])])])])]) ).

fof(c_0_2530,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X19)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X22)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X23)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1359])])])])]) ).

fof(c_0_2531,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X22)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X22)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1360])])])])]) ).

fof(c_0_2532,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X19))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X22)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X23),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X22)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1361])])])]) ).

fof(c_0_2533,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X19))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X22)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X23),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X22)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1362])])])]) ).

fof(c_0_2534,plain,
    ! [X22,X23,X24,X25] :
      ( ~ class_Rings_Olinordered__semidom(X25)
      | c_Power_Opower__class_Opower(X25,X24,X23) != c_Power_Opower__class_Opower(X25,X22,X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25),X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25),X22)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23)
      | X24 = X22 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1363])]) ).

fof(c_0_2535,plain,
    ! [X22,X23,X24,X25] :
      ( ~ class_Rings_Olinordered__semidom(X25)
      | ~ c_Orderings_Oord__class_Oless__eq(X25,X24,X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25),X24)
      | c_Orderings_Oord__class_Oless__eq(X25,c_Power_Opower__class_Opower(X25,X24,X22),c_Power_Opower__class_Opower(X25,X23,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1364])]) ).

fof(c_0_2536,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Oordered__semiring(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,X36,X35)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Ozero__class_Ozero(X37),X34)
      | c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Otimes__class_Otimes(X37,X36,X34),c_Groups_Otimes__class_Otimes(X37,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1365])]) ).

fof(c_0_2537,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Oordered__semiring(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,X36,X35)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Ozero__class_Ozero(X37),X34)
      | c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Otimes__class_Otimes(X37,X34,X36),c_Groups_Otimes__class_Otimes(X37,X34,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1366])]) ).

fof(c_0_2538,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Oordered__comm__semiring(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,X36,X35)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Ozero__class_Ozero(X37),X34)
      | c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Otimes__class_Otimes(X37,X34,X36),c_Groups_Otimes__class_Otimes(X37,X34,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1367])]) ).

fof(c_0_2539,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Oordered__ring(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,X36,X35)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,X34,c_Groups_Ozero__class_Ozero(X37))
      | c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Otimes__class_Otimes(X37,X35,X34),c_Groups_Otimes__class_Otimes(X37,X36,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1368])]) ).

fof(c_0_2540,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Oordered__ring(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,X36,X35)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,X34,c_Groups_Ozero__class_Ozero(X37))
      | c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Otimes__class_Otimes(X37,X34,X35),c_Groups_Otimes__class_Otimes(X37,X34,X36)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1369])]) ).

fof(c_0_2541,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Olinordered__semiring__strict(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,X36,X35)
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X34)
      | c_Orderings_Oord__class_Oless(X37,c_Groups_Otimes__class_Otimes(X37,X36,X34),c_Groups_Otimes__class_Otimes(X37,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1370])]) ).

fof(c_0_2542,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Olinordered__semiring__strict(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,X36,X35)
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X34)
      | c_Orderings_Oord__class_Oless(X37,c_Groups_Otimes__class_Otimes(X37,X34,X36),c_Groups_Otimes__class_Otimes(X37,X34,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1371])]) ).

fof(c_0_2543,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Olinordered__comm__semiring__strict(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,X36,X35)
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X34)
      | c_Orderings_Oord__class_Oless(X37,c_Groups_Otimes__class_Otimes(X37,X34,X36),c_Groups_Otimes__class_Otimes(X37,X34,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1372])]) ).

fof(c_0_2544,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Olinordered__ring__strict(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,X36,X35)
      | ~ c_Orderings_Oord__class_Oless(X37,X34,c_Groups_Ozero__class_Ozero(X37))
      | c_Orderings_Oord__class_Oless(X37,c_Groups_Otimes__class_Otimes(X37,X35,X34),c_Groups_Otimes__class_Otimes(X37,X36,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1373])]) ).

fof(c_0_2545,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Olinordered__ring__strict(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,X36,X35)
      | ~ c_Orderings_Oord__class_Oless(X37,X34,c_Groups_Ozero__class_Ozero(X37))
      | c_Orderings_Oord__class_Oless(X37,c_Groups_Otimes__class_Otimes(X37,X34,X35),c_Groups_Otimes__class_Otimes(X37,X34,X36)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1374])]) ).

fof(c_0_2546,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Olinordered__idom(X26)
      | ~ c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Ozero__class_Ozero(X26),X25)
      | ~ c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Ozero__class_Ozero(X26),X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X26,X24,c_Groups_Oone__class_Oone(X26))
      | c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Otimes__class_Otimes(X26,X25,X24),X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1375])]) ).

fof(c_0_2547,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Olinordered__idom(X26)
      | ~ c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Ozero__class_Ozero(X26),X25)
      | ~ c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Ozero__class_Ozero(X26),X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X26,X24,c_Groups_Oone__class_Oone(X26))
      | c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Otimes__class_Otimes(X26,X24,X25),X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1376])]) ).

fof(c_0_2548,plain,
    ! [X63,X64,X65,X66] :
      ( ~ class_Rings_Olinordered__semidom(X66)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X65,X64)
      | ~ c_Orderings_Oord__class_Oless(X66,c_Groups_Oone__class_Oone(X66),X63)
      | c_Orderings_Oord__class_Oless(X66,c_Power_Opower__class_Opower(X66,X63,X65),c_Power_Opower__class_Opower(X66,X63,X64)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1377])]) ).

fof(c_0_2549,plain,
    ! [X63,X64,X65,X66] :
      ( ~ class_Rings_Olinordered__semidom(X66)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X64)
      | ~ c_Orderings_Oord__class_Oless__eq(X66,c_Groups_Oone__class_Oone(X66),X63)
      | c_Orderings_Oord__class_Oless__eq(X66,c_Power_Opower__class_Opower(X66,X63,X65),c_Power_Opower__class_Opower(X66,X63,X64)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1378])]) ).

fof(c_0_2550,plain,
    ! [X17,X18,X19] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | X18 != c_Groups_Ozero__class_Ozero(X19)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X18)
        | X18 != c_Groups_Ozero__class_Ozero(X19)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | X18 = c_Groups_Ozero__class_Ozero(X19)
        | c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | ~ c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),X18)
        | c_Orderings_Oord__class_Oless(X19,c_Groups_Ozero__class_Ozero(X19),c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)))
        | ~ class_Rings_Olinordered__idom(X19) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1379])])]) ).

fof(c_0_2551,plain,
    ! [X21,X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X22)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21),X23)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1380])]) ).

fof(c_0_2552,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X39)
      | ~ c_Orderings_Oord__class_Oless(X39,X38,X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,X36,X35)
      | c_Orderings_Oord__class_Oless(X39,c_Groups_Oplus__class_Oplus(X39,X38,X36),c_Groups_Oplus__class_Oplus(X39,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1381])]) ).

fof(c_0_2553,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X39)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,X38,X37)
      | ~ c_Orderings_Oord__class_Oless(X39,X36,X35)
      | c_Orderings_Oord__class_Oless(X39,c_Groups_Oplus__class_Oplus(X39,X38,X36),c_Groups_Oplus__class_Oplus(X39,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1382])]) ).

fof(c_0_2554,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X39)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,X38,X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X39,X36,X35)
      | c_Orderings_Oord__class_Oless__eq(X39,c_Groups_Oplus__class_Oplus(X39,X38,X36),c_Groups_Oplus__class_Oplus(X39,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1383])]) ).

fof(c_0_2555,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X39)
      | ~ c_Orderings_Oord__class_Oless(X39,X38,X37)
      | ~ c_Orderings_Oord__class_Oless(X39,X36,X35)
      | c_Orderings_Oord__class_Oless(X39,c_Groups_Oplus__class_Oplus(X39,X38,X36),c_Groups_Oplus__class_Oplus(X39,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1384])]) ).

fof(c_0_2556,plain,
    ! [X35,X36,X37,X38,X39] :
      ( ~ class_Rings_Ocomm__semiring__1(X39)
      | ~ c_Rings_Odvd__class_Odvd(X39,X38,X37)
      | ~ c_Rings_Odvd__class_Odvd(X39,X36,X35)
      | c_Rings_Odvd__class_Odvd(X39,c_Groups_Otimes__class_Otimes(X39,X38,X36),c_Groups_Otimes__class_Otimes(X39,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1385])]) ).

fof(c_0_2557,plain,
    ! [X21,X22,X23] :
      ( ( X22 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X23,X21,X22) = c_Groups_Oone__class_Oone(X23)
        | ~ class_Power_Opower(X23) )
      & ( X22 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X23,X21,X22) = c_Groups_Otimes__class_Otimes(X23,X21,c_Power_Opower__class_Opower(X23,X21,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ class_Power_Opower(X23) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1386])])]) ).

fof(c_0_2558,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X22) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1387])]) ).

fof(c_0_2559,plain,
    ! [X24,X25,X26,X27,X28] :
      ( ~ class_Rings_Ocomm__semiring__1(X28)
      | ~ c_Rings_Odvd__class_Odvd(X28,X27,X26)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X25,X24)
      | c_Rings_Odvd__class_Odvd(X28,c_Power_Opower__class_Opower(X28,X27,X25),c_Power_Opower__class_Opower(X28,X26,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1388])]) ).

fof(c_0_2560,plain,
    ! [X16,X17,X18] :
      ( ( X17 = c_Groups_Ozero__class_Ozero(X18)
        | c_Groups_Oplus__class_Oplus(X18,c_Groups_Otimes__class_Otimes(X18,X17,X17),c_Groups_Otimes__class_Otimes(X18,X16,X16)) != c_Groups_Ozero__class_Ozero(X18)
        | ~ class_Rings_Olinordered__ring__strict(X18) )
      & ( X16 = c_Groups_Ozero__class_Ozero(X18)
        | c_Groups_Oplus__class_Oplus(X18,c_Groups_Otimes__class_Otimes(X18,X17,X17),c_Groups_Otimes__class_Otimes(X18,X16,X16)) != c_Groups_Ozero__class_Ozero(X18)
        | ~ class_Rings_Olinordered__ring__strict(X18) )
      & ( X17 != c_Groups_Ozero__class_Ozero(X18)
        | X16 != c_Groups_Ozero__class_Ozero(X18)
        | c_Groups_Oplus__class_Oplus(X18,c_Groups_Otimes__class_Otimes(X18,X17,X17),c_Groups_Otimes__class_Otimes(X18,X16,X16)) = c_Groups_Ozero__class_Ozero(X18)
        | ~ class_Rings_Olinordered__ring__strict(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1389])])]) ).

fof(c_0_2561,plain,
    ! [X17,X18,X19] :
      ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(X19,c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)),c_Groups_Ozero__class_Ozero(X19))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | ~ c_Orderings_Oord__class_Oless__eq(X19,c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)),c_Groups_Ozero__class_Ozero(X19))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( X18 = c_Groups_Ozero__class_Ozero(X19)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | ~ c_Orderings_Oord__class_Oless__eq(X19,c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)),c_Groups_Ozero__class_Ozero(X19))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | c_Orderings_Oord__class_Oless__eq(X19,X18,c_Groups_Ozero__class_Ozero(X19))
        | ~ c_Orderings_Oord__class_Oless__eq(X19,c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)),c_Groups_Ozero__class_Ozero(X19))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( X18 = c_Groups_Ozero__class_Ozero(X19)
        | c_Orderings_Oord__class_Oless__eq(X19,X18,c_Groups_Ozero__class_Ozero(X19))
        | ~ c_Orderings_Oord__class_Oless__eq(X19,c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)),c_Groups_Ozero__class_Ozero(X19))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | ~ c_Orderings_Oord__class_Oless__eq(X19,X18,c_Groups_Ozero__class_Ozero(X19))
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(X19,c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)),c_Groups_Ozero__class_Ozero(X19))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | X18 != c_Groups_Ozero__class_Ozero(X19)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(X19,c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)),c_Groups_Ozero__class_Ozero(X19))
        | ~ class_Rings_Olinordered__idom(X19) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1390])])]) ).

fof(c_0_2562,plain,
    ! [X17,X18,X19] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | ~ c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | ~ c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | ~ c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),X18)
        | c_Orderings_Oord__class_Oless__eq(X19,c_Groups_Ozero__class_Ozero(X19),c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)))
        | ~ class_Rings_Olinordered__idom(X19) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1391])])]) ).

fof(c_0_2563,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),c_Groups_Otimes__class_Otimes(X37,X34,X35)) = c_Groups_Otimes__class_Otimes(X37,c_Divides_Odiv__class_Omod(X37,X36,X34),X35) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1392])]) ).

fof(c_0_2564,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),c_Groups_Otimes__class_Otimes(X37,X36,X34)) = c_Groups_Otimes__class_Otimes(X37,X36,c_Divides_Odiv__class_Omod(X37,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1393])]) ).

fof(c_0_2565,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Oplus__class_Oplus(X37,X36,c_Groups_Otimes__class_Otimes(X37,X35,X34)),X34) = c_Divides_Odiv__class_Omod(X37,X36,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1394])]) ).

fof(c_0_2566,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | c_Divides_Odiv__class_Omod(X37,c_Groups_Oplus__class_Oplus(X37,X36,c_Groups_Otimes__class_Otimes(X37,X35,X34)),X35) = c_Divides_Odiv__class_Omod(X37,X36,X35) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1395])]) ).

fof(c_0_2567,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_RealVector_Oreal__normed__algebra(X48)
      | c_Groups_Otimes__class_Otimes(X48,c_Groups_Ominus__class_Ominus(X48,X47,X46),X45) = c_Groups_Ominus__class_Ominus(X48,c_Groups_Otimes__class_Otimes(X48,X47,X45),c_Groups_Otimes__class_Otimes(X48,X46,X45)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1396])]) ).

fof(c_0_2568,plain,
    ! [X44,X45,X46,X47] :
      ( ~ class_RealVector_Oreal__normed__algebra(X47)
      | c_Groups_Otimes__class_Otimes(X47,c_Groups_Ominus__class_Ominus(X47,X46,X45),X44) = c_Groups_Ominus__class_Ominus(X47,c_Groups_Otimes__class_Otimes(X47,X46,X44),c_Groups_Otimes__class_Otimes(X47,X45,X44)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1397])]) ).

fof(c_0_2569,plain,
    ! [X41,X42,X43,X44] :
      ( ~ class_RealVector_Oreal__normed__algebra(X44)
      | c_Groups_Otimes__class_Otimes(X44,X43,c_Groups_Ominus__class_Ominus(X44,X42,X41)) = c_Groups_Ominus__class_Ominus(X44,c_Groups_Otimes__class_Otimes(X44,X43,X42),c_Groups_Otimes__class_Otimes(X44,X43,X41)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1398])]) ).

fof(c_0_2570,plain,
    ! [X40,X41,X42,X43] :
      ( ~ class_RealVector_Oreal__normed__algebra(X43)
      | c_Groups_Otimes__class_Otimes(X43,X42,c_Groups_Ominus__class_Ominus(X43,X41,X40)) = c_Groups_Ominus__class_Ominus(X43,c_Groups_Otimes__class_Otimes(X43,X42,X41),c_Groups_Otimes__class_Otimes(X43,X42,X40)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1399])]) ).

fof(c_0_2571,plain,
    ! [X22,X23,X24,X25] :
      ( ~ class_Groups_Ocomm__monoid__mult(X25)
      | c_Power_Opower__class_Opower(X25,c_Groups_Otimes__class_Otimes(X25,X24,X23),X22) = c_Groups_Otimes__class_Otimes(X25,c_Power_Opower__class_Opower(X25,X24,X22),c_Power_Opower__class_Opower(X25,X23,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1400])]) ).

fof(c_0_2572,plain,
    ! [X22,X23,X24,X25] :
      ( ~ class_Rings_Ocomm__semiring__1(X25)
      | c_Groups_Oplus__class_Oplus(X25,c_Groups_Otimes__class_Otimes(X25,X24,X23),c_Groups_Otimes__class_Otimes(X25,X22,X23)) = c_Groups_Otimes__class_Otimes(X25,c_Groups_Oplus__class_Oplus(X25,X24,X22),X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1401])]) ).

fof(c_0_2573,plain,
    ! [X45,X46,X47,X48] :
      ( ~ class_RealVector_Oreal__normed__algebra(X48)
      | c_Groups_Otimes__class_Otimes(X48,c_Groups_Oplus__class_Oplus(X48,X47,X46),X45) = c_Groups_Oplus__class_Oplus(X48,c_Groups_Otimes__class_Otimes(X48,X47,X45),c_Groups_Otimes__class_Otimes(X48,X46,X45)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1402])]) ).

fof(c_0_2574,plain,
    ! [X44,X45,X46,X47] :
      ( ~ class_RealVector_Oreal__normed__algebra(X47)
      | c_Groups_Otimes__class_Otimes(X47,c_Groups_Oplus__class_Oplus(X47,X46,X45),X44) = c_Groups_Oplus__class_Oplus(X47,c_Groups_Otimes__class_Otimes(X47,X46,X44),c_Groups_Otimes__class_Otimes(X47,X45,X44)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1403])]) ).

fof(c_0_2575,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Ocomm__semiring__1(X37)
      | c_Groups_Otimes__class_Otimes(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),X34) = c_Groups_Oplus__class_Oplus(X37,c_Groups_Otimes__class_Otimes(X37,X36,X34),c_Groups_Otimes__class_Otimes(X37,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1404])]) ).

fof(c_0_2576,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Ocomm__semiring(X37)
      | c_Groups_Otimes__class_Otimes(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),X34) = c_Groups_Oplus__class_Oplus(X37,c_Groups_Otimes__class_Otimes(X37,X36,X34),c_Groups_Otimes__class_Otimes(X37,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1405])]) ).

fof(c_0_2577,plain,
    ! [X41,X42,X43,X44] :
      ( ~ class_RealVector_Oreal__normed__algebra(X44)
      | c_Groups_Otimes__class_Otimes(X44,X43,c_Groups_Oplus__class_Oplus(X44,X42,X41)) = c_Groups_Oplus__class_Oplus(X44,c_Groups_Otimes__class_Otimes(X44,X43,X42),c_Groups_Otimes__class_Otimes(X44,X43,X41)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1406])]) ).

fof(c_0_2578,plain,
    ! [X24,X25,X26,X27] :
      ( ~ class_Rings_Ocomm__semiring__1(X27)
      | c_Groups_Otimes__class_Otimes(X27,X26,c_Groups_Oplus__class_Oplus(X27,X25,X24)) = c_Groups_Oplus__class_Oplus(X27,c_Groups_Otimes__class_Otimes(X27,X26,X25),c_Groups_Otimes__class_Otimes(X27,X26,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1407])]) ).

fof(c_0_2579,plain,
    ! [X40,X41,X42,X43] :
      ( ~ class_RealVector_Oreal__normed__algebra(X43)
      | c_Groups_Otimes__class_Otimes(X43,X42,c_Groups_Oplus__class_Oplus(X43,X41,X40)) = c_Groups_Oplus__class_Oplus(X43,c_Groups_Otimes__class_Otimes(X43,X42,X41),c_Groups_Otimes__class_Otimes(X43,X42,X40)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1408])]) ).

fof(c_0_2580,plain,
    ! [X36,X37,X38,X39] :
      ( ~ class_Rings_Ocomm__semiring__1(X39)
      | c_Power_Opower__class_Opower(X39,c_Groups_Otimes__class_Otimes(X39,X38,X37),X36) = c_Groups_Otimes__class_Otimes(X39,c_Power_Opower__class_Opower(X39,X38,X36),c_Power_Opower__class_Opower(X39,X37,X36)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1409])]) ).

fof(c_0_2581,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Groups_Omonoid__mult(X24)
      | c_Power_Opower__class_Opower(X24,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)) = c_Groups_Otimes__class_Otimes(X24,c_Power_Opower__class_Opower(X24,X23,X22),c_Power_Opower__class_Opower(X24,X23,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1410])]) ).

fof(c_0_2582,plain,
    ! [X39,X40,X41,X42] :
      ( ~ class_Rings_Ocomm__semiring__1(X42)
      | c_Groups_Otimes__class_Otimes(X42,c_Power_Opower__class_Opower(X42,X41,X40),c_Power_Opower__class_Opower(X42,X41,X39)) = c_Power_Opower__class_Opower(X42,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,X39)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1411])]) ).

fof(c_0_2583,plain,
    ! [X44,X45,X46] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X46,X45)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X44)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X46,X44),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X45,X44)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1412])]) ).

fof(c_0_2584,plain,
    ! [X44,X45,X46] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X46,X45)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X44,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X45,X44),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X46,X44)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1413])]) ).

fof(c_0_2585,plain,
    ! [X24,X25,X26] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X26)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X25,X24)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X26,X25),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X26,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1414])]) ).

fof(c_0_2586,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,X55)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X54)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X54,X56),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X54,X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1415])]) ).

fof(c_0_2587,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,X55)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X54)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X56,X54),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X55,X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1416])]) ).

fof(c_0_2588,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X56,X55)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X54,X56),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X54,X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1417])]) ).

fof(c_0_2589,plain,
    ! [X39,X40,X41,X42] :
      ( ( X40 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(tc_Nat_Onat,X39,X40) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X42 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(tc_Nat_Onat,X41,X42) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X41,c_Power_Opower__class_Opower(tc_Nat_Onat,X41,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1418])])])]) ).

fof(c_0_2590,plain,
    ! [X21,X22,X23,X24] :
      ( ( X22 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X24 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X23)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1419])])])]) ).

fof(c_0_2591,plain,
    ! [X56,X57,X58,X59,X60,X61] :
      ( ( X56 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(X58,X57))
        | ~ hBOOL(hAPP(X58,c_Divides_Odiv__class_Omod(tc_Int_Oint,X57,X56))) )
      & ( epred1_3(X58,X57,X56)
        | ~ hBOOL(hAPP(X58,c_Divides_Odiv__class_Omod(tc_Int_Oint,X57,X56))) )
      & ( X59 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ epred1_3(X61,X60,X59)
        | hBOOL(hAPP(X61,c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X59))) )
      & ( ~ hBOOL(hAPP(X61,X60))
        | ~ epred1_3(X61,X60,X59)
        | hBOOL(hAPP(X61,c_Divides_Odiv__class_Omod(tc_Int_Oint,X60,X59))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1420])])])])]) ).

fof(c_0_2592,plain,
    ! [X72,X73,X74,X75] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X75,X74)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X73,X72)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X75,X73),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X74,X72)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1421])]) ).

fof(c_0_2593,plain,
    ! [X54,X55,X56,X57] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X55,X54)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X57,X55),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X56,X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1422])]) ).

fof(c_0_2594,plain,
    ! [X54,X55,X56,X57] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X57,X56)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X55,X54)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X55),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1423])]) ).

fof(c_0_2595,plain,
    ! [X21,X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X22)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X21)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X23)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1424])]) ).

fof(c_0_2596,plain,
    ! [X34,X35,X36] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X35)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X36)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X34),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1425])]) ).

fof(c_0_2597,plain,
    ! [X54,X55,X56,X57] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X57,X56)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X54)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X57,X55),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1426])]) ).

fof(c_0_2598,plain,
    ! [X26,X27] :
      ( ( ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),c_Power_Opower__class_Opower(X27,X26,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | X26 != c_Groups_Ozero__class_Ozero(X27)
        | ~ class_Rings_Olinordered__idom(X27) )
      & ( X26 = c_Groups_Ozero__class_Ozero(X27)
        | c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),c_Power_Opower__class_Opower(X27,X26,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | ~ class_Rings_Olinordered__idom(X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1427])])]) ).

fof(c_0_2599,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Olinordered__semiring__strict(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),c_Groups_Otimes__class_Otimes(X24,X23,X22))
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X23)
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1428])]) ).

fof(c_0_2600,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Olinordered__semiring__strict(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),c_Groups_Otimes__class_Otimes(X24,X23,X22))
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X22)
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1429])]) ).

fof(c_0_2601,plain,
    ! [X32,X34,X35] :
      ( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X32)
        | X32 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk12_1(X32)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
      & ( X34 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X35),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X34) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1430])])])])]) ).

fof(c_0_2602,plain,
    ! [X26,X27] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X27)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X27,X26))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X27) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X27,X26))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X27) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X27)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X27,X26))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1431])])]) ).

fof(c_0_2603,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Olinordered__idom(X5)
      | ~ c_Orderings_Oord__class_Oless(X5,c_Power_Opower__class_Opower(X5,X4,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1432])]) ).

fof(c_0_2604,plain,
    ! [X10,X11] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X11)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X10))) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X11),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X10))),
    inference(variable_rename,[status(thm)],[c_0_1433]) ).

fof(c_0_2605,plain,
    ! [X16,X17,X18,X19] :
      ( ( X17 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X17,X17),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X16,X16)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X16 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X17,X17),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X16,X16)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X19 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | X18 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X19,X19),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X18,X18)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1434])])])])]) ).

fof(c_0_2606,plain,
    ! [X21,X22,X23] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X22),X21),X22) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_1435]) ).

fof(c_0_2607,plain,
    ! [X21,X22,X23] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23,X22),X21) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X21),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21)),
    inference(variable_rename,[status(thm)],[c_0_1436]) ).

fof(c_0_2608,plain,
    ! [X21,X22,X23] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,X21)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X22),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X21)),
    inference(variable_rename,[status(thm)],[c_0_1437]) ).

fof(c_0_2609,plain,
    ! [X14,X15,X16] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X16,X15),X14) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X16,X14),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X14)),
    inference(variable_rename,[status(thm)],[c_0_1438]) ).

fof(c_0_2610,plain,
    ! [X21,X22,X23] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X23,X22),X21) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X21),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21)),
    inference(variable_rename,[status(thm)],[c_0_1439]) ).

fof(c_0_2611,plain,
    ! [X21,X22,X23] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X22),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X21)),
    inference(variable_rename,[status(thm)],[c_0_1440]) ).

fof(c_0_2612,plain,
    ! [X14,X15,X16] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X16,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X15,X14)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X16,X15),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X16,X14)),
    inference(variable_rename,[status(thm)],[c_0_1441]) ).

fof(c_0_2613,plain,
    ! [X14,X15,X16] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X16,X15),X14) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X16,X14),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X15,X14)),
    inference(variable_rename,[status(thm)],[c_0_1442]) ).

fof(c_0_2614,plain,
    ! [X14,X15,X16] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,X15),X14) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X16,X14),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X15,X14)),
    inference(variable_rename,[status(thm)],[c_0_1443]) ).

fof(c_0_2615,plain,
    ! [X14,X15,X16] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X14)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X16,X15),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X16,X14)),
    inference(variable_rename,[status(thm)],[c_0_1444]) ).

fof(c_0_2616,plain,
    ! [X21,X22,X23] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22),X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X21),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21)),
    inference(variable_rename,[status(thm)],[c_0_1445]) ).

fof(c_0_2617,plain,
    ! [X21,X22,X23] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X22),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X21)),
    inference(variable_rename,[status(thm)],[c_0_1446]) ).

fof(c_0_2618,plain,
    ! [X24,X25,X26] : c_Power_Opower__class_Opower(tc_Int_Oint,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X26,X25),c_Power_Opower__class_Opower(tc_Int_Oint,X26,X24)),
    inference(variable_rename,[status(thm)],[c_0_1447]) ).

fof(c_0_2619,plain,
    ! [X67,X68,X69,X70,X71,X72] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X69,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X68,X67))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X69,X67),X68) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X72,X70),X71)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X72,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X71,X70)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1448])])])]) ).

fof(c_0_2620,plain,
    ! [X67,X68,X69,X70,X71,X72] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X69,X68),X67)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X69,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X67,X68)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X72,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X70,X71))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X72,X71),X70) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1449])])])]) ).

fof(c_0_2621,plain,
    ! [X17,X18,X19] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | ~ c_Orderings_Oord__class_Oless(X19,c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)),c_Groups_Ozero__class_Ozero(X19))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( c_Orderings_Oord__class_Oless(X19,X18,c_Groups_Ozero__class_Ozero(X19))
        | ~ c_Orderings_Oord__class_Oless(X19,c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)),c_Groups_Ozero__class_Ozero(X19))
        | ~ class_Rings_Olinordered__idom(X19) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17))
        | ~ c_Orderings_Oord__class_Oless(X19,X18,c_Groups_Ozero__class_Ozero(X19))
        | c_Orderings_Oord__class_Oless(X19,c_Power_Opower__class_Opower(X19,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)),c_Groups_Ozero__class_Ozero(X19))
        | ~ class_Rings_Olinordered__idom(X19) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1450])])]) ).

fof(c_0_2622,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | ~ c_Rings_Odvd__class_Odvd(X24,X23,c_Divides_Odiv__class_Omod(X24,X22,X21))
      | ~ c_Rings_Odvd__class_Odvd(X24,X23,X21)
      | c_Rings_Odvd__class_Odvd(X24,X23,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1451])]) ).

fof(c_0_2623,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Rings_Odvd__class_Odvd(X22,X21,c_Divides_Odiv__class_Omod(X22,X19,X20))
        | c_Rings_Odvd__class_Odvd(X22,X21,X19)
        | ~ c_Rings_Odvd__class_Odvd(X22,X21,X20)
        | ~ class_Divides_Osemiring__div(X22) )
      & ( ~ c_Rings_Odvd__class_Odvd(X22,X21,X19)
        | c_Rings_Odvd__class_Odvd(X22,X21,c_Divides_Odiv__class_Omod(X22,X19,X20))
        | ~ c_Rings_Odvd__class_Odvd(X22,X21,X20)
        | ~ class_Divides_Osemiring__div(X22) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1452])])]) ).

fof(c_0_2624,plain,
    ! [X34,X35,X36] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X36)
      | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X35,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X34,X36)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X35,X34),X36) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1453])]) ).

fof(c_0_2625,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,X56)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X54,X56),X55) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1454])]) ).

fof(c_0_2626,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X54,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,X56)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X54,X55),X56) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1455])]) ).

fof(c_0_2627,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X54,X55),X56) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X54,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,X56)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1456])]) ).

fof(c_0_2628,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,X56),X54) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X54),X56) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1457])]) ).

fof(c_0_2629,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X54),X56) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,X56),X54) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1458])]) ).

fof(c_0_2630,plain,
    ! [X26,X27] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X26,X27))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X27) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X26,X27))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1459])])]) ).

fof(c_0_2631,plain,
    ! [X26,X27] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X26,X27))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X26,X27))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X27,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1460])])]) ).

fof(c_0_2632,plain,
    ! [X17,X18,X19,X20] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17)))
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) )
      & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X19) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X19))) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X19))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1461])])])])]) ).

fof(c_0_2633,plain,
    ! [X67,X68] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X67,X68))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,X67)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X68) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,X67)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X67,X68))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X68) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1462])])]) ).

fof(c_0_2634,plain,
    ! [X26,X27,X28] :
      ( ( c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
        | ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Otimes__class_Otimes(X28,X27,X26))
        | ~ class_Rings_Olinordered__ring__strict(X28) )
      & ( c_Orderings_Oord__class_Oless__eq(X28,X26,c_Groups_Ozero__class_Ozero(X28))
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
        | ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Otimes__class_Otimes(X28,X27,X26))
        | ~ class_Rings_Olinordered__ring__strict(X28) )
      & ( c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X26)
        | ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Otimes__class_Otimes(X28,X27,X26))
        | ~ class_Rings_Olinordered__ring__strict(X28) )
      & ( c_Orderings_Oord__class_Oless__eq(X28,X26,c_Groups_Ozero__class_Ozero(X28))
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X26)
        | ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Otimes__class_Otimes(X28,X27,X26))
        | ~ class_Rings_Olinordered__ring__strict(X28) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
        | ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X26)
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Otimes__class_Otimes(X28,X27,X26))
        | ~ class_Rings_Olinordered__ring__strict(X28) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
        | ~ c_Orderings_Oord__class_Oless__eq(X28,X26,c_Groups_Ozero__class_Ozero(X28))
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Groups_Otimes__class_Otimes(X28,X27,X26))
        | ~ class_Rings_Olinordered__ring__strict(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1463])])]) ).

fof(c_0_2635,plain,
    ! [X26,X27,X28] :
      ( ( c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
        | ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Otimes__class_Otimes(X28,X27,X26),c_Groups_Ozero__class_Ozero(X28))
        | ~ class_Rings_Olinordered__ring__strict(X28) )
      & ( c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X26)
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
        | ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Otimes__class_Otimes(X28,X27,X26),c_Groups_Ozero__class_Ozero(X28))
        | ~ class_Rings_Olinordered__ring__strict(X28) )
      & ( c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
        | c_Orderings_Oord__class_Oless__eq(X28,X26,c_Groups_Ozero__class_Ozero(X28))
        | ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Otimes__class_Otimes(X28,X27,X26),c_Groups_Ozero__class_Ozero(X28))
        | ~ class_Rings_Olinordered__ring__strict(X28) )
      & ( c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X26)
        | c_Orderings_Oord__class_Oless__eq(X28,X26,c_Groups_Ozero__class_Ozero(X28))
        | ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Otimes__class_Otimes(X28,X27,X26),c_Groups_Ozero__class_Ozero(X28))
        | ~ class_Rings_Olinordered__ring__strict(X28) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
        | ~ c_Orderings_Oord__class_Oless__eq(X28,X26,c_Groups_Ozero__class_Ozero(X28))
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Otimes__class_Otimes(X28,X27,X26),c_Groups_Ozero__class_Ozero(X28))
        | ~ class_Rings_Olinordered__ring__strict(X28) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X28,X27,c_Groups_Ozero__class_Ozero(X28))
        | ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X26)
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Otimes__class_Otimes(X28,X27,X26),c_Groups_Ozero__class_Ozero(X28))
        | ~ class_Rings_Olinordered__ring__strict(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1464])])]) ).

fof(c_0_2636,plain,
    ! [X22,X23,X24,X25] :
      ( ~ class_Rings_Olinordered__semidom(X25)
      | c_Power_Opower__class_Opower(X25,X24,c_Nat_OSuc(X23)) != c_Power_Opower__class_Opower(X25,X22,c_Nat_OSuc(X23))
      | ~ c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25),X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X25,c_Groups_Ozero__class_Ozero(X25),X22)
      | X24 = X22 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1465])]) ).

fof(c_0_2637,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X22)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X21),X22) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1466])]) ).

fof(c_0_2638,plain,
    ! [X21,X22,X23,X24] :
      ( ( X22 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21) = X21 )
      & ( X24 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X23) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X23)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1467])])])]) ).

fof(c_0_2639,plain,
    ! [X21,X22,X23] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X23,c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X21))
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X23,X21)
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X23,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1468])]) ).

fof(c_0_2640,plain,
    ! [X21,X22,X23] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X23,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X22,X21))
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X23,X21)
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X23,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1469])]) ).

fof(c_0_2641,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__semidom(X23)
      | ~ c_Orderings_Oord__class_Oless(X23,c_Groups_Ozero__class_Ozero(X23),X22)
      | ~ c_Orderings_Oord__class_Oless(X23,X22,c_Groups_Oone__class_Oone(X23))
      | c_Orderings_Oord__class_Oless(X23,c_Power_Opower__class_Opower(X23,X22,c_Nat_OSuc(X21)),c_Groups_Oone__class_Oone(X23)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1470])]) ).

fof(c_0_2642,plain,
    ! [X19,X20,X21,X22] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1471])])])])]) ).

fof(c_0_2643,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1472])]) ).

fof(c_0_2644,plain,
    ! [X24,X25,X26,X27] :
      ( ~ class_Rings_Olinordered__idom(X27)
      | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X26)
      | ~ c_Orderings_Oord__class_Oless__eq(X27,X25,X24)
      | c_Orderings_Oord__class_Oless__eq(X27,c_Power_Opower__class_Opower(X27,X25,X26),c_Power_Opower__class_Opower(X27,X24,X26)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1473])]) ).

fof(c_0_2645,plain,
    ! [X55,X56,X57] :
      ( ~ class_Rings_Olinordered__semidom(X57)
      | ~ c_Orderings_Oord__class_Oless__eq(X57,c_Groups_Ozero__class_Ozero(X57),X56)
      | ~ c_Orderings_Oord__class_Oless__eq(X57,X56,c_Groups_Oone__class_Oone(X57))
      | c_Orderings_Oord__class_Oless__eq(X57,c_Power_Opower__class_Opower(X57,X56,c_Nat_OSuc(X55)),X56) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1474])]) ).

fof(c_0_2646,plain,
    ! [X22,X23,X24] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,X23,c_Groups_Ozero__class_Ozero(X24))
      | ~ c_Orderings_Oord__class_Oless(X24,X22,c_Groups_Ozero__class_Ozero(X24))
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Oplus__class_Oplus(X24,X23,X22),c_Groups_Ozero__class_Ozero(X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1475])]) ).

fof(c_0_2647,plain,
    ! [X22,X23,X24] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,X23,c_Groups_Ozero__class_Ozero(X24))
      | ~ c_Orderings_Oord__class_Oless__eq(X24,X22,c_Groups_Ozero__class_Ozero(X24))
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Oplus__class_Oplus(X24,X23,X22),c_Groups_Ozero__class_Ozero(X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1476])]) ).

fof(c_0_2648,plain,
    ! [X22,X23,X24] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X23)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X22)
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),c_Groups_Oplus__class_Oplus(X24,X23,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1477])]) ).

fof(c_0_2649,plain,
    ! [X22,X23,X24] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X22)
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),c_Groups_Oplus__class_Oplus(X24,X23,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1478])]) ).

fof(c_0_2650,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__semidom(X23)
      | ~ c_Orderings_Oord__class_Oless(X23,c_Groups_Oone__class_Oone(X23),X22)
      | ~ c_Orderings_Oord__class_Oless(X23,c_Groups_Oone__class_Oone(X23),X21)
      | c_Orderings_Oord__class_Oless(X23,c_Groups_Oone__class_Oone(X23),c_Groups_Otimes__class_Otimes(X23,X22,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1479])]) ).

fof(c_0_2651,plain,
    ! [X22,X23,X24] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,X23,c_Groups_Ozero__class_Ozero(X24))
      | ~ c_Orderings_Oord__class_Oless__eq(X24,X22,c_Groups_Ozero__class_Ozero(X24))
      | c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Oplus__class_Oplus(X24,X23,X22),c_Groups_Ozero__class_Ozero(X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1480])]) ).

fof(c_0_2652,plain,
    ! [X22,X23,X24] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X22)
      | c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),c_Groups_Oplus__class_Oplus(X24,X23,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1481])]) ).

fof(c_0_2653,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Oordered__cancel__semiring(X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X22)
      | c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),c_Groups_Otimes__class_Otimes(X24,X23,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1482])]) ).

fof(c_0_2654,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Oordered__cancel__semiring(X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,X22,c_Groups_Ozero__class_Ozero(X24))
      | c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Otimes__class_Otimes(X24,X23,X22),c_Groups_Ozero__class_Ozero(X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1483])]) ).

fof(c_0_2655,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Oordered__cancel__semiring(X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,X22,c_Groups_Ozero__class_Ozero(X24))
      | c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Otimes__class_Otimes(X24,X22,X23),c_Groups_Ozero__class_Ozero(X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1484])]) ).

fof(c_0_2656,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Oordered__cancel__semiring(X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,X23,c_Groups_Ozero__class_Ozero(X24))
      | ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X22)
      | c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Otimes__class_Otimes(X24,X23,X22),c_Groups_Ozero__class_Ozero(X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1485])]) ).

fof(c_0_2657,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Oordered__ring(X24)
      | ~ c_Orderings_Oord__class_Oless__eq(X24,X23,c_Groups_Ozero__class_Ozero(X24))
      | ~ c_Orderings_Oord__class_Oless__eq(X24,X22,c_Groups_Ozero__class_Ozero(X24))
      | c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),c_Groups_Otimes__class_Otimes(X24,X23,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1486])]) ).

fof(c_0_2658,plain,
    ! [X22,X23,X24] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X23)
        | ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X22)
        | c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),c_Groups_Otimes__class_Otimes(X24,X23,X22))
        | ~ class_Rings_Oordered__ring(X24) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X24,X23,c_Groups_Ozero__class_Ozero(X24))
        | ~ c_Orderings_Oord__class_Oless__eq(X24,X22,c_Groups_Ozero__class_Ozero(X24))
        | c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),c_Groups_Otimes__class_Otimes(X24,X23,X22))
        | ~ class_Rings_Oordered__ring(X24) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1487])])]) ).

fof(c_0_2659,plain,
    ! [X22,X23,X24] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X23)
        | ~ c_Orderings_Oord__class_Oless__eq(X24,X22,c_Groups_Ozero__class_Ozero(X24))
        | c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Otimes__class_Otimes(X24,X23,X22),c_Groups_Ozero__class_Ozero(X24))
        | ~ class_Rings_Oordered__cancel__semiring(X24) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X24,X23,c_Groups_Ozero__class_Ozero(X24))
        | ~ c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Ozero__class_Ozero(X24),X22)
        | c_Orderings_Oord__class_Oless__eq(X24,c_Groups_Otimes__class_Otimes(X24,X23,X22),c_Groups_Ozero__class_Ozero(X24))
        | ~ class_Rings_Oordered__cancel__semiring(X24) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1488])])]) ).

fof(c_0_2660,plain,
    ! [X22,X23,X24] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X23)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X22)
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),c_Groups_Oplus__class_Oplus(X24,X23,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1489])]) ).

fof(c_0_2661,plain,
    ! [X22,X23,X24] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,X23,c_Groups_Ozero__class_Ozero(X24))
      | ~ c_Orderings_Oord__class_Oless(X24,X22,c_Groups_Ozero__class_Ozero(X24))
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Oplus__class_Oplus(X24,X23,X22),c_Groups_Ozero__class_Ozero(X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1490])]) ).

fof(c_0_2662,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Olinordered__semiring__strict(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X23)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X22)
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),c_Groups_Otimes__class_Otimes(X24,X23,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1491])]) ).

fof(c_0_2663,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Olinordered__semiring__strict(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X23)
      | ~ c_Orderings_Oord__class_Oless(X24,X22,c_Groups_Ozero__class_Ozero(X24))
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Otimes__class_Otimes(X24,X23,X22),c_Groups_Ozero__class_Ozero(X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1492])]) ).

fof(c_0_2664,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Olinordered__semiring__strict(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X23)
      | ~ c_Orderings_Oord__class_Oless(X24,X22,c_Groups_Ozero__class_Ozero(X24))
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Otimes__class_Otimes(X24,X22,X23),c_Groups_Ozero__class_Ozero(X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1493])]) ).

fof(c_0_2665,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Olinordered__semiring__strict(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,X23,c_Groups_Ozero__class_Ozero(X24))
      | ~ c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),X22)
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Otimes__class_Otimes(X24,X23,X22),c_Groups_Ozero__class_Ozero(X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1494])]) ).

fof(c_0_2666,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Olinordered__ring__strict(X24)
      | ~ c_Orderings_Oord__class_Oless(X24,X23,c_Groups_Ozero__class_Ozero(X24))
      | ~ c_Orderings_Oord__class_Oless(X24,X22,c_Groups_Ozero__class_Ozero(X24))
      | c_Orderings_Oord__class_Oless(X24,c_Groups_Ozero__class_Ozero(X24),c_Groups_Otimes__class_Otimes(X24,X23,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1495])]) ).

fof(c_0_2667,plain,
    ! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X20))),
    inference(variable_rename,[status(thm)],[c_0_1496]) ).

fof(c_0_2668,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X22)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1497])])])])]) ).

fof(c_0_2669,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1498])]) ).

fof(c_0_2670,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1499])]) ).

fof(c_0_2671,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,X36,X35)
      | c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Oplus__class_Oplus(X37,X36,X34),c_Groups_Oplus__class_Oplus(X37,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1500])]) ).

fof(c_0_2672,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,X36,X35)
      | c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Oplus__class_Oplus(X37,X34,X36),c_Groups_Oplus__class_Oplus(X37,X34,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1501])]) ).

fof(c_0_2673,plain,
    ! [X24,X25,X26,X27] :
      ( ~ class_Rings_Ocomm__semiring__1(X27)
      | ~ c_Rings_Odvd__class_Odvd(X27,X26,X25)
      | c_Rings_Odvd__class_Odvd(X27,c_Power_Opower__class_Opower(X27,X26,X24),c_Power_Opower__class_Opower(X27,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1502])]) ).

fof(c_0_2674,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,X36,X35)
      | c_Orderings_Oord__class_Oless(X37,c_Groups_Oplus__class_Oplus(X37,X34,X36),c_Groups_Oplus__class_Oplus(X37,X34,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1503])]) ).

fof(c_0_2675,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,X36,X35)
      | c_Orderings_Oord__class_Oless(X37,c_Groups_Oplus__class_Oplus(X37,X36,X34),c_Groups_Oplus__class_Oplus(X37,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1504])]) ).

fof(c_0_2676,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__semidom(X23)
      | ~ c_Orderings_Oord__class_Oless(X23,c_Groups_Oone__class_Oone(X23),X22)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
      | c_Orderings_Oord__class_Oless(X23,c_Groups_Oone__class_Oone(X23),c_Power_Opower__class_Opower(X23,X22,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1505])]) ).

fof(c_0_2677,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Rings_Ocomm__semiring__1(X24)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X22)
      | c_Rings_Odvd__class_Odvd(X24,c_Power_Opower__class_Opower(X24,X21,X23),c_Power_Opower__class_Opower(X24,X21,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1506])]) ).

fof(c_0_2678,plain,
    ! [X24,X25,X26] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X24)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X26) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X26)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X26) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1507])])]) ).

fof(c_0_2679,plain,
    ! [X18,X19,X20,X21,X22,X23] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20,X19) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X18,X19)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X19,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X20,X18)) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X22,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,X21))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X22) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X22) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1508])])])]) ).

fof(c_0_2680,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Ozero__class_Ozero(X37),X36)
      | ~ c_Orderings_Oord__class_Oless(X37,X35,X34)
      | c_Orderings_Oord__class_Oless(X37,X35,c_Groups_Oplus__class_Oplus(X37,X36,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1509])]) ).

fof(c_0_2681,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X36)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,X35,X34)
      | c_Orderings_Oord__class_Oless(X37,X35,c_Groups_Oplus__class_Oplus(X37,X36,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1510])]) ).

fof(c_0_2682,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Ozero__class_Ozero(X37),X36)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,X35,X34)
      | c_Orderings_Oord__class_Oless__eq(X37,X35,c_Groups_Oplus__class_Oplus(X37,X34,X36)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1511])]) ).

fof(c_0_2683,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X37)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,c_Groups_Ozero__class_Ozero(X37),X36)
      | ~ c_Orderings_Oord__class_Oless__eq(X37,X35,X34)
      | c_Orderings_Oord__class_Oless__eq(X37,X35,c_Groups_Oplus__class_Oplus(X37,X36,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1512])]) ).

fof(c_0_2684,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Olinordered__semidom(X37)
      | ~ c_Orderings_Oord__class_Oless(X37,c_Groups_Ozero__class_Ozero(X37),X36)
      | ~ c_Orderings_Oord__class_Oless(X37,X35,X34)
      | c_Orderings_Oord__class_Oless(X37,X35,c_Groups_Oplus__class_Oplus(X37,X36,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1513])]) ).

fof(c_0_2685,plain,
    ! [X62,X63,X64] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X64,c_Int_Onumber__class_Onumber__of(X64,X63),c_Int_Onumber__class_Onumber__of(X64,X62))
        | ~ c_Orderings_Oord__class_Oless(X64,c_Int_Onumber__class_Onumber__of(X64,X62),c_Int_Onumber__class_Onumber__of(X64,X63))
        | ~ class_Int_Onumber(X64)
        | ~ class_Orderings_Olinorder(X64) )
      & ( c_Orderings_Oord__class_Oless(X64,c_Int_Onumber__class_Onumber__of(X64,X62),c_Int_Onumber__class_Onumber__of(X64,X63))
        | c_Orderings_Oord__class_Oless__eq(X64,c_Int_Onumber__class_Onumber__of(X64,X63),c_Int_Onumber__class_Onumber__of(X64,X62))
        | ~ class_Int_Onumber(X64)
        | ~ class_Orderings_Olinorder(X64) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1514])])]) ).

fof(c_0_2686,plain,
    ! [X18,X19,X20] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X19,X18))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( c_Orderings_Oord__class_Oless(X20,c_Groups_Ozero__class_Ozero(X20),X19)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X19,X18))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | X19 != c_Groups_Ozero__class_Ozero(X20)
        | X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X19,X18))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( c_Orderings_Oord__class_Oless(X20,c_Groups_Ozero__class_Ozero(X20),X19)
        | X19 != c_Groups_Ozero__class_Ozero(X20)
        | X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X19,X18))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( X18 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X19,X18))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | X19 = c_Groups_Ozero__class_Ozero(X20)
        | c_Orderings_Oord__class_Oless(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X19,X18))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | ~ c_Orderings_Oord__class_Oless(X20,c_Groups_Ozero__class_Ozero(X20),X19)
        | c_Orderings_Oord__class_Oless(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X19,X18))
        | ~ class_Rings_Olinordered__idom(X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1515])])]) ).

fof(c_0_2687,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X22,X21)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X21,X22)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1516])]) ).

fof(c_0_2688,plain,
    ! [X18,X19,X20] :
      ( ( X18 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(X20,c_Power_Opower__class_Opower(X20,X19,X18),c_Groups_Ozero__class_Ozero(X20))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X20,c_Power_Opower__class_Opower(X20,X19,X18),c_Groups_Ozero__class_Ozero(X20))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( X19 = c_Groups_Ozero__class_Ozero(X20)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X20,c_Power_Opower__class_Opower(X20,X19,X18),c_Groups_Ozero__class_Ozero(X20))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | c_Orderings_Oord__class_Oless__eq(X20,X19,c_Groups_Ozero__class_Ozero(X20))
        | ~ c_Orderings_Oord__class_Oless__eq(X20,c_Power_Opower__class_Opower(X20,X19,X18),c_Groups_Ozero__class_Ozero(X20))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( X19 = c_Groups_Ozero__class_Ozero(X20)
        | c_Orderings_Oord__class_Oless__eq(X20,X19,c_Groups_Ozero__class_Ozero(X20))
        | ~ c_Orderings_Oord__class_Oless__eq(X20,c_Power_Opower__class_Opower(X20,X19,X18),c_Groups_Ozero__class_Ozero(X20))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X20,X19,c_Groups_Ozero__class_Ozero(X20))
        | X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(X20,c_Power_Opower__class_Opower(X20,X19,X18),c_Groups_Ozero__class_Ozero(X20))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | X19 != c_Groups_Ozero__class_Ozero(X20)
        | X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(X20,c_Power_Opower__class_Opower(X20,X19,X18),c_Groups_Ozero__class_Ozero(X20))
        | ~ class_Rings_Olinordered__idom(X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1517])])]) ).

fof(c_0_2689,plain,
    ! [X18,X19,X20] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X19,X18))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( c_Orderings_Oord__class_Oless__eq(X20,c_Groups_Ozero__class_Ozero(X20),X19)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X19,X18))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | c_Orderings_Oord__class_Oless__eq(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X19,X18))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X20,c_Groups_Ozero__class_Ozero(X20),X19)
        | c_Orderings_Oord__class_Oless__eq(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X19,X18))
        | ~ class_Rings_Olinordered__idom(X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1518])])]) ).

fof(c_0_2690,plain,
    ! [X26,X27,X28] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Power_Opower__class_Opower(X28,X27,X26))
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X26)
        | ~ class_Rings_Olinordered__idom(X28) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),X27)
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Power_Opower__class_Opower(X28,X27,X26))
        | ~ class_Rings_Olinordered__idom(X28) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X26)
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ozero__class_Ozero(X28),c_Power_Opower__class_Opower(X28,X27,X26))
        | ~ class_Rings_Olinordered__idom(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1519])])]) ).

fof(c_0_2691,plain,
    ! [X18,X19,X20] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X18,X19))
        | c_Orderings_Oord__class_Oless__eq(X20,c_Groups_Ozero__class_Ozero(X20),X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X19)
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X20,c_Groups_Ozero__class_Ozero(X20),X18)
        | c_Orderings_Oord__class_Oless__eq(X20,c_Groups_Ozero__class_Ozero(X20),c_Power_Opower__class_Opower(X20,X18,X19))
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X19)
        | ~ class_Rings_Olinordered__idom(X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1520])])]) ).

fof(c_0_2692,plain,
    ! [X21,X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X22)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X23,X21),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1521])]) ).

fof(c_0_2693,plain,
    ! [X21,X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X22)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X23)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1522])]) ).

fof(c_0_2694,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X56,X55)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,X56),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1523])]) ).

fof(c_0_2695,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X54,X56),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X54,X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1524])]) ).

fof(c_0_2696,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X56,X54),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X55,X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1525])]) ).

fof(c_0_2697,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X54),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1526])]) ).

fof(c_0_2698,plain,
    ! [X24,X25,X26] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X25)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X24,X26),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X24,X25)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1527])]) ).

fof(c_0_2699,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,X55)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X54),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1528])]) ).

fof(c_0_2700,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X56,X55)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X56,X54),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1529])]) ).

fof(c_0_2701,plain,
    ! [X20,X21,X22] :
      ( ~ class_Rings_Ocomm__semiring__1(X22)
      | c_Groups_Oplus__class_Oplus(X22,c_Groups_Otimes__class_Otimes(X22,X21,X20),X20) = c_Groups_Otimes__class_Otimes(X22,c_Groups_Oplus__class_Oplus(X22,X21,c_Groups_Oone__class_Oone(X22)),X20) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1530])]) ).

fof(c_0_2702,plain,
    ! [X20,X21,X22] :
      ( ~ class_Rings_Ocomm__semiring__1(X22)
      | c_Groups_Oplus__class_Oplus(X22,X21,c_Groups_Otimes__class_Otimes(X22,X20,X21)) = c_Groups_Otimes__class_Otimes(X22,c_Groups_Oplus__class_Oplus(X22,X20,c_Groups_Oone__class_Oone(X22)),X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1531])]) ).

fof(c_0_2703,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | ~ c_Rings_Odvd__class_Odvd(X24,X23,X22)
      | ~ c_Rings_Odvd__class_Odvd(X24,X23,X21)
      | c_Rings_Odvd__class_Odvd(X24,X23,c_Divides_Odiv__class_Omod(X24,X22,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1532])]) ).

fof(c_0_2704,plain,
    ! [X24,X25,X26,X27] :
      ( ~ class_Rings_Ocomm__ring__1(X27)
      | ~ c_Rings_Odvd__class_Odvd(X27,X26,X25)
      | ~ c_Rings_Odvd__class_Odvd(X27,X26,X24)
      | c_Rings_Odvd__class_Odvd(X27,X26,c_Groups_Ominus__class_Ominus(X27,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1533])]) ).

fof(c_0_2705,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Ocomm__semiring__1(X37)
      | ~ c_Rings_Odvd__class_Odvd(X37,X36,X35)
      | ~ c_Rings_Odvd__class_Odvd(X37,X36,X34)
      | c_Rings_Odvd__class_Odvd(X37,X36,c_Groups_Oplus__class_Oplus(X37,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1534])]) ).

fof(c_0_2706,plain,
    ! [X18,X20,X21] :
      ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | X18 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk3_1(X18))) )
      & ( X20 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21))
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1535])])])])]) ).

fof(c_0_2707,plain,
    ! [X19,X20] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20),X20)
        | X19 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) )
      & ( X19 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20),X20)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1536])])]) ).

fof(c_0_2708,plain,
    ! [X19,X20] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19),X20)
        | X19 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) )
      & ( X19 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19),X20)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1537])])]) ).

fof(c_0_2709,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X23,X22),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1538])]) ).

fof(c_0_2710,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X23,X22),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1539])]) ).

fof(c_0_2711,plain,
    ! [X24,X25] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1540])]) ).

fof(c_0_2712,plain,
    ! [X24,X25] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1541])]) ).

fof(c_0_2713,plain,
    ! [X24,X25] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1542])]) ).

fof(c_0_2714,plain,
    ! [X24,X25] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X25)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1543])]) ).

fof(c_0_2715,plain,
    ! [X19,X20,X21,X22] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X22)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1544])])])])]) ).

fof(c_0_2716,plain,
    ! [X19,X20,X21] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X21) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X21)
        | X20 = X19
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X19)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20) )
      & ( X20 != X19
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X21) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X21)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X19)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1545])])]) ).

fof(c_0_2717,plain,
    ! [X24,X25] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X25,X24),X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1546])]) ).

fof(c_0_2718,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X22)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22),X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1547])]) ).

fof(c_0_2719,plain,
    ! [X26,X27] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Oplus__class_Oplus(X27,X26,X26),c_Groups_Ozero__class_Ozero(X27))
        | c_Orderings_Oord__class_Oless__eq(X27,X26,c_Groups_Ozero__class_Ozero(X27))
        | ~ class_Groups_Olinordered__ab__group__add(X27) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X27,X26,c_Groups_Ozero__class_Ozero(X27))
        | c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Oplus__class_Oplus(X27,X26,X26),c_Groups_Ozero__class_Ozero(X27))
        | ~ class_Groups_Olinordered__ab__group__add(X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1548])])]) ).

fof(c_0_2720,plain,
    ! [X26,X27] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),c_Groups_Oplus__class_Oplus(X27,X26,X26))
        | c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X26)
        | ~ class_Groups_Olinordered__ab__group__add(X27) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),X26)
        | c_Orderings_Oord__class_Oless__eq(X27,c_Groups_Ozero__class_Ozero(X27),c_Groups_Oplus__class_Oplus(X27,X26,X26))
        | ~ class_Groups_Olinordered__ab__group__add(X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1549])])]) ).

fof(c_0_2721,plain,
    ! [X26,X27] :
      ( ( ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Oplus__class_Oplus(X27,X26,X26),c_Groups_Ozero__class_Ozero(X27))
        | c_Orderings_Oord__class_Oless(X27,X26,c_Groups_Ozero__class_Ozero(X27))
        | ~ class_Groups_Olinordered__ab__group__add(X27) )
      & ( ~ c_Orderings_Oord__class_Oless(X27,X26,c_Groups_Ozero__class_Ozero(X27))
        | c_Orderings_Oord__class_Oless(X27,c_Groups_Oplus__class_Oplus(X27,X26,X26),c_Groups_Ozero__class_Ozero(X27))
        | ~ class_Groups_Olinordered__ab__group__add(X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1550])])]) ).

fof(c_0_2722,plain,
    ! [X26,X27] :
      ( ( ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),c_Groups_Oplus__class_Oplus(X27,X26,X26))
        | c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26)
        | ~ class_Groups_Olinordered__ab__group__add(X27) )
      & ( ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),X26)
        | c_Orderings_Oord__class_Oless(X27,c_Groups_Ozero__class_Ozero(X27),c_Groups_Oplus__class_Oplus(X27,X26,X26))
        | ~ class_Groups_Olinordered__ab__group__add(X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1551])])]) ).

fof(c_0_2723,plain,
    ! [X18,X19,X20] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | ~ c_Orderings_Oord__class_Oless(X20,c_Power_Opower__class_Opower(X20,X19,X18),c_Groups_Ozero__class_Ozero(X20))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( c_Orderings_Oord__class_Oless(X20,X19,c_Groups_Ozero__class_Ozero(X20))
        | ~ c_Orderings_Oord__class_Oless(X20,c_Power_Opower__class_Opower(X20,X19,X18),c_Groups_Ozero__class_Ozero(X20))
        | ~ class_Rings_Olinordered__idom(X20) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | ~ c_Orderings_Oord__class_Oless(X20,X19,c_Groups_Ozero__class_Ozero(X20))
        | c_Orderings_Oord__class_Oless(X20,c_Power_Opower__class_Opower(X20,X19,X18),c_Groups_Ozero__class_Ozero(X20))
        | ~ class_Rings_Olinordered__idom(X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1552])])]) ).

fof(c_0_2724,plain,
    ! [X26,X27] :
      ( ( ~ c_Orderings_Oord__class_Oless(X27,c_Groups_Oplus__class_Oplus(X27,X26,X26),c_Groups_Ozero__class_Ozero(X27))
        | c_Orderings_Oord__class_Oless(X27,X26,c_Groups_Ozero__class_Ozero(X27))
        | ~ class_Rings_Olinordered__idom(X27) )
      & ( ~ c_Orderings_Oord__class_Oless(X27,X26,c_Groups_Ozero__class_Ozero(X27))
        | c_Orderings_Oord__class_Oless(X27,c_Groups_Oplus__class_Oplus(X27,X26,X26),c_Groups_Ozero__class_Ozero(X27))
        | ~ class_Rings_Olinordered__idom(X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1553])])]) ).

fof(c_0_2725,plain,
    ! [X21,X22,X23] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X23),X22),c_Nat_OSuc(X21)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X23,X22),X21),
    inference(variable_rename,[status(thm)],[c_0_1554]) ).

fof(c_0_2726,plain,
    ! [X21,X22,X23] :
      ( ~ class_Groups_Omonoid__mult(X23)
      | c_Groups_Otimes__class_Otimes(X23,c_Power_Opower__class_Opower(X23,X22,X21),X22) = c_Groups_Otimes__class_Otimes(X23,X22,c_Power_Opower__class_Opower(X23,X22,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1555])]) ).

fof(c_0_2727,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oab__semigroup__add(X37)
      | c_Groups_Oplus__class_Oplus(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),X34) = c_Groups_Oplus__class_Oplus(X37,X36,c_Groups_Oplus__class_Oplus(X37,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1556])]) ).

fof(c_0_2728,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Oab__semigroup__mult(X37)
      | c_Groups_Otimes__class_Otimes(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),X34) = c_Groups_Otimes__class_Otimes(X37,X36,c_Groups_Otimes__class_Otimes(X37,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1557])]) ).

fof(c_0_2729,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Ocomm__semiring__1(X37)
      | c_Groups_Oplus__class_Oplus(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),X34) = c_Groups_Oplus__class_Oplus(X37,c_Groups_Oplus__class_Oplus(X37,X36,X34),X35) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1558])]) ).

fof(c_0_2730,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Ocomm__semiring__1(X37)
      | c_Groups_Oplus__class_Oplus(X37,c_Groups_Oplus__class_Oplus(X37,X36,X35),X34) = c_Groups_Oplus__class_Oplus(X37,X36,c_Groups_Oplus__class_Oplus(X37,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1559])]) ).

fof(c_0_2731,plain,
    ! [X35,X36,X37,X38] :
      ( ~ class_Rings_Ocomm__semiring__1(X38)
      | c_Groups_Oplus__class_Oplus(X38,X37,c_Groups_Oplus__class_Oplus(X38,X36,X35)) = c_Groups_Oplus__class_Oplus(X38,c_Groups_Oplus__class_Oplus(X38,X37,X36),X35) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1560])]) ).

fof(c_0_2732,plain,
    ! [X35,X36,X37,X38] :
      ( ~ class_Rings_Ocomm__semiring__1(X38)
      | c_Groups_Oplus__class_Oplus(X38,X37,c_Groups_Oplus__class_Oplus(X38,X36,X35)) = c_Groups_Oplus__class_Oplus(X38,X36,c_Groups_Oplus__class_Oplus(X38,X37,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1561])]) ).

fof(c_0_2733,plain,
    ! [X30,X31,X32,X33] :
      ( ~ class_Rings_Ocomm__semiring__1(X33)
      | c_Groups_Otimes__class_Otimes(X33,X32,c_Groups_Otimes__class_Otimes(X33,X31,X30)) = c_Groups_Otimes__class_Otimes(X33,X31,c_Groups_Otimes__class_Otimes(X33,X32,X30)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1562])]) ).

fof(c_0_2734,plain,
    ! [X30,X31,X32,X33] :
      ( ~ class_Rings_Ocomm__semiring__1(X33)
      | c_Groups_Otimes__class_Otimes(X33,X32,c_Groups_Otimes__class_Otimes(X33,X31,X30)) = c_Groups_Otimes__class_Otimes(X33,c_Groups_Otimes__class_Otimes(X33,X32,X31),X30) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1563])]) ).

fof(c_0_2735,plain,
    ! [X30,X31,X32,X33] :
      ( ~ class_Rings_Ocomm__semiring__1(X33)
      | c_Groups_Otimes__class_Otimes(X33,c_Groups_Otimes__class_Otimes(X33,X32,X31),X30) = c_Groups_Otimes__class_Otimes(X33,X32,c_Groups_Otimes__class_Otimes(X33,X31,X30)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1564])]) ).

fof(c_0_2736,plain,
    ! [X30,X31,X32,X33] :
      ( ~ class_Rings_Ocomm__semiring__1(X33)
      | c_Groups_Otimes__class_Otimes(X33,c_Groups_Otimes__class_Otimes(X33,X32,X31),X30) = c_Groups_Otimes__class_Otimes(X33,c_Groups_Otimes__class_Otimes(X33,X32,X30),X31) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1565])]) ).

fof(c_0_2737,plain,
    ! [X21,X22,X23,X24] :
      ( ~ class_Groups_Omonoid__mult(X24)
      | c_Power_Opower__class_Opower(X24,X23,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21)) = c_Power_Opower__class_Opower(X24,c_Power_Opower__class_Opower(X24,X23,X22),X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1566])]) ).

fof(c_0_2738,plain,
    ! [X39,X40,X41,X42] :
      ( ~ class_Rings_Ocomm__semiring__1(X42)
      | c_Power_Opower__class_Opower(X42,c_Power_Opower__class_Opower(X42,X41,X40),X39) = c_Power_Opower__class_Opower(X42,X41,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X40,X39)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1567])]) ).

fof(c_0_2739,plain,
    ! [X26,X27,X28] :
      ( ( ~ c_Orderings_Oord__class_Oless(X28,X27,X26)
        | c_Orderings_Oord__class_Oless(X28,c_Groups_Ominus__class_Ominus(X28,X27,X26),c_Groups_Ozero__class_Ozero(X28))
        | ~ class_Groups_Oordered__ab__group__add(X28) )
      & ( ~ c_Orderings_Oord__class_Oless(X28,c_Groups_Ominus__class_Ominus(X28,X27,X26),c_Groups_Ozero__class_Ozero(X28))
        | c_Orderings_Oord__class_Oless(X28,X27,X26)
        | ~ class_Groups_Oordered__ab__group__add(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1568])])]) ).

fof(c_0_2740,plain,
    ! [X26,X27,X28] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X28,X27,X26)
        | c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ominus__class_Ominus(X28,X27,X26),c_Groups_Ozero__class_Ozero(X28))
        | ~ class_Groups_Oordered__ab__group__add(X28) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X28,c_Groups_Ominus__class_Ominus(X28,X27,X26),c_Groups_Ozero__class_Ozero(X28))
        | c_Orderings_Oord__class_Oless__eq(X28,X27,X26)
        | ~ class_Groups_Oordered__ab__group__add(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1569])])]) ).

fof(c_0_2741,plain,
    ! [X21,X22] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X22),X21) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,X21)),X21),
    inference(variable_rename,[status(thm)],[c_0_1570]) ).

fof(c_0_2742,plain,
    ! [X8,X9] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X9),X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)),X8),
    inference(variable_rename,[status(thm)],[c_0_1571]) ).

fof(c_0_2743,plain,
    ! [X76,X77,X78] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X78,X77)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X78,X76)
      | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X78,c_Divides_Odiv__class_Omod(tc_Int_Oint,X77,X76)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1572])]) ).

fof(c_0_2744,plain,
    ! [X21,X22,X23] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X21)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1573])]) ).

fof(c_0_2745,plain,
    ! [X16,X17] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X16,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X16,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X17,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X17,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1574])])])]) ).

fof(c_0_2746,plain,
    ! [X43,X44,X45,X46,X47] :
      ( ( ~ c_Orderings_Oord__class_Oless(X47,X46,X45)
        | c_Orderings_Oord__class_Oless(X47,X44,X43)
        | c_Groups_Ominus__class_Ominus(X47,X46,X45) != c_Groups_Ominus__class_Ominus(X47,X44,X43)
        | ~ class_Groups_Oordered__ab__group__add(X47) )
      & ( ~ c_Orderings_Oord__class_Oless(X47,X44,X43)
        | c_Orderings_Oord__class_Oless(X47,X46,X45)
        | c_Groups_Ominus__class_Ominus(X47,X46,X45) != c_Groups_Ominus__class_Ominus(X47,X44,X43)
        | ~ class_Groups_Oordered__ab__group__add(X47) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1575])])]) ).

fof(c_0_2747,plain,
    ! [X43,X44,X45,X46,X47] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X47,X46,X45)
        | c_Orderings_Oord__class_Oless__eq(X47,X44,X43)
        | c_Groups_Ominus__class_Ominus(X47,X46,X45) != c_Groups_Ominus__class_Ominus(X47,X44,X43)
        | ~ class_Groups_Oordered__ab__group__add(X47) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(X47,X44,X43)
        | c_Orderings_Oord__class_Oless__eq(X47,X46,X45)
        | c_Groups_Ominus__class_Ominus(X47,X46,X45) != c_Groups_Ominus__class_Ominus(X47,X44,X43)
        | ~ class_Groups_Oordered__ab__group__add(X47) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1576])])]) ).

fof(c_0_2748,plain,
    ! [X33,X34,X35,X36] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X34,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X34),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X33)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X33) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X35,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X36),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X35)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X36)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X36,c_Int_OPls) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X35,c_Int_OPls)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X36),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X35)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X36,X35))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X36,c_Int_OPls) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1577])])])])]) ).

fof(c_0_2749,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Ocomm__semiring__1(X37)
      | ~ c_Rings_Odvd__class_Odvd(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),X34)
      | c_Rings_Odvd__class_Odvd(X37,X35,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1578])]) ).

fof(c_0_2750,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Ocomm__semiring__1(X37)
      | ~ c_Rings_Odvd__class_Odvd(X37,c_Groups_Otimes__class_Otimes(X37,X36,X35),X34)
      | c_Rings_Odvd__class_Odvd(X37,X36,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1579])]) ).

fof(c_0_2751,plain,
    ! [X54,X55,X56] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X55),X54) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X54),X55),
    inference(variable_rename,[status(thm)],[c_0_1580]) ).

fof(c_0_2752,plain,
    ! [X14,X15,X16] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X16,X15),X14) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X16,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X14)),
    inference(variable_rename,[status(thm)],[c_0_1581]) ).

fof(c_0_2753,plain,
    ! [X21,X22,X23] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X22)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X23,X21),
    inference(variable_rename,[status(thm)],[c_0_1582]) ).

fof(c_0_2754,plain,
    ! [X21,X22,X23] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X21)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21),
    inference(variable_rename,[status(thm)],[c_0_1583]) ).

fof(c_0_2755,plain,
    ! [X54,X55,X56] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,X55),X54) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X56,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X54)),
    inference(variable_rename,[status(thm)],[c_0_1584]) ).

fof(c_0_2756,plain,
    ! [X14,X15,X16] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,X15),X14) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X14)),
    inference(variable_rename,[status(thm)],[c_0_1585]) ).

fof(c_0_2757,plain,
    ! [X24,X25,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X24)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X24)),
    inference(variable_rename,[status(thm)],[c_0_1586]) ).

fof(c_0_2758,plain,
    ! [X24,X25,X26] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X26,X25),X24) = c_Power_Opower__class_Opower(tc_Int_Oint,X26,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X25,X24)),
    inference(variable_rename,[status(thm)],[c_0_1587]) ).

fof(c_0_2759,plain,
    ! [X21,X22,X23] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22),X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)),
    inference(variable_rename,[status(thm)],[c_0_1588]) ).

fof(c_0_2760,plain,
    ! [X24,X25,X26] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,X24)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X25,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X26,X24)),
    inference(variable_rename,[status(thm)],[c_0_1589]) ).

fof(c_0_2761,plain,
    ! [X21,X22,X23] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,X22),X21) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X23,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21)),
    inference(variable_rename,[status(thm)],[c_0_1590]) ).

fof(c_0_2762,plain,
    ! [X14,X15,X16] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X16,X15),X14) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X16,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X15,X14)),
    inference(variable_rename,[status(thm)],[c_0_1591]) ).

fof(c_0_2763,plain,
    ! [X47,X48,X49,X50] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X47,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X47)
        | X48 = X47 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( X50 != X49
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1592])])])])]) ).

fof(c_0_2764,plain,
    ! [X18,X19,X20,X21] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X19,X18))
        | X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19) )
      & ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X21,X20)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X21,X20)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1593])])])])]) ).

fof(c_0_2765,plain,
    ! [X18,X19,X20,X21] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X19,X18))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
        | X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X21,X20)) )
      & ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X21,X20)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1594])])])])]) ).

fof(c_0_2766,plain,
    ! [X47,X48,X49,X50] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X47,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,X47) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X49,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1595])])])]) ).

fof(c_0_2767,plain,
    ! [X47,X48,X49,X50] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X48,c_Groups_Oone__class_Oone(tc_Int_Oint)),X47)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X47) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X50,c_Groups_Oone__class_Oone(tc_Int_Oint)),X49) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1596])])])]) ).

fof(c_0_2768,plain,
    ! [X47,X48,X49,X50] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X47,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X47) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X49,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1597])])])]) ).

fof(c_0_2769,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Divides_Osemiring__div(X37)
      | ~ c_Rings_Odvd__class_Odvd(X37,X36,X35)
      | c_Divides_Odiv__class_Omod(X37,c_Divides_Odiv__class_Omod(X37,X34,X35),X36) = c_Divides_Odiv__class_Omod(X37,X34,X36) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1598])]) ).

fof(c_0_2770,plain,
    ! [X6,X7,X8,X9] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,X6)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X8),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,X8) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1599])])])]) ).

fof(c_0_2771,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X19))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X22)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1600])])])]) ).

fof(c_0_2772,plain,
    ! [X16,X17,X18,X19] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,X16)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X17,X16),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X19,X18),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,X18) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1601])])])]) ).

fof(c_0_2773,plain,
    ! [X24,X25,X26] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X24)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X26) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X26)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X26) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1602])])]) ).

fof(c_0_2774,plain,
    ! [X24,X25,X26] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X24)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X26)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1603])])]) ).

fof(c_0_2775,plain,
    ! [X21,X22,X23,X24] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X23)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X23) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X21)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1604])]) ).

fof(c_0_2776,plain,
    ! [X18] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1605])])]) ).

fof(c_0_2777,plain,
    ! [X21,X22,X23] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X21)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22),X21) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22),X21) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1606])])]) ).

fof(c_0_2778,plain,
    ! [X21,X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22),X21)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X23,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1607])]) ).

fof(c_0_2779,plain,
    ! [X21,X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22),X21)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1608])])])]) ).

fof(c_0_2780,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X56,X55),X54)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,X54) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1609])]) ).

fof(c_0_2781,plain,
    ! [X18,X19,X20,X21] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X19))
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X18) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X20)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X21)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1610])])])]) ).

fof(c_0_2782,plain,
    ! [X10] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X10))
      | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X10) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1611])]) ).

fof(c_0_2783,plain,
    ! [X16,X17,X18] :
      ( ( X17 = c_Groups_Ozero__class_Ozero(X18)
        | c_Groups_Oplus__class_Oplus(X18,X17,X16) != c_Groups_Ozero__class_Ozero(X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X18,c_Groups_Ozero__class_Ozero(X18),X16)
        | ~ c_Orderings_Oord__class_Oless__eq(X18,c_Groups_Ozero__class_Ozero(X18),X17)
        | ~ class_Groups_Oordered__comm__monoid__add(X18) )
      & ( X16 = c_Groups_Ozero__class_Ozero(X18)
        | c_Groups_Oplus__class_Oplus(X18,X17,X16) != c_Groups_Ozero__class_Ozero(X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X18,c_Groups_Ozero__class_Ozero(X18),X16)
        | ~ c_Orderings_Oord__class_Oless__eq(X18,c_Groups_Ozero__class_Ozero(X18),X17)
        | ~ class_Groups_Oordered__comm__monoid__add(X18) )
      & ( X17 != c_Groups_Ozero__class_Ozero(X18)
        | X16 != c_Groups_Ozero__class_Ozero(X18)
        | c_Groups_Oplus__class_Oplus(X18,X17,X16) = c_Groups_Ozero__class_Ozero(X18)
        | ~ c_Orderings_Oord__class_Oless__eq(X18,c_Groups_Ozero__class_Ozero(X18),X16)
        | ~ c_Orderings_Oord__class_Oless__eq(X18,c_Groups_Ozero__class_Ozero(X18),X17)
        | ~ class_Groups_Oordered__comm__monoid__add(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1612])])]) ).

fof(c_0_2784,plain,
    ! [X16,X17,X18] :
      ( ( ~ c_Rings_Odvd__class_Odvd(X18,c_Int_Onumber__class_Onumber__of(X18,X17),c_Int_Onumber__class_Onumber__of(X18,X16))
        | c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(X18,X16),c_Int_Onumber__class_Onumber__of(X18,X17)) = c_Groups_Ozero__class_Ozero(X18)
        | ~ class_Divides_Osemiring__div(X18)
        | ~ class_Int_Onumber(X18) )
      & ( c_Divides_Odiv__class_Omod(X18,c_Int_Onumber__class_Onumber__of(X18,X16),c_Int_Onumber__class_Onumber__of(X18,X17)) != c_Groups_Ozero__class_Ozero(X18)
        | c_Rings_Odvd__class_Odvd(X18,c_Int_Onumber__class_Onumber__of(X18,X17),c_Int_Onumber__class_Onumber__of(X18,X16))
        | ~ class_Divides_Osemiring__div(X18)
        | ~ class_Int_Onumber(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1613])])]) ).

fof(c_0_2785,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21,X22) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22),X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1614])]) ).

fof(c_0_2786,plain,
    ! [X62,X63,X64,X65] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,X62)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X62)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X63),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X62)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,X62)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X63),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X62)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X65,X64)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X65,X64)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X64)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X64)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X65,X64)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X64)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1615])])])])]) ).

fof(c_0_2787,plain,
    ! [X32,X34,X35] :
      ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X32)
        | X32 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk5_1(X32))) )
      & ( X34 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X35))
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X34) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1616])])])])]) ).

fof(c_0_2788,plain,
    ! [X21,X22] :
      ( ~ class_Int_Onumber__ring(X22)
      | c_Power_Opower__class_Opower(X22,c_Int_Onumber__class_Onumber__of(X22,c_Int_OMin),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)) = c_Groups_Oone__class_Oone(X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1617])]) ).

fof(c_0_2789,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__semidom(X23)
      | ~ c_Orderings_Oord__class_Oless(X23,c_Groups_Oone__class_Oone(X23),X22)
      | c_Orderings_Oord__class_Oless(X23,c_Groups_Oone__class_Oone(X23),c_Power_Opower__class_Opower(X23,X22,c_Nat_OSuc(X21))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1618])]) ).

fof(c_0_2790,plain,
    ! [X9,X10] :
      ( ~ class_Int_Onumber__ring(X10)
      | c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(X9)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Int_Onumber__class_Onumber__of(X10,X9)),c_Int_Onumber__class_Onumber__of(X10,X9)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1619])]) ).

fof(c_0_2791,plain,
    ! [X9,X10] :
      ( ~ class_Int_Onumber__ring(X10)
      | c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit0(X9)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(X10,X9)),c_Int_Onumber__class_Onumber__of(X10,X9)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1620])]) ).

fof(c_0_2792,plain,
    ! [X26,X27,X28,X29] :
      ( ( c_Power_Opower__class_Opower(X29,X28,X27) != c_Power_Opower__class_Opower(X29,X28,X26)
        | X27 = X26
        | ~ c_Orderings_Oord__class_Oless(X29,c_Groups_Oone__class_Oone(X29),X28)
        | ~ class_Rings_Olinordered__semidom(X29) )
      & ( X27 != X26
        | c_Power_Opower__class_Opower(X29,X28,X27) = c_Power_Opower__class_Opower(X29,X28,X26)
        | ~ c_Orderings_Oord__class_Oless(X29,c_Groups_Oone__class_Oone(X29),X28)
        | ~ class_Rings_Olinordered__semidom(X29) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1621])])]) ).

fof(c_0_2793,plain,
    ! [X21,X22,X23,X24] :
      ( ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,X21)) != X21
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X22),X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X23)) = X23
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X24),X23) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X23)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1622])])])]) ).

fof(c_0_2794,plain,
    ! [X24,X25] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1623])]) ).

fof(c_0_2795,plain,
    ! [X22,X23] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1624])]) ).

fof(c_0_2796,plain,
    ! [X24,X25] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1625])]) ).

fof(c_0_2797,plain,
    ! [X24,X25] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1626])]) ).

fof(c_0_2798,plain,
    ! [X54,X55] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X55)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,X55,X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1627])]) ).

fof(c_0_2799,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__semidom(X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Ozero__class_Ozero(X23),X22)
      | c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Ozero__class_Ozero(X23),c_Power_Opower__class_Opower(X23,X22,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1628])]) ).

fof(c_0_2800,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__semidom(X23)
      | ~ c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Oone__class_Oone(X23),X22)
      | c_Orderings_Oord__class_Oless__eq(X23,c_Groups_Oone__class_Oone(X23),c_Power_Opower__class_Opower(X23,X22,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1629])]) ).

fof(c_0_2801,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Olinordered__semidom(X23)
      | ~ c_Orderings_Oord__class_Oless(X23,c_Groups_Ozero__class_Ozero(X23),X22)
      | c_Orderings_Oord__class_Oless(X23,c_Groups_Ozero__class_Ozero(X23),c_Power_Opower__class_Opower(X23,X22,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1630])]) ).

fof(c_0_2802,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Olinordered__ring(X5)
      | ~ c_Orderings_Oord__class_Oless(X5,c_Groups_Otimes__class_Otimes(X5,X4,X4),c_Groups_Ozero__class_Ozero(X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1631])]) ).

fof(c_0_2803,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Omonoid__mult(X5)
      | c_Power_Opower__class_Opower(X5,X4,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X5,c_Groups_Otimes__class_Otimes(X5,X4,X4),X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1632])]) ).

fof(c_0_2804,plain,
    ! [X16,X17,X18,X19] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X16)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X16)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X19)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18)) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X19)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X18)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1633])])])])]) ).

fof(c_0_2805,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Olinordered__idom(X5)
      | c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Power_Opower__class_Opower(X5,X4,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1634])]) ).

fof(c_0_2806,plain,
    ! [X54,X55] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X54))),
    inference(variable_rename,[status(thm)],[c_0_1635]) ).

fof(c_0_2807,plain,
    ! [X54,X55] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X54,X55))),
    inference(variable_rename,[status(thm)],[c_0_1636]) ).

fof(c_0_2808,plain,
    ! [X33,X34,X35,X36] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X34,c_Int_OPls)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X34),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X33)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X36,c_Int_OPls)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X36),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X35)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X36,X35)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1637])])])]) ).

fof(c_0_2809,plain,
    ! [X21,X22,X23,X24] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,X21) = X22 )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X23)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X23) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X23),X23) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1638])])])]) ).

fof(c_0_2810,plain,
    ! [X21,X22] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,X21) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21),X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1639])]) ).

fof(c_0_2811,plain,
    ! [X62,X63,X64,X65] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X63),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X62))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X63,X62)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X63,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X65,X64)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X64)) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X65,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X65),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X64)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1640])])])])]) ).

fof(c_0_2812,plain,
    ! [X11] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X11),X11) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[c_0_1641]) ).

fof(c_0_2813,plain,
    ! [X16,X17,X18,X19] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X17),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X16))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X16),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X17)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X18),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X19)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X19),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X18)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1642])])])]) ).

fof(c_0_2814,plain,
    ! [X54,X55] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X55)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X55,c_Nat_OSuc(X54)),X55) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1643])]) ).

fof(c_0_2815,plain,
    ! [X16,X17] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X16,X16))
        | X16 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X17 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X17,X17)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1644])])])]) ).

fof(c_0_2816,plain,
    ! [X24,X25,X26] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25)
        | c_Rings_Odvd__class_Odvd(X26,X24,c_Power_Opower__class_Opower(X26,X24,X25))
        | ~ class_Rings_Ocomm__semiring__1(X26) )
      & ( X24 != c_Groups_Oone__class_Oone(X26)
        | c_Rings_Odvd__class_Odvd(X26,X24,c_Power_Opower__class_Opower(X26,X24,X25))
        | ~ class_Rings_Ocomm__semiring__1(X26) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1645])])]) ).

fof(c_0_2817,plain,
    ! [X19,X20,X21] :
      ( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19)
        | X20 = X19
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) )
      & ( X20 != X19
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1646])])]) ).

fof(c_0_2818,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X22)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1647])]) ).

fof(c_0_2819,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X21)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X21,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1648])]) ).

fof(c_0_2820,plain,
    ! [X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | ~ c_Rings_Odvd__class_Odvd(X24,X23,X22)
      | c_Groups_Otimes__class_Otimes(X24,X23,c_Divides_Odiv__class_Odiv(X24,X22,X23)) = X22 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1649])]) ).

fof(c_0_2821,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Ocomm__semiring__1(X37)
      | ~ c_Rings_Odvd__class_Odvd(X37,X36,X35)
      | c_Rings_Odvd__class_Odvd(X37,X36,c_Groups_Otimes__class_Otimes(X37,X34,X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1650])]) ).

fof(c_0_2822,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Ocomm__semiring__1(X37)
      | ~ c_Rings_Odvd__class_Odvd(X37,X36,X35)
      | c_Rings_Odvd__class_Odvd(X37,X36,c_Groups_Otimes__class_Otimes(X37,X35,X34)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1651])]) ).

fof(c_0_2823,plain,
    ! [X11] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X11)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1652])]) ).

fof(c_0_2824,plain,
    ! [X21] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),
    inference(variable_rename,[status(thm)],[c_0_1653]) ).

fof(c_0_2825,plain,
    ! [X24] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | X24 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X24 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1654])]) ).

fof(c_0_2826,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X21),X22) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1655])]) ).

fof(c_0_2827,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X23)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1656])]) ).

fof(c_0_2828,plain,
    ! [X22,X23] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X23))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X23),X23)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1657])])]) ).

fof(c_0_2829,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1658])]) ).

fof(c_0_2830,plain,
    ! [X22,X23] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X23))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1659])])]) ).

fof(c_0_2831,plain,
    ! [X24,X25] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1660])]) ).

fof(c_0_2832,plain,
    ! [X31,X32] :
      ( ~ class_Groups_Omonoid__mult(X32)
      | ~ class_Int_Onumber(X32)
      | c_Power_Opower__class_Opower(X32,c_Int_Onumber__class_Onumber__of(X32,X31),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X32,c_Int_Onumber__class_Onumber__of(X32,X31),c_Int_Onumber__class_Onumber__of(X32,X31)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1661])]) ).

fof(c_0_2833,plain,
    ! [X20,X21] :
      ( ~ class_Rings_Ocomm__semiring__1(X21)
      | c_Groups_Oplus__class_Oplus(X21,X20,X20) = c_Groups_Otimes__class_Otimes(X21,c_Groups_Oplus__class_Oplus(X21,c_Groups_Oone__class_Oone(X21),c_Groups_Oone__class_Oone(X21)),X20) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1662])]) ).

fof(c_0_2834,plain,
    ! [X11,X12] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X11)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,c_Groups_Oone__class_Oone(tc_Int_Oint)),X11) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1663])]) ).

fof(c_0_2835,plain,
    ! [X54,X55] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X54),X55),
    inference(variable_rename,[status(thm)],[c_0_1664]) ).

fof(c_0_2836,plain,
    ! [X54,X55] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X54),X54),
    inference(variable_rename,[status(thm)],[c_0_1665]) ).

fof(c_0_2837,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X22)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21,X22),X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1666])]) ).

fof(c_0_2838,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X22)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21,X22),X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1667])]) ).

fof(c_0_2839,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X23),X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1668])]) ).

fof(c_0_2840,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X23)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1669])]) ).

fof(c_0_2841,plain,
    ! [X20,X21] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X20),X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1670])]) ).

fof(c_0_2842,plain,
    ! [X60,X61,X63,X64,X65] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X61,X60)
        | X60 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X61,esk11_2(X60,X61))) )
      & ( X63 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X64,X65))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X64,X63) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1671])])])])]) ).

fof(c_0_2843,plain,
    ! [X54,X55] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X55,X54)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X55)) = X55 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1672])]) ).

fof(c_0_2844,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22)) = X21 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1673])]) ).

fof(c_0_2845,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22),X22) = X21 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1674])]) ).

fof(c_0_2846,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X54,X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1675])]) ).

fof(c_0_2847,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1676])]) ).

fof(c_0_2848,plain,
    ! [X52,X53,X54] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X54,X53)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X52),X53) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1677])]) ).

fof(c_0_2849,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,X55)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1678])]) ).

fof(c_0_2850,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,X55)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X54,X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1679])]) ).

fof(c_0_2851,plain,
    ! [X16,X17,X18,X19] :
      ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X17,X16)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X16)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X19)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X19,X18)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1680])])])])]) ).

fof(c_0_2852,plain,
    ! [X9,X10] :
      ( ~ class_Int_Onumber__ring(X10)
      | c_Groups_Otimes__class_Otimes(X10,c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Oone__class_Oone(X10)),c_Int_Onumber__class_Onumber__of(X10,X9)) = c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit0(X9)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1681])]) ).

fof(c_0_2853,plain,
    ! [X16,X17,X18] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X18,c_Int_Onumber__class_Onumber__of(X18,X17),c_Int_Onumber__class_Onumber__of(X18,X16))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,X16)
        | ~ class_Int_Onumber__ring(X18)
        | ~ class_Rings_Olinordered__idom(X18) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,X16)
        | c_Orderings_Oord__class_Oless__eq(X18,c_Int_Onumber__class_Onumber__of(X18,X17),c_Int_Onumber__class_Onumber__of(X18,X16))
        | ~ class_Int_Onumber__ring(X18)
        | ~ class_Rings_Olinordered__idom(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1682])])]) ).

fof(c_0_2854,plain,
    ! [X16,X17,X18] :
      ( ( ~ c_Orderings_Oord__class_Oless(X18,c_Int_Onumber__class_Onumber__of(X18,X17),c_Int_Onumber__class_Onumber__of(X18,X16))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X16)
        | ~ class_Int_Onumber__ring(X18)
        | ~ class_Rings_Olinordered__idom(X18) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X16)
        | c_Orderings_Oord__class_Oless(X18,c_Int_Onumber__class_Onumber__of(X18,X17),c_Int_Onumber__class_Onumber__of(X18,X16))
        | ~ class_Int_Onumber__ring(X18)
        | ~ class_Rings_Olinordered__idom(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1683])])]) ).

fof(c_0_2855,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Rings_Ocomm__semiring__1(X37)
      | ~ c_Rings_Odvd__class_Odvd(X37,X36,X35)
      | ~ c_Rings_Odvd__class_Odvd(X37,X35,X34)
      | c_Rings_Odvd__class_Odvd(X37,X36,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1684])]) ).

fof(c_0_2856,plain,
    ! [X10,X11,X12] :
      ( ~ class_Int_Onumber__ring(X12)
      | c_Int_Onumber__class_Onumber__of(X12,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X11,X10)) = c_Groups_Ominus__class_Ominus(X12,c_Int_Onumber__class_Onumber__of(X12,X11),c_Int_Onumber__class_Onumber__of(X12,X10)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1685])]) ).

fof(c_0_2857,plain,
    ! [X10,X11,X12] :
      ( ~ class_Int_Onumber__ring(X12)
      | c_Int_Onumber__class_Onumber__of(X12,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X10)) = c_Groups_Oplus__class_Oplus(X12,c_Int_Onumber__class_Onumber__of(X12,X11),c_Int_Onumber__class_Onumber__of(X12,X10)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1686])]) ).

fof(c_0_2858,plain,
    ! [X10,X11,X12] :
      ( ~ class_Int_Onumber__ring(X12)
      | c_Groups_Oplus__class_Oplus(X12,c_Int_Onumber__class_Onumber__of(X12,X11),c_Int_Onumber__class_Onumber__of(X12,X10)) = c_Int_Onumber__class_Onumber__of(X12,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X10)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1687])]) ).

fof(c_0_2859,plain,
    ! [X10,X11,X12] :
      ( ~ class_Int_Onumber__ring(X12)
      | c_Groups_Otimes__class_Otimes(X12,c_Int_Onumber__class_Onumber__of(X12,X11),c_Int_Onumber__class_Onumber__of(X12,X10)) = c_Int_Onumber__class_Onumber__of(X12,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X11,X10)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1688])]) ).

fof(c_0_2860,plain,
    ! [X10,X11,X12] :
      ( ~ class_Int_Onumber__ring(X12)
      | c_Int_Onumber__class_Onumber__of(X12,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X11,X10)) = c_Groups_Otimes__class_Otimes(X12,c_Int_Onumber__class_Onumber__of(X12,X11),c_Int_Onumber__class_Onumber__of(X12,X10)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1689])]) ).

fof(c_0_2861,plain,
    ! [X21,X22,X23] :
      ( ~ class_Groups_Omonoid__mult(X23)
      | c_Power_Opower__class_Opower(X23,X22,c_Nat_OSuc(X21)) = c_Groups_Otimes__class_Otimes(X23,c_Power_Opower__class_Opower(X23,X22,X21),X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1690])]) ).

fof(c_0_2862,plain,
    ! [X21,X22,X23] :
      ( ~ class_Power_Opower(X23)
      | c_Power_Opower__class_Opower(X23,X22,c_Nat_OSuc(X21)) = c_Groups_Otimes__class_Otimes(X23,X22,c_Power_Opower__class_Opower(X23,X22,X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1691])]) ).

fof(c_0_2863,plain,
    ! [X36,X37,X38] :
      ( ~ class_Rings_Ocomm__semiring__1(X38)
      | c_Power_Opower__class_Opower(X38,X37,c_Nat_OSuc(X36)) = c_Groups_Otimes__class_Otimes(X38,X37,c_Power_Opower__class_Opower(X38,X37,X36)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1692])]) ).

fof(c_0_2864,plain,
    ! [X36,X37,X38] :
      ( ~ class_Rings_Ocomm__semiring__1(X38)
      | c_Groups_Otimes__class_Otimes(X38,X37,c_Power_Opower__class_Opower(X38,X37,X36)) = c_Power_Opower__class_Opower(X38,X37,c_Nat_OSuc(X36)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1693])]) ).

fof(c_0_2865,plain,
    ! [X36,X37,X38] :
      ( ~ class_Rings_Ocomm__semiring__1(X38)
      | c_Groups_Otimes__class_Otimes(X38,c_Power_Opower__class_Opower(X38,X37,X36),X37) = c_Power_Opower__class_Opower(X38,X37,c_Nat_OSuc(X36)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1694])]) ).

fof(c_0_2866,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X22)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X22)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1695])]) ).

fof(c_0_2867,plain,
    ! [X67,X68,X69,X70] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X68)
        | X67 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X68,X67) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X67,X68)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X68)
        | X67 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X68,X67) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X68,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X68,X67)
        | X67 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X68,X67) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X67,X68)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X68,X67)
        | X67 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X68,X67) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X69 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X70,X69) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X70)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X70,X69)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X70,X69) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X70,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X69,X70)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X70,X69) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1696])])])])]) ).

fof(c_0_2868,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,X22)
      | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X23,X22) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1697])]) ).

fof(c_0_2869,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X23)
      | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X23,X22) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1698])]) ).

fof(c_0_2870,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X56,X55)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X54)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X56),X54) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1699])]) ).

fof(c_0_2871,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,X22)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X22) = X23 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1700])]) ).

fof(c_0_2872,plain,
    ! [X22,X23] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X23)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X22) = X23 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1701])]) ).

fof(c_0_2873,plain,
    ! [X21,X22] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X22,X21)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1702])]) ).

fof(c_0_2874,plain,
    ! [X21,X22] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X21)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1703])]) ).

fof(c_0_2875,plain,
    ! [X34,X35,X36] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X34)
        | X35 != X34
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X35)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X36) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X34,X36)
        | X35 != X34
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X35)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X36) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1704])])]) ).

fof(c_0_2876,plain,
    ! [X34,X35,X36] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X34)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X34)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X34,X35)
        | X36 != X35 )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X34,X36)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X34)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X34,X35)
        | X36 != X35 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1705])])]) ).

fof(c_0_2877,plain,
    ! [X67,X68,X69] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X68,X69) != X67
        | X68 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X67,X69)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X69,X68) )
      & ( X68 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X67,X69)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X68,X69) = X67
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X69,X68) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1706])])]) ).

fof(c_0_2878,plain,
    ! [X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(X24,c_Divides_Odiv__class_Omod(X24,X23,X22),X22) = c_Divides_Odiv__class_Omod(X24,X23,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1707])]) ).

fof(c_0_2879,plain,
    ! [X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(X24,c_Groups_Oplus__class_Oplus(X24,X23,X22),X23) = c_Divides_Odiv__class_Omod(X24,X22,X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1708])]) ).

fof(c_0_2880,plain,
    ! [X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(X24,c_Groups_Oplus__class_Oplus(X24,X23,X22),X22) = c_Divides_Odiv__class_Omod(X24,X23,X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1709])]) ).

fof(c_0_2881,plain,
    ! [X21] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
      | c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X21 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1710])]) ).

fof(c_0_2882,plain,
    ! [X21,X22] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,c_Nat_OSuc(X21)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X21),
    inference(variable_rename,[status(thm)],[c_0_1711]) ).

fof(c_0_2883,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X55)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X55,X54)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X56,X54) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1712])]) ).

fof(c_0_2884,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X56,X55)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X55,X54)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X56,X54) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1713])]) ).

fof(c_0_2885,plain,
    ! [X54,X55,X56] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X56,X55)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X55,X54)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X56,X54) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1714])]) ).

fof(c_0_2886,plain,
    ! [X24,X25,X26] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X25)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X26,X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1715])]) ).

fof(c_0_2887,plain,
    ! [X10,X11] :
      ( ~ class_Int_Onumber__ring(X11)
      | c_Groups_Oplus__class_Oplus(X11,c_Int_Onumber__class_Onumber__of(X11,X10),c_Groups_Oone__class_Oone(X11)) = c_Int_Onumber__class_Onumber__of(X11,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1716])]) ).

fof(c_0_2888,plain,
    ! [X9,X10] :
      ( ~ class_Int_Onumber__ring(X10)
      | c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Int_Onumber__class_Onumber__of(X10,X9)) = c_Int_Onumber__class_Onumber__of(X10,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X9)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1717])]) ).

fof(c_0_2889,plain,
    ! [X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),X22) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X22,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1718])]) ).

fof(c_0_2890,plain,
    ! [X16,X17,X18,X19] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X17)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X16)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X17)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X16)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X16)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X16)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X19)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X19,X18)) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X19)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X19,X18)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1719])])])])]) ).

fof(c_0_2891,plain,
    ! [X24,X25] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X25)
      | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X24)
      | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1720])]) ).

fof(c_0_2892,plain,
    ! [X24,X25] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X25)
      | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X24)
      | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1721])]) ).

fof(c_0_2893,plain,
    ! [X16,X17,X18,X19] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X17)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X16)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X17)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X16)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X16)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X16)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X19)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,X18)) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X19)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X19,X18)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1722])])])])]) ).

fof(c_0_2894,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X19)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19)) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X19)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X22)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X21)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X22)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X21)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1723])])])])]) ).

fof(c_0_2895,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X19)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X19)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X22)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X21)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X22)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X21)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1724])])])])]) ).

fof(c_0_2896,plain,
    ! [X16,X17,X18,X19] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X16)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X19)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18)) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X19)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X18)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1725])])])])]) ).

fof(c_0_2897,plain,
    ! [X21] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X21)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X21)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X21)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X21)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1726])])]) ).

fof(c_0_2898,plain,
    ! [X21,X22] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X22),X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21)),
    inference(variable_rename,[status(thm)],[c_0_1727]) ).

fof(c_0_2899,plain,
    ! [X21,X22] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,c_Nat_OSuc(X21)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21)),
    inference(variable_rename,[status(thm)],[c_0_1728]) ).

fof(c_0_2900,plain,
    ! [X10,X11] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X11),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X10)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X10)),
    inference(variable_rename,[status(thm)],[c_0_1729]) ).

fof(c_0_2901,plain,
    ! [X10,X11] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X11),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X10)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X11,X10)),
    inference(variable_rename,[status(thm)],[c_0_1730]) ).

fof(c_0_2902,plain,
    ! [X21,X22] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21)) = X22 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1731])]) ).

fof(c_0_2903,plain,
    ! [X16,X17,X18,X19] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X17,X16))
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X16) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X19)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X19,X18)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X19,X18)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1732])])])])]) ).

fof(c_0_2904,plain,
    ! [X24,X25] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X25)
      | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X24)
      | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1733])]) ).

fof(c_0_2905,plain,
    ! [X16,X17,X18,X19] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X16))
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X19)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X18)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X18)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1734])])])])]) ).

fof(c_0_2906,plain,
    ! [X6,X7,X8,X9] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X7),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X6))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X7,X6) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X9,X8)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1735])])])]) ).

fof(c_0_2907,plain,
    ! [X6,X7,X8,X9] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X7),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X6))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,X6) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,X8)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1736])])])]) ).

fof(c_0_2908,plain,
    ! [X16,X17] :
      ( ( ~ c_Orderings_Oord__class_Oless(X17,c_Int_Onumber__class_Onumber__of(X17,X16),c_Groups_Oone__class_Oone(X17))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Int_OBit1(c_Int_OPls))
        | ~ class_Int_Onumber__ring(X17)
        | ~ class_Rings_Olinordered__idom(X17) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Int_OBit1(c_Int_OPls))
        | c_Orderings_Oord__class_Oless(X17,c_Int_Onumber__class_Onumber__of(X17,X16),c_Groups_Oone__class_Oone(X17))
        | ~ class_Int_Onumber__ring(X17)
        | ~ class_Rings_Olinordered__idom(X17) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1737])])]) ).

fof(c_0_2909,plain,
    ! [X15,X16] :
      ( ( ~ c_Orderings_Oord__class_Oless(X16,c_Groups_Oone__class_Oone(X16),c_Int_Onumber__class_Onumber__of(X16,X15))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X15)
        | ~ class_Int_Onumber__ring(X16)
        | ~ class_Rings_Olinordered__idom(X16) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X15)
        | c_Orderings_Oord__class_Oless(X16,c_Groups_Oone__class_Oone(X16),c_Int_Onumber__class_Onumber__of(X16,X15))
        | ~ class_Int_Onumber__ring(X16)
        | ~ class_Rings_Olinordered__idom(X16) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1738])])]) ).

fof(c_0_2910,plain,
    ! [X15,X16] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X16,c_Groups_Oone__class_Oone(X16),c_Int_Onumber__class_Onumber__of(X16,X15))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X15)
        | ~ class_Int_Onumber__ring(X16)
        | ~ class_Rings_Olinordered__idom(X16) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X15)
        | c_Orderings_Oord__class_Oless__eq(X16,c_Groups_Oone__class_Oone(X16),c_Int_Onumber__class_Onumber__of(X16,X15))
        | ~ class_Int_Onumber__ring(X16)
        | ~ class_Rings_Olinordered__idom(X16) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1739])])]) ).

fof(c_0_2911,plain,
    ! [X16,X17] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X17,c_Int_Onumber__class_Onumber__of(X17,X16),c_Groups_Oone__class_Oone(X17))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,c_Int_OBit1(c_Int_OPls))
        | ~ class_Int_Onumber__ring(X17)
        | ~ class_Rings_Olinordered__idom(X17) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,c_Int_OBit1(c_Int_OPls))
        | c_Orderings_Oord__class_Oless__eq(X17,c_Int_Onumber__class_Onumber__of(X17,X16),c_Groups_Oone__class_Oone(X17))
        | ~ class_Int_Onumber__ring(X17)
        | ~ class_Rings_Olinordered__idom(X17) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1740])])]) ).

fof(c_0_2912,plain,
    ! [X21] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
      | X21 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1741])]) ).

fof(c_0_2913,plain,
    ! [X21] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21)
      | c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X21 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1742])]) ).

fof(c_0_2914,plain,
    ! [X16,X17] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X17,c_Int_Onumber__class_Onumber__of(X17,X16),c_Groups_Ozero__class_Ozero(X17))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,c_Int_OPls)
        | ~ class_Int_Onumber__ring(X17)
        | ~ class_Rings_Olinordered__idom(X17) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(X17,c_Int_Onumber__class_Onumber__of(X17,X16),c_Groups_Ozero__class_Ozero(X17))
        | ~ class_Int_Onumber__ring(X17)
        | ~ class_Rings_Olinordered__idom(X17) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1743])])]) ).

fof(c_0_2915,plain,
    ! [X15,X16] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(X16,c_Groups_Ozero__class_Ozero(X16),c_Int_Onumber__class_Onumber__of(X16,X15))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X15)
        | ~ class_Int_Onumber__ring(X16)
        | ~ class_Rings_Olinordered__idom(X16) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X15)
        | c_Orderings_Oord__class_Oless__eq(X16,c_Groups_Ozero__class_Ozero(X16),c_Int_Onumber__class_Onumber__of(X16,X15))
        | ~ class_Int_Onumber__ring(X16)
        | ~ class_Rings_Olinordered__idom(X16) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1744])])]) ).

fof(c_0_2916,plain,
    ! [X16,X17] :
      ( ( ~ c_Orderings_Oord__class_Oless(X17,c_Int_Onumber__class_Onumber__of(X17,X16),c_Groups_Ozero__class_Ozero(X17))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Int_OPls)
        | ~ class_Int_Onumber__ring(X17)
        | ~ class_Rings_Olinordered__idom(X17) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Int_OPls)
        | c_Orderings_Oord__class_Oless(X17,c_Int_Onumber__class_Onumber__of(X17,X16),c_Groups_Ozero__class_Ozero(X17))
        | ~ class_Int_Onumber__ring(X17)
        | ~ class_Rings_Olinordered__idom(X17) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1745])])]) ).

fof(c_0_2917,plain,
    ! [X15,X16] :
      ( ( ~ c_Orderings_Oord__class_Oless(X16,c_Groups_Ozero__class_Ozero(X16),c_Int_Onumber__class_Onumber__of(X16,X15))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X15)
        | ~ class_Int_Onumber__ring(X16)
        | ~ class_Rings_Olinordered__idom(X16) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X15)
        | c_Orderings_Oord__class_Oless(X16,c_Groups_Ozero__class_Ozero(X16),c_Int_Onumber__class_Onumber__of(X16,X15))
        | ~ class_Int_Onumber__ring(X16)
        | ~ class_Rings_Olinordered__idom(X16) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1746])])]) ).

fof(c_0_2918,plain,
    ! [X24,X25,X26] :
      ( ~ class_Groups_Omonoid__mult(X26)
      | ~ class_Rings_Olinordered__ring(X26)
      | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X25)
      | c_Orderings_Oord__class_Oless__eq(X26,c_Groups_Ozero__class_Ozero(X26),c_Power_Opower__class_Opower(X26,X24,X25)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1747])]) ).

fof(c_0_2919,plain,
    ! [X4] :
      ( ~ class_Rings_Olinordered__semidom(X4)
      | c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Oplus__class_Oplus(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Oone__class_Oone(X4))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1748])]) ).

fof(c_0_2920,plain,
    ! [X18,X19,X20,X21] :
      ( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X19)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X19,X18)) )
      & ( X18 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X19,X18)) )
      & ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X21)
        | X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X21,X20)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1749])])])])]) ).

fof(c_0_2921,plain,
    ! [X24,X25] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X25)
      | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1750])]) ).

fof(c_0_2922,plain,
    ! [X24,X25] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1751])]) ).

fof(c_0_2923,plain,
    ! [X16,X17,X18,X19] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X16)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X16)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X16,X17) )
      & ( X17 != X16
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X16)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X16,X17) )
      & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X18)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X18)
        | X19 = X18 )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,X19)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X18)
        | X19 = X18 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1752])])])])]) ).

fof(c_0_2924,plain,
    ! [X16,X17,X18,X19] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X16)
        | X17 = X16
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X16) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X16,X17)
        | X17 = X16
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X16) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X18)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,X19)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X18) )
      & ( X19 != X18
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X18) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1753])])])])]) ).

fof(c_0_2925,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X21),X20) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X21),X19)
        | X20 = X19 )
      & ( X23 != X22
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X24),X23) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X24),X22) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1754])])])]) ).

fof(c_0_2926,plain,
    ! [X43,X44,X45,X46,X47] :
      ( ( X46 != X45
        | X44 = X43
        | c_Groups_Ominus__class_Ominus(X47,X46,X45) != c_Groups_Ominus__class_Ominus(X47,X44,X43)
        | ~ class_Groups_Oab__group__add(X47) )
      & ( X44 != X43
        | X46 = X45
        | c_Groups_Ominus__class_Ominus(X47,X46,X45) != c_Groups_Ominus__class_Ominus(X47,X44,X43)
        | ~ class_Groups_Oab__group__add(X47) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1755])])]) ).

fof(c_0_2927,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Olinordered__semidom(X5)
      | c_Orderings_Oord__class_Oless(X5,X4,c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Oone__class_Oone(X5))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1756])]) ).

fof(c_0_2928,plain,
    ! [X26,X27,X28] :
      ( ( X27 = c_Groups_Ozero__class_Ozero(X28)
        | c_Power_Opower__class_Opower(X28,X27,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X26)) != c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Power_Opower(X28)
        | ~ class_Rings_Omult__zero(X28)
        | ~ class_Rings_Ono__zero__divisors(X28)
        | ~ class_Rings_Ozero__neq__one(X28) )
      & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X26) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X28,X27,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X26)) != c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Power_Opower(X28)
        | ~ class_Rings_Omult__zero(X28)
        | ~ class_Rings_Ono__zero__divisors(X28)
        | ~ class_Rings_Ozero__neq__one(X28) )
      & ( X27 != c_Groups_Ozero__class_Ozero(X28)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X26) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X28,X27,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X26)) = c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Power_Opower(X28)
        | ~ class_Rings_Omult__zero(X28)
        | ~ class_Rings_Ono__zero__divisors(X28)
        | ~ class_Rings_Ozero__neq__one(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1757])])]) ).

fof(c_0_2929,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Ocancel__semigroup__add(X37)
      | c_Groups_Oplus__class_Oplus(X37,X36,X35) != c_Groups_Oplus__class_Oplus(X37,X34,X35)
      | X36 = X34 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1758])]) ).

fof(c_0_2930,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Ocancel__ab__semigroup__add(X37)
      | c_Groups_Oplus__class_Oplus(X37,X36,X35) != c_Groups_Oplus__class_Oplus(X37,X36,X34)
      | X35 = X34 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1759])]) ).

fof(c_0_2931,plain,
    ! [X34,X35,X36,X37] :
      ( ~ class_Groups_Ocancel__semigroup__add(X37)
      | c_Groups_Oplus__class_Oplus(X37,X36,X35) != c_Groups_Oplus__class_Oplus(X37,X36,X34)
      | X35 = X34 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1760])]) ).

fof(c_0_2932,plain,
    ! [X43,X44,X45,X46] :
      ( ( c_Groups_Oplus__class_Oplus(X46,X45,X44) != c_Groups_Oplus__class_Oplus(X46,X43,X44)
        | X45 = X43
        | ~ class_Groups_Ocancel__semigroup__add(X46) )
      & ( X45 != X43
        | c_Groups_Oplus__class_Oplus(X46,X45,X44) = c_Groups_Oplus__class_Oplus(X46,X43,X44)
        | ~ class_Groups_Ocancel__semigroup__add(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1761])])]) ).

fof(c_0_2933,plain,
    ! [X43,X44,X45,X46] :
      ( ( c_Groups_Oplus__class_Oplus(X46,X45,X44) != c_Groups_Oplus__class_Oplus(X46,X45,X43)
        | X44 = X43
        | ~ class_Groups_Ocancel__semigroup__add(X46) )
      & ( X44 != X43
        | c_Groups_Oplus__class_Oplus(X46,X45,X44) = c_Groups_Oplus__class_Oplus(X46,X45,X43)
        | ~ class_Groups_Ocancel__semigroup__add(X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1762])])]) ).

fof(c_0_2934,plain,
    ! [X19,X20] :
      ( ( X20 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X20,X19) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20) )
      & ( X19 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X20,X19) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20) )
      & ( X20 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X19 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X20,X19) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1763])])]) ).

fof(c_0_2935,plain,
    ! [X19,X20] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20))
        | X19 = X20
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19) )
      & ( X19 != X20
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1764])])]) ).

fof(c_0_2936,plain,
    ! [X26,X27] :
      ( ( c_Power_Opower__class_Opower(X27,X26,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X27)
        | X26 = c_Groups_Ozero__class_Ozero(X27)
        | ~ class_Rings_Oring__1__no__zero__divisors(X27) )
      & ( X26 != c_Groups_Ozero__class_Ozero(X27)
        | c_Power_Opower__class_Opower(X27,X26,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X27)
        | ~ class_Rings_Oring__1__no__zero__divisors(X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1765])])]) ).

fof(c_0_2937,plain,
    ! [X19,X20,X21,X22] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X20) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X21),X22)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1766])])])]) ).

fof(c_0_2938,plain,
    ! [X19,X20,X21,X22] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Nat_OSuc(X22))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1767])])])]) ).

fof(c_0_2939,plain,
    ! [X21,X22] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X22) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1768])]) ).

fof(c_0_2940,plain,
    ! [X59,X60,X62,X63,X64] :
      ( ( X60 = c_Nat_OSuc(esk9_2(X59,X60))
        | X60 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X60,c_Nat_OSuc(X59)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk9_2(X59,X60),X59)
        | X60 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X60,c_Nat_OSuc(X59)) )
      & ( X63 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X63,c_Nat_OSuc(X62)) )
      & ( X63 != c_Nat_OSuc(X64)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X64,X62)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X63,c_Nat_OSuc(X62)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1769])])])])])]) ).

fof(c_0_2941,plain,
    ! [X62,X63] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X62))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X62) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X63)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X63)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1770])])])]) ).

fof(c_0_2942,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Olinordered__ring(X5)
      | c_Orderings_Oord__class_Oless__eq(X5,c_Groups_Ozero__class_Ozero(X5),c_Groups_Otimes__class_Otimes(X5,X4,X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1771])]) ).

fof(c_0_2943,plain,
    ! [X16,X17] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X16)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X16,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X17,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X17) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1772])])])]) ).

fof(c_0_2944,plain,
    ! [X8,X9] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X9),c_Int_OBit1(X8)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X8)),
    inference(variable_rename,[status(thm)],[c_0_1773]) ).

fof(c_0_2945,plain,
    ! [X8,X9] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X9),c_Int_OBit0(X8)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X8)),
    inference(variable_rename,[status(thm)],[c_0_1774]) ).

fof(c_0_2946,plain,
    ! [X8,X9] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(X9),c_Int_OBit0(X8)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X8)),
    inference(variable_rename,[status(thm)],[c_0_1775]) ).

fof(c_0_2947,plain,
    ! [X8,X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X9),c_Int_OBit1(X8)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)),
    inference(variable_rename,[status(thm)],[c_0_1776]) ).

fof(c_0_2948,plain,
    ! [X8,X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X9),c_Int_OBit0(X8)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)),
    inference(variable_rename,[status(thm)],[c_0_1777]) ).

fof(c_0_2949,plain,
    ! [X8,X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X9),c_Int_OBit0(X8)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)),
    inference(variable_rename,[status(thm)],[c_0_1778]) ).

fof(c_0_2950,plain,
    ! [X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Odiv(X24,c_Divides_Odiv__class_Omod(X24,X23,X22),X22) = c_Groups_Ozero__class_Ozero(X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1779])]) ).

fof(c_0_2951,plain,
    ! [X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(X24,c_Groups_Otimes__class_Otimes(X24,X23,X22),X22) = c_Groups_Ozero__class_Ozero(X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1780])]) ).

fof(c_0_2952,plain,
    ! [X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | c_Divides_Odiv__class_Omod(X24,c_Groups_Otimes__class_Otimes(X24,X23,X22),X23) = c_Groups_Ozero__class_Ozero(X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1781])]) ).

fof(c_0_2953,plain,
    ! [X43,X44,X45] :
      ( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X45,X44) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X45,X43)
        | X44 = X43
        | X45 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X44 != X43
        | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X45,X44) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X45,X43)
        | X45 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1782])])]) ).

fof(c_0_2954,plain,
    ! [X43,X44,X45] :
      ( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X44,X45) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X43,X45)
        | X44 = X43
        | X45 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( X44 != X43
        | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X44,X45) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X43,X45)
        | X45 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1783])])]) ).

fof(c_0_2955,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19)
        | X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20 = X19 )
      & ( X24 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X22) )
      & ( X23 != X22
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X22) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1784])])])])]) ).

fof(c_0_2956,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X19)
        | X20 = X19
        | X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X23 != X22
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X22) )
      & ( X24 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X22) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1785])])])])]) ).

fof(c_0_2957,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X20) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)
        | X21 = X19
        | X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X24 != X22
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X23) )
      & ( X23 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X24,X23) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X23) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1786])])])])]) ).

fof(c_0_2958,plain,
    ! [X32,X34,X35] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X32)
        | X32 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk4_1(X32)) )
      & ( X34 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X35)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X34) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1787])])])])]) ).

fof(c_0_2959,plain,
    ! [X18,X20,X21] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
        | X18 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk2_1(X18)) )
      & ( X20 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1788])])])])]) ).

fof(c_0_2960,plain,
    ! [X16,X17] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X16)
        | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X16) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X17) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1789])])])]) ).

fof(c_0_2961,plain,
    ! [X16,X17] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X16) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1790])])])]) ).

fof(c_0_2962,plain,
    ! [X21] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X21 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1791])]) ).

fof(c_0_2963,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X22)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1792])]) ).

fof(c_0_2964,plain,
    ! [X11,X12] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X11)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,X12)
      | X12 = X11 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1793])]) ).

fof(c_0_2965,plain,
    ! [X11,X12] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12,X11)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X12)
      | X12 = X11 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1794])]) ).

fof(c_0_2966,plain,
    ! [X24,X25] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
      | X25 = X24 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1795])]) ).

fof(c_0_2967,plain,
    ! [X21,X22] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X21)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X22)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1796])]) ).

fof(c_0_2968,plain,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        | X23 = X22
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
        | X23 = X22
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1797])])]) ).

fof(c_0_2969,plain,
    ! [X24,X25] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
        | X25 = X24
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24) )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
        | X25 = X24
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1798])])]) ).

fof(c_0_2970,plain,
    ! [X16,X17] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X16,X17)
        | X16 = X17
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X16) )
      & ( X16 != X17
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X16,X17)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X16) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1799])])]) ).

fof(c_0_2971,plain,
    ! [X22,X23] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        | X23 = X22 )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
        | X23 = X22 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1800])])]) ).

fof(c_0_2972,plain,
    ! [X16,X17,X18,X19] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X17,X16)
        | X17 != X16 )
      & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X16,X17)
        | X17 != X16 )
      & ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X18)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,X19)
        | X19 = X18 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1801])])])])]) ).

fof(c_0_2973,plain,
    ! [X22,X23,X24] :
      ( ~ class_Groups_Ogroup__add(X24)
      | c_Groups_Oplus__class_Oplus(X24,c_Groups_Ominus__class_Ominus(X24,X23,X22),X22) = X23 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1802])]) ).

fof(c_0_2974,plain,
    ! [X22,X23,X24] :
      ( ~ class_Groups_Ogroup__add(X24)
      | c_Groups_Ominus__class_Ominus(X24,c_Groups_Oplus__class_Oplus(X24,X23,X22),X22) = X23 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1803])]) ).

fof(c_0_2975,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Ocomm__semiring__1(X24)
      | c_Rings_Odvd__class_Odvd(X24,X23,c_Groups_Otimes__class_Otimes(X24,X22,X23)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1804])]) ).

fof(c_0_2976,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Ocomm__semiring__1(X24)
      | c_Rings_Odvd__class_Odvd(X24,X23,c_Groups_Otimes__class_Otimes(X24,X23,X22)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1805])]) ).

fof(c_0_2977,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X20) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)
        | X21 = X19 )
      & ( X24 != X22
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X23) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X23) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1806])])])]) ).

fof(c_0_2978,plain,
    ! [X19,X20,X21,X22,X23,X24] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X20) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X19)
        | X20 = X19 )
      & ( X23 != X22
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X23) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X22) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1807])])])]) ).

fof(c_0_2979,plain,
    ! [X77,X78,X80,X81,X82] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X78,X77) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X78 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X77,esk17_2(X77,X78)) )
      & ( X81 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X80,X82)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X81,X80) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1808])])])])]) ).

fof(c_0_2980,plain,
    ! [X77,X78,X80,X81,X82] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X78,X77) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X78 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X77,esk16_2(X77,X78)) )
      & ( X81 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,X80,X82)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X81,X80) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1809])])])])]) ).

fof(c_0_2981,plain,
    ! [X8] : c_Int_OBit1(X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X8),X8),
    inference(variable_rename,[status(thm)],[c_0_1810]) ).

fof(c_0_2982,plain,
    ! [X21,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X22),X21) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)),
    inference(variable_rename,[status(thm)],[c_0_1811]) ).

fof(c_0_2983,plain,
    ! [X21,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Nat_OSuc(X21)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)),
    inference(variable_rename,[status(thm)],[c_0_1812]) ).

fof(c_0_2984,plain,
    ! [X8,X9] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X9),X8) = c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)),
    inference(variable_rename,[status(thm)],[c_0_1813]) ).

fof(c_0_2985,plain,
    ! [X11,X12] :
      ( ~ class_Int_Onumber__ring(X12)
      | c_Groups_Otimes__class_Otimes(X12,c_Int_Onumber__class_Onumber__of(X12,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X11) = c_Groups_Oplus__class_Oplus(X12,X11,X11) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1814])]) ).

fof(c_0_2986,plain,
    ! [X11,X12] :
      ( ~ class_Int_Onumber__ring(X12)
      | c_Groups_Otimes__class_Otimes(X12,X11,c_Int_Onumber__class_Onumber__of(X12,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X12,X11,X11) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1815])]) ).

fof(c_0_2987,plain,
    ! [X60,X61,X63,X64,X65] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X61,X60)
        | X60 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X61,esk13_2(X60,X61)) )
      & ( X63 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X64,X65)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X64,X63) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1816])])])])]) ).

fof(c_0_2988,plain,
    ! [X24,X25] :
      ( ~ class_Rings_Ocomm__semiring__1(X25)
      | c_Groups_Otimes__class_Otimes(X25,X24,X24) = c_Power_Opower__class_Opower(X25,X24,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1817])]) ).

fof(c_0_2989,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Omonoid__mult(X5)
      | c_Power_Opower__class_Opower(X5,X4,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X5,X4,X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1818])]) ).

fof(c_0_2990,plain,
    ! [X21,X22] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21),c_Nat_OSuc(X22)),
    inference(variable_rename,[status(thm)],[c_0_1819]) ).

fof(c_0_2991,plain,
    ! [X16,X17] :
      ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X16,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1820])])])]) ).

fof(c_0_2992,plain,
    ! [X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X7)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X7)),
    inference(variable_rename,[status(thm)],[c_0_1821]) ).

fof(c_0_2993,plain,
    ! [X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X7)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X7)),
    inference(variable_rename,[status(thm)],[c_0_1822]) ).

fof(c_0_2994,plain,
    ! [X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X7)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X7)),
    inference(variable_rename,[status(thm)],[c_0_1823]) ).

fof(c_0_2995,plain,
    ! [X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X7)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X7)),
    inference(variable_rename,[status(thm)],[c_0_1824]) ).

fof(c_0_2996,plain,
    ! [X22,X23] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X22),X22) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[c_0_1825]) ).

fof(c_0_2997,plain,
    ! [X21,X22] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[c_0_1826]) ).

fof(c_0_2998,plain,
    ! [X21,X22] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21),X22) = X21,
    inference(variable_rename,[status(thm)],[c_0_1827]) ).

fof(c_0_2999,plain,
    ! [X21,X22] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21),X21) = X22,
    inference(variable_rename,[status(thm)],[c_0_1828]) ).

fof(c_0_3000,plain,
    ! [X24,X25] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X25)
      | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X24)
      | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1829])]) ).

fof(c_0_3001,plain,
    ! [X21,X22] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,X21),X22),
    inference(variable_rename,[status(thm)],[c_0_1830]) ).

fof(c_0_3002,plain,
    ! [X21,X22] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21),X22),
    inference(variable_rename,[status(thm)],[c_0_1831]) ).

fof(c_0_3003,plain,
    ! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X20)),
    inference(variable_rename,[status(thm)],[c_0_1832]) ).

fof(c_0_3004,plain,
    ! [X21,X22] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21)),
    inference(variable_rename,[status(thm)],[c_0_1833]) ).

fof(c_0_3005,plain,
    ! [X21,X22] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X22)),
    inference(variable_rename,[status(thm)],[c_0_1834]) ).

fof(c_0_3006,plain,
    ! [X51,X52,X53,X54] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X52),c_Int_OBit0(X51))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X52,X51) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X53)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X54),c_Int_OBit0(X53)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1835])])])]) ).

fof(c_0_3007,plain,
    ! [X6,X7,X8,X9] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit0(X6))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,X6) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,X8)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X9),c_Int_OBit0(X8)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1836])])])]) ).

fof(c_0_3008,plain,
    ! [X51,X52,X53,X54] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X52),c_Int_OBit1(X51))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,X51) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,X53)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X54),c_Int_OBit1(X53)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1837])])])]) ).

fof(c_0_3009,plain,
    ! [X6,X7,X8,X9] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit1(X6))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X7,X6) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X9,X8)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X9),c_Int_OBit1(X8)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1838])])])]) ).

fof(c_0_3010,plain,
    ! [X51,X52,X53,X54] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X52),c_Int_OBit1(X51))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,X51) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,X53)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X54),c_Int_OBit1(X53)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1839])])])]) ).

fof(c_0_3011,plain,
    ! [X6,X7,X8,X9] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit1(X6))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X7,X6) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X9,X8)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X9),c_Int_OBit1(X8)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1840])])])]) ).

fof(c_0_3012,plain,
    ! [X51,X52,X53,X54] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X52),c_Int_OBit0(X51))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,X51) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,X53)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X54),c_Int_OBit0(X53)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1841])])])]) ).

fof(c_0_3013,plain,
    ! [X6,X7,X8,X9] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit0(X6))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X7,X6) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X9,X8)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X9),c_Int_OBit0(X8)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1842])])])]) ).

fof(c_0_3014,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X20),c_Nat_OSuc(X19))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X22),c_Nat_OSuc(X21)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1843])])])]) ).

fof(c_0_3015,plain,
    ! [X51,X52,X53,X54] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X52),c_Int_OBit1(X51))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,X51) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,X53)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X54),c_Int_OBit1(X53)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1844])])])]) ).

fof(c_0_3016,plain,
    ! [X6,X7,X8,X9] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit1(X6))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X7,X6) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X9,X8)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X9),c_Int_OBit1(X8)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1845])])])]) ).

fof(c_0_3017,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X20),c_Nat_OSuc(X19))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X22),c_Nat_OSuc(X21)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1846])])])]) ).

fof(c_0_3018,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X22),c_Nat_OSuc(X21))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1847])]) ).

fof(c_0_3019,plain,
    ! [X51,X52,X53,X54] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X52),c_Int_OBit0(X51))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X52,X51) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X53)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X54),c_Int_OBit0(X53)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1848])])])]) ).

fof(c_0_3020,plain,
    ! [X6,X7,X8,X9] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit0(X6))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,X6) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,X8)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X9),c_Int_OBit0(X8)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1849])])])]) ).

fof(c_0_3021,plain,
    ! [X51,X52,X53,X54] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X52),c_Int_OBit0(X51))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X52,X51) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X53)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X54),c_Int_OBit0(X53)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1850])])])]) ).

fof(c_0_3022,plain,
    ! [X6,X7,X8,X9] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit0(X6))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,X6) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,X8)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X9),c_Int_OBit0(X8)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1851])])])]) ).

fof(c_0_3023,plain,
    ! [X51,X52,X53,X54] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X52),c_Int_OBit1(X51))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X52,X51) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X53)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X54),c_Int_OBit1(X53)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1852])])])]) ).

fof(c_0_3024,plain,
    ! [X6,X7,X8,X9] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit1(X6))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,X6) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,X8)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X9),c_Int_OBit1(X8)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1853])])])]) ).

fof(c_0_3025,plain,
    ! [X17,X18] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X18),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1854])])])]) ).

fof(c_0_3026,plain,
    ! [X17,X18] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X17),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X18),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1855])])])]) ).

fof(c_0_3027,plain,
    ! [X26,X27,X28] :
      ( ( ~ c_Rings_Odvd__class_Odvd(X28,X27,X26)
        | c_Divides_Odiv__class_Omod(X28,X26,X27) = c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Divides_Osemiring__div(X28) )
      & ( c_Divides_Odiv__class_Omod(X28,X26,X27) != c_Groups_Ozero__class_Ozero(X28)
        | c_Rings_Odvd__class_Odvd(X28,X27,X26)
        | ~ class_Divides_Osemiring__div(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1856])])]) ).

fof(c_0_3028,plain,
    ! [X11] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X11,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X11),
    inference(variable_rename,[status(thm)],[c_0_1857]) ).

fof(c_0_3029,plain,
    ! [X11] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X11) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X11,X11),
    inference(variable_rename,[status(thm)],[c_0_1858]) ).

fof(c_0_3030,plain,
    ! [X22,X23,X24] :
      ( ~ class_Divides_Osemiring__div(X24)
      | ~ c_Rings_Odvd__class_Odvd(X24,X23,X22)
      | c_Divides_Odiv__class_Omod(X24,X22,X23) = c_Groups_Ozero__class_Ozero(X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1859])]) ).

fof(c_0_3031,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Nat_OSuc(X21))
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
      | X22 = c_Nat_OSuc(X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1860])]) ).

fof(c_0_3032,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,c_Nat_OSuc(X19))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
        | X20 = c_Nat_OSuc(X19) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Nat_OSuc(X21)) )
      & ( X22 != c_Nat_OSuc(X21)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Nat_OSuc(X21)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1861])])])])]) ).

fof(c_0_3033,plain,
    ! [X22,X23,X24,X25] :
      ( ~ class_Rings_Odvd(X25)
      | X24 != c_Groups_Otimes__class_Otimes(X25,X23,X22)
      | c_Rings_Odvd__class_Odvd(X25,X23,X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1862])]) ).

fof(c_0_3034,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X22),c_Nat_OSuc(X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1863])]) ).

fof(c_0_3035,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(X19))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
        | X20 = X19 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Nat_OSuc(X21)) )
      & ( X22 != X21
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Nat_OSuc(X21)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1864])])])])]) ).

fof(c_0_3036,plain,
    ! [X19,X20] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(X19))
        | X20 = X19
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19) )
      & ( X20 != X19
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(X19))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1865])])]) ).

fof(c_0_3037,plain,
    ! [X21,X22] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Nat_OSuc(X21))
      | X21 = X22 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1866])]) ).

fof(c_0_3038,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Nat_OSuc(X21))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | X22 = X21 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1867])]) ).

fof(c_0_3039,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | c_Nat_OSuc(X22) = X21
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X22),X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1868])]) ).

fof(c_0_3040,plain,
    ! [X16,X17] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X16,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X17,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1869])])])]) ).

fof(c_0_3041,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X22),X21)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1870])]) ).

fof(c_0_3042,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X20),X19)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X22),X21) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1871])])])]) ).

fof(c_0_3043,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(X19))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Nat_OSuc(X21)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1872])])])]) ).

fof(c_0_3044,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X20),X19) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X22),X21)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1873])])])]) ).

fof(c_0_3045,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X22),X21)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1874])]) ).

fof(c_0_3046,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X22),X21)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1875])]) ).

fof(c_0_3047,plain,
    ! [X32,X34,X35] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X32)
        | X32 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk6_1(X32)) )
      & ( X34 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X35)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X34) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1876])])])])]) ).

fof(c_0_3048,plain,
    ! [X47,X48] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X47)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X47) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X48) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1877])])])]) ).

fof(c_0_3049,plain,
    ! [X24] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | X24 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X24 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1878])]) ).

fof(c_0_3050,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X22),X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1879])]) ).

fof(c_0_3051,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Nat_OSuc(X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1880])]) ).

fof(c_0_3052,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,c_Nat_OSuc(X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1881])]) ).

fof(c_0_3053,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,c_Nat_OSuc(X21)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1882])]) ).

fof(c_0_3054,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X6),c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OPls) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1883])])])]) ).

fof(c_0_3055,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X6))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X6) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X7)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X7)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1884])])])]) ).

fof(c_0_3056,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X6),c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X7,c_Int_OPls)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OPls) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1885])])])]) ).

fof(c_0_3057,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X6))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X6) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X7)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X7)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1886])])])]) ).

fof(c_0_3058,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X6))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X6) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X7)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X7)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1887])])])]) ).

fof(c_0_3059,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X6))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X6) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X7)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X7)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1888])])])]) ).

fof(c_0_3060,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X6))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X6) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X7)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X7)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1889])])])]) ).

fof(c_0_3061,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X6),c_Int_OMin)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,c_Int_OMin) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,c_Int_OMin)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OMin) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1890])])])]) ).

fof(c_0_3062,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X6),c_Int_OMin)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Int_OMin) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X7,c_Int_OMin)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OMin) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1891])])])]) ).

fof(c_0_3063,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X6))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X6) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X7)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X7)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1892])])])]) ).

fof(c_0_3064,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X6),c_Int_OMin)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Int_OMin) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X7,c_Int_OMin)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OMin) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1893])])])]) ).

fof(c_0_3065,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X6))
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X6) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X7)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X7)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1894])])])]) ).

fof(c_0_3066,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X6),c_Int_OMin)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X6,c_Int_OMin) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X7,c_Int_OMin)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OMin) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1895])])])]) ).

fof(c_0_3067,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X6),c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OPls) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1896])])])]) ).

fof(c_0_3068,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X6))
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X6) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X7)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X7)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1897])])])]) ).

fof(c_0_3069,plain,
    ! [X6,X7] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X6),c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X7,c_Int_OPls)
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OPls) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1898])])])]) ).

fof(c_0_3070,plain,
    ! [X24,X25] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X25)
      | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X24)
      | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1899])]) ).

fof(c_0_3071,plain,
    ! [X19,X20,X21,X22] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X19) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1900])])])]) ).

fof(c_0_3072,plain,
    ! [X24,X25] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
      | X24 != X25 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1901])]) ).

fof(c_0_3073,plain,
    ! [X24,X25] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
      | X25 != X24 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1902])]) ).

fof(c_0_3074,plain,
    ! [X24,X25] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X25)
      | X25 != X24 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1903])]) ).

fof(c_0_3075,plain,
    ! [X34,X35,X36] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X35)
      | X35 != X34
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1904])]) ).

fof(c_0_3076,plain,
    ! [X34,X35,X36] :
      ( X36 != X35
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X35,X34)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X36,X34) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1905])]) ).

fof(c_0_3077,plain,
    ! [X47,X48,X49,X50] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,X47)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X47) )
      & ( X48 != X47
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,X47) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49)
        | X50 = X49
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1906])])])])]) ).

fof(c_0_3078,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1907])]) ).

fof(c_0_3079,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
      | X22 = X21
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1908])]) ).

fof(c_0_3080,plain,
    ! [X19,X20,X21,X22] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
        | X20 = X19 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21) )
      & ( X22 != X21
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1909])])])])]) ).

fof(c_0_3081,plain,
    ! [X19,X20,X21,X22] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19) )
      & ( X20 != X19
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
        | X22 = X21
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1910])])])])]) ).

fof(c_0_3082,plain,
    ! [X16,X17,X18,X19] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,X16)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,X16) )
      & ( X17 != X16
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,X16) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,X18)
        | X19 = X18
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X19,X18) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1911])])])])]) ).

fof(c_0_3083,plain,
    ! [X16,X17,X18,X19] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,X16)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,X16)
        | X17 = X16 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X19,X18)
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,X18) )
      & ( X19 != X18
        | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X19,X18) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1912])])])])]) ).

fof(c_0_3084,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,X21) = X22 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1913])]) ).

fof(c_0_3085,plain,
    ! [X17,X18] :
      ( ( ~ c_Int_Oiszero(X18,c_Int_Onumber__class_Onumber__of(X18,c_Int_OBit0(X17)))
        | c_Int_Oiszero(X18,c_Int_Onumber__class_Onumber__of(X18,X17))
        | ~ class_Int_Onumber__ring(X18)
        | ~ class_Int_Oring__char__0(X18) )
      & ( ~ c_Int_Oiszero(X18,c_Int_Onumber__class_Onumber__of(X18,X17))
        | c_Int_Oiszero(X18,c_Int_Onumber__class_Onumber__of(X18,c_Int_OBit0(X17)))
        | ~ class_Int_Onumber__ring(X18)
        | ~ class_Int_Oring__char__0(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1914])])]) ).

fof(c_0_3086,plain,
    ! [X21,X22] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21) )
      & ( X22 != X21
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1915])])]) ).

fof(c_0_3087,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1916])]) ).

fof(c_0_3088,plain,
    ! [X24,X25] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X25)
      | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X25,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1917])]) ).

fof(c_0_3089,plain,
    ! [X24,X25] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X25)
      | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X24,X25)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1918])]) ).

fof(c_0_3090,plain,
    ! [X26,X27,X28] :
      ( ( X27 = c_Groups_Ozero__class_Ozero(X28)
        | c_Power_Opower__class_Opower(X28,X27,X26) != c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Power_Opower(X28)
        | ~ class_Rings_Omult__zero(X28)
        | ~ class_Rings_Ono__zero__divisors(X28)
        | ~ class_Rings_Ozero__neq__one(X28) )
      & ( X26 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X28,X27,X26) != c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Power_Opower(X28)
        | ~ class_Rings_Omult__zero(X28)
        | ~ class_Rings_Ono__zero__divisors(X28)
        | ~ class_Rings_Ozero__neq__one(X28) )
      & ( X27 != c_Groups_Ozero__class_Ozero(X28)
        | X26 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X28,X27,X26) = c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Power_Opower(X28)
        | ~ class_Rings_Omult__zero(X28)
        | ~ class_Rings_Ono__zero__divisors(X28)
        | ~ class_Rings_Ozero__neq__one(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1919])])]) ).

fof(c_0_3091,plain,
    ! [X9,X10] :
      ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9)) = c_Groups_Oone__class_Oone(X10)
        | ~ class_Power_Opower(X10)
        | ~ class_Rings_Osemiring__0(X10) )
      & ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X10,c_Groups_Ozero__class_Ozero(X10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9)) = c_Groups_Ozero__class_Ozero(X10)
        | ~ class_Power_Opower(X10)
        | ~ class_Rings_Osemiring__0(X10) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1920])])]) ).

fof(c_0_3092,plain,
    ! [X21] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X21))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X21),
    inference(variable_rename,[status(thm)],[c_0_1921]) ).

fof(c_0_3093,plain,
    ! [X4] :
      ( ~ class_Rings_Osemiring__1(X4)
      | c_Power_Opower__class_Opower(X4,c_Groups_Oone__class_Oone(X4),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1922])]) ).

fof(c_0_3094,plain,
    ! [X4] :
      ( ~ class_Rings_Osemiring__1(X4)
      | c_Power_Opower__class_Opower(X4,c_Groups_Ozero__class_Ozero(X4),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1923])]) ).

fof(c_0_3095,plain,
    ! [X24,X25,X26] :
      ( ~ class_Rings_Olinordered__idom(X26)
      | X25 = X24
      | c_Orderings_Oord__class_Oless(X26,X25,X24)
      | c_Orderings_Oord__class_Oless(X26,X24,X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1924])]) ).

fof(c_0_3096,plain,
    ! [X21,X22] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X22),c_Nat_OSuc(X21)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X22,X21),
    inference(variable_rename,[status(thm)],[c_0_1925]) ).

fof(c_0_3097,plain,
    ! [X21,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X22),X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Nat_OSuc(X21)),
    inference(variable_rename,[status(thm)],[c_0_1926]) ).

fof(c_0_3098,plain,
    ! [X34,X35,X36] :
      ( ~ class_Rings_Ocomm__semiring__1(X36)
      | c_Groups_Oplus__class_Oplus(X36,X35,X34) = c_Groups_Oplus__class_Oplus(X36,X34,X35) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1927])]) ).

fof(c_0_3099,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Ocomm__semiring__1(X24)
      | c_Groups_Otimes__class_Otimes(X24,X23,X22) = c_Groups_Otimes__class_Otimes(X24,X22,X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1928])]) ).

fof(c_0_3100,plain,
    ! [X4] :
      ( ~ class_Rings_Olinordered__semidom(X4)
      | ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Ozero__class_Ozero(X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1929])]) ).

fof(c_0_3101,plain,
    ! [X4] :
      ( ~ class_Rings_Olinordered__semidom(X4)
      | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Ozero__class_Ozero(X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1930])]) ).

fof(c_0_3102,plain,
    ! [X19,X20,X21,X22] :
      ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X19 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X20 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X19 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X21 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X21 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1931])])])])]) ).

fof(c_0_3103,plain,
    ! [X19,X20,X21,X22] :
      ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19) )
      & ( X19 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X20 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19) )
      & ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19) )
      & ( X19 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19) )
      & ( X22 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X21 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21) )
      & ( X22 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X21 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1932])])])])]) ).

fof(c_0_3104,plain,
    ! [X19,X20] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X19 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X20 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1933])])])]) ).

fof(c_0_3105,plain,
    ! [X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21) = c_Nat_OSuc(c_Nat_OSuc(X21)),
    inference(variable_rename,[status(thm)],[c_0_1934]) ).

fof(c_0_3106,plain,
    ! [X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X21)),
    inference(variable_rename,[status(thm)],[c_0_1935]) ).

fof(c_0_3107,plain,
    ! [X24,X25] :
      ( ~ class_Int_Onumber__ring(X25)
      | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X24)
      | c_Power_Opower__class_Opower(X25,c_Int_Onumber__class_Onumber__of(X25,c_Int_OMin),X24) = c_Int_Onumber__class_Onumber__of(X25,c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1936])]) ).

fof(c_0_3108,plain,
    ! [X24,X25] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X24)
        | c_Power_Opower__class_Opower(X25,c_Int_Onumber__class_Onumber__of(X25,c_Int_OMin),X24) = c_Groups_Oone__class_Oone(X25)
        | ~ class_Int_Onumber__ring(X25) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X24)
        | c_Power_Opower__class_Opower(X25,c_Int_Onumber__class_Onumber__of(X25,c_Int_OMin),X24) = c_Int_Onumber__class_Onumber__of(X25,c_Int_OMin)
        | ~ class_Int_Onumber__ring(X25) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1937])])]) ).

fof(c_0_3109,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Ono__zero__divisors(X24)
      | c_Groups_Otimes__class_Otimes(X24,X23,X22) != c_Groups_Ozero__class_Ozero(X24)
      | X23 = c_Groups_Ozero__class_Ozero(X24)
      | X22 = c_Groups_Ozero__class_Ozero(X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1938])]) ).

fof(c_0_3110,plain,
    ! [X22,X23,X24] :
      ( ~ class_Rings_Ono__zero__divisors(X24)
      | X23 = c_Groups_Ozero__class_Ozero(X24)
      | X22 = c_Groups_Ozero__class_Ozero(X24)
      | c_Groups_Otimes__class_Otimes(X24,X23,X22) != c_Groups_Ozero__class_Ozero(X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1939])]) ).

fof(c_0_3111,plain,
    ! [X26,X27,X28] :
      ( ( c_Groups_Otimes__class_Otimes(X28,X27,X26) != c_Groups_Ozero__class_Ozero(X28)
        | X27 = c_Groups_Ozero__class_Ozero(X28)
        | X26 = c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Rings_Oring__no__zero__divisors(X28) )
      & ( X27 != c_Groups_Ozero__class_Ozero(X28)
        | c_Groups_Otimes__class_Otimes(X28,X27,X26) = c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Rings_Oring__no__zero__divisors(X28) )
      & ( X26 != c_Groups_Ozero__class_Ozero(X28)
        | c_Groups_Otimes__class_Otimes(X28,X27,X26) = c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Rings_Oring__no__zero__divisors(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1940])])]) ).

fof(c_0_3112,plain,
    ! [X24,X25] :
      ( ~ class_Int_Onumber__ring(X25)
      | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X24)
      | c_Power_Opower__class_Opower(X25,c_Int_Onumber__class_Onumber__of(X25,c_Int_OMin),X24) = c_Groups_Oone__class_Oone(X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1941])]) ).

fof(c_0_3113,plain,
    ! [X24,X25] :
      ( X25 = X24
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X24,X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1942])]) ).

fof(c_0_3114,plain,
    ! [X19,X20,X21,X22] :
      ( ( X20 = X19
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
        | X22 != X21 )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X22)
        | X22 != X21 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1943])])])])]) ).

fof(c_0_3115,plain,
    ! [X24,X25] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X24)
      | X25 = X24
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,X25) ),
    inference(variable_rename,[status(thm)],[c_0_1944]) ).

fof(c_0_3116,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Ocomm__semiring__1(X5)
      | ~ c_Rings_Odvd__class_Odvd(X5,c_Groups_Ozero__class_Ozero(X5),X4)
      | X4 = c_Groups_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1945])]) ).

fof(c_0_3117,plain,
    ! [X11] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X11),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X11,
    inference(variable_rename,[status(thm)],[c_0_1946]) ).

fof(c_0_3118,plain,
    ! [X19,X20,X21,X22] :
      ( ( c_Power_Opower__class_Opower(tc_Nat_Onat,X20,X19) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X21 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(tc_Nat_Onat,X22,X21) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Power_Opower__class_Opower(tc_Nat_Onat,X22,X21) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1947])])])])]) ).

fof(c_0_3119,plain,
    ! [X18,X19] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1948])])])]) ).

fof(c_0_3120,plain,
    ! [X21,X22] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X22) ),
    inference(variable_rename,[status(thm)],[c_0_1949]) ).

fof(c_0_3121,plain,
    ! [X11,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X12,X11)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X11,X12) ),
    inference(variable_rename,[status(thm)],[c_0_1950]) ).

fof(c_0_3122,plain,
    ! [X11,X12] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12,X11)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X11,X12) ),
    inference(variable_rename,[status(thm)],[c_0_1951]) ).

fof(c_0_3123,plain,
    ! [X24] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X24)
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1952])]) ).

fof(c_0_3124,plain,
    ! [X11,X12] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X12,X11) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X11,X12),
    inference(variable_rename,[status(thm)],[c_0_1953]) ).

fof(c_0_3125,plain,
    ! [X11,X12] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,X11) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,X12),
    inference(variable_rename,[status(thm)],[c_0_1954]) ).

fof(c_0_3126,plain,
    ! [X21,X22] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_1955]) ).

fof(c_0_3127,plain,
    ! [X21,X22] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,X22),
    inference(variable_rename,[status(thm)],[c_0_1956]) ).

fof(c_0_3128,plain,
    ! [X11,X12] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12,X11) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X11,X12),
    inference(variable_rename,[status(thm)],[c_0_1957]) ).

fof(c_0_3129,plain,
    ! [X21,X22,X23] :
      ( ~ class_Rings_Oring__1__no__zero__divisors(X23)
      | X22 = c_Groups_Ozero__class_Ozero(X23)
      | c_Power_Opower__class_Opower(X23,X22,X21) != c_Groups_Ozero__class_Ozero(X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1958])]) ).

fof(c_0_3130,plain,
    ! [X26,X27] :
      ( ( c_Groups_Ozero__class_Ozero(X27) != c_Groups_Oplus__class_Oplus(X27,X26,X26)
        | X26 = c_Groups_Ozero__class_Ozero(X27)
        | ~ class_Groups_Olinordered__ab__group__add(X27) )
      & ( X26 != c_Groups_Ozero__class_Ozero(X27)
        | c_Groups_Ozero__class_Ozero(X27) = c_Groups_Oplus__class_Oplus(X27,X26,X26)
        | ~ class_Groups_Olinordered__ab__group__add(X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1959])])]) ).

fof(c_0_3131,plain,
    ! [X26,X27] :
      ( ( c_Groups_Oplus__class_Oplus(X27,X26,X26) != c_Groups_Ozero__class_Ozero(X27)
        | X26 = c_Groups_Ozero__class_Ozero(X27)
        | ~ class_Groups_Olinordered__ab__group__add(X27) )
      & ( X26 != c_Groups_Ozero__class_Ozero(X27)
        | c_Groups_Oplus__class_Oplus(X27,X26,X26) = c_Groups_Ozero__class_Ozero(X27)
        | ~ class_Groups_Olinordered__ab__group__add(X27) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1960])])]) ).

fof(c_0_3132,plain,
    ! [X24] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X24)
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1961])]) ).

fof(c_0_3133,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    c_0_1962 ).

fof(c_0_3134,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    c_0_1963 ).

fof(c_0_3135,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    c_0_1964 ).

fof(c_0_3136,plain,
    ! [X19,X20,X21,X22] :
      ( ( X20 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
        | X20 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X20,X19) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X19 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
        | X20 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X20,X19) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X20 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
        | X19 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X20,X19) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X19 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
        | X19 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X20,X19) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X22 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X21 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X22,X21) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X22 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
        | X21 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
        | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X22,X21) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1965])])])])]) ).

fof(c_0_3137,plain,
    ! [X21,X22] :
      ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X22,X21) != c_Groups_Oone__class_Oone(tc_Int_Oint)
      | X22 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | X22 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1966])]) ).

fof(c_0_3138,plain,
    ! [X19,X20,X21,X22] :
      ( ( X20 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X19 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X22 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X21 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1967])])])])]) ).

fof(c_0_3139,plain,
    ! [X26,X27,X28] :
      ( ( X27 != X26
        | c_Groups_Ominus__class_Ominus(X28,X27,X26) = c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Groups_Oab__group__add(X28) )
      & ( c_Groups_Ominus__class_Ominus(X28,X27,X26) != c_Groups_Ozero__class_Ozero(X28)
        | X27 = X26
        | ~ class_Groups_Oab__group__add(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1968])])]) ).

fof(c_0_3140,plain,
    ! [X26,X27,X28] :
      ( ( c_Groups_Ominus__class_Ominus(X28,X27,X26) != c_Groups_Ozero__class_Ozero(X28)
        | X27 = X26
        | ~ class_Groups_Ogroup__add(X28) )
      & ( X27 != X26
        | c_Groups_Ominus__class_Ominus(X28,X27,X26) = c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Groups_Ogroup__add(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1969])])]) ).

fof(c_0_3141,plain,
    ! [X4] :
      ( ~ class_Int_Onumber__ring(X4)
      | c_Groups_Oplus__class_Oplus(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Oone__class_Oone(X4)) = c_Int_Onumber__class_Onumber__of(X4,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1970])]) ).

fof(c_0_3142,plain,
    ! [X18,X20,X21] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
        | X18 = c_Nat_OSuc(esk10_1(X18)) )
      & ( X20 != c_Nat_OSuc(X21)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1971])])])])]) ).

fof(c_0_3143,plain,
    ! [X26,X27,X28] :
      ( ( X27 != c_Groups_Oplus__class_Oplus(X28,X27,X26)
        | X26 = c_Groups_Ozero__class_Ozero(X28)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X28) )
      & ( X26 != c_Groups_Ozero__class_Ozero(X28)
        | X27 = c_Groups_Oplus__class_Oplus(X28,X27,X26)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X28) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1972])])]) ).

fof(c_0_3144,plain,
    v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk1_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_1973])]) ).

fof(c_0_3145,plain,
    ! [X9,X10] :
      ( ~ class_Int_Onumber__ring(X10)
      | ~ class_Int_Oring__char__0(X10)
      | ~ c_Int_Oiszero(X10,c_Int_Onumber__class_Onumber__of(X10,c_Int_OBit1(X9))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1974])]) ).

fof(c_0_3146,plain,
    ! [X62,X63] :
      ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X62) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X62,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X63,c_Int_OPls)
        | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X63) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1975])])])]) ).

fof(c_0_3147,plain,
    ! [X62,X63] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X62)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X62,c_Int_OPls) )
      & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X63,c_Int_OPls)
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X63) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1976])])])]) ).

fof(c_0_3148,plain,
    ! [X19,X20,X21,X22] :
      ( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X21 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1977])])])])]) ).

fof(c_0_3149,plain,
    ! [X4,X5] :
      ( ~ class_Int_Onumber__ring(X5)
      | c_Groups_Otimes__class_Otimes(X5,c_Int_Onumber__class_Onumber__of(X5,c_Int_OBit1(c_Int_OPls)),X4) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1978])]) ).

fof(c_0_3150,plain,
    ! [X4,X5] :
      ( ~ class_Int_Onumber__ring(X5)
      | c_Groups_Otimes__class_Otimes(X5,X4,c_Int_Onumber__class_Onumber__of(X5,c_Int_OBit1(c_Int_OPls))) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1979])]) ).

fof(c_0_3151,plain,
    ! [X18,X19] :
      ( ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) )
      & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
        | X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1980])])])]) ).

fof(c_0_3152,plain,
    ! [X21] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X21),X21),
    inference(variable_rename,[status(thm)],[c_0_1981]) ).

fof(c_0_3153,plain,
    ! [X21,X22] :
      ( X22 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21)
      | X21 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | X22 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1982])]) ).

fof(c_0_3154,plain,
    ! [X19,X20] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | X19 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X20 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1983])])])]) ).

fof(c_0_3155,plain,
    ! [X18,X19] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1984])])])]) ).

fof(c_0_3156,plain,
    ! [X19,X20,X21,X22] :
      ( ( X20 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X19 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X22 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X21 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1985])])])])]) ).

fof(c_0_3157,plain,
    ! [X19,X20,X21,X22] :
      ( ( X20 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19) )
      & ( X19 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19) )
      & ( X22 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X21 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X21) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1986])])])])]) ).

fof(c_0_3158,plain,
    ! [X19,X20,X21,X22] :
      ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X22 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X21 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1987])])])])]) ).

fof(c_0_3159,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | X21 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1988])])])]) ).

fof(c_0_3160,plain,
    ! [X21,X22] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X21) != X22
      | X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1989])])])]) ).

fof(c_0_3161,plain,
    ! [X21] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[c_0_1990]) ).

fof(c_0_3162,plain,
    ! [X21] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[c_0_1991]) ).

fof(c_0_3163,plain,
    ! [X21] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[c_0_1992]) ).

fof(c_0_3164,plain,
    ! [X65,X66] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X66,X65)
      | X66 != X65 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1993])]) ).

fof(c_0_3165,plain,
    ! [X21,X22] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X21)
      | X21 != X22 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1994])]) ).

fof(c_0_3166,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    c_0_1995 ).

fof(c_0_3167,plain,
    ! [X4,X5] :
      ( ~ class_Int_Onumber__ring(X5)
      | c_Groups_Oplus__class_Oplus(X5,c_Int_Onumber__class_Onumber__of(X5,c_Int_OPls),X4) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1996])]) ).

fof(c_0_3168,plain,
    ! [X4,X5] :
      ( ~ class_Int_Onumber__ring(X5)
      | c_Groups_Oplus__class_Oplus(X5,X4,c_Int_Onumber__class_Onumber__of(X5,c_Int_OPls)) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1997])]) ).

fof(c_0_3169,plain,
    ! [X21,X22] :
      ( ~ class_Power_Opower(X22)
      | ~ class_Rings_Osemiring__0(X22)
      | c_Power_Opower__class_Opower(X22,c_Groups_Ozero__class_Ozero(X22),c_Nat_OSuc(X21)) = c_Groups_Ozero__class_Ozero(X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1998])]) ).

fof(c_0_3170,plain,
    ! [X21,X22] :
      ( ( X21 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X22,c_Groups_Ozero__class_Ozero(X22),X21) = c_Groups_Oone__class_Oone(X22)
        | ~ class_Power_Opower(X22)
        | ~ class_Rings_Osemiring__0(X22) )
      & ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Power_Opower__class_Opower(X22,c_Groups_Ozero__class_Ozero(X22),X21) = c_Groups_Ozero__class_Ozero(X22)
        | ~ class_Power_Opower(X22)
        | ~ class_Rings_Osemiring__0(X22) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1999])])]) ).

fof(c_0_3171,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    c_0_2000 ).

fof(c_0_3172,plain,
    ! [X21] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X21),
    inference(variable_rename,[status(thm)],[c_0_2001]) ).

fof(c_0_3173,plain,
    ! [X21] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X21),
    inference(variable_rename,[status(thm)],[c_0_2002]) ).

fof(c_0_3174,plain,
    ! [X4] :
      ( ~ class_Int_Onumber__ring(X4)
      | ~ c_Int_Oiszero(X4,c_Int_Onumber__class_Onumber__of(X4,c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2003])]) ).

fof(c_0_3175,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
    c_0_2004 ).

fof(c_0_3176,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
    c_0_2005 ).

fof(c_0_3177,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
    c_0_2006 ).

fof(c_0_3178,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    c_0_2007 ).

fof(c_0_3179,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    c_0_2008 ).

fof(c_0_3180,plain,
    ! [X3] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[c_0_2009]) ).

fof(c_0_3181,plain,
    ! [X4] :
      ( ~ class_Rings_Olinordered__semidom(X4)
      | c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Oone__class_Oone(X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2010])]) ).

fof(c_0_3182,plain,
    ! [X4] :
      ( ~ class_Rings_Olinordered__semidom(X4)
      | c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Oone__class_Oone(X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2011])]) ).

fof(c_0_3183,plain,
    ! [X21] : c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[c_0_2012]) ).

fof(c_0_3184,plain,
    ! [X4,X5] :
      ( ~ class_Divides_Osemiring__div(X5)
      | c_Divides_Odiv__class_Omod(X5,X4,c_Groups_Oone__class_Oone(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2013])]) ).

fof(c_0_3185,plain,
    ! [X4,X5] :
      ( ~ class_Divides_Osemiring__div(X5)
      | c_Divides_Odiv__class_Omod(X5,c_Groups_Ozero__class_Ozero(X5),X4) = c_Groups_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2014])]) ).

fof(c_0_3186,plain,
    ! [X21,X22] :
      ( ~ class_Groups_Omonoid__mult(X22)
      | c_Power_Opower__class_Opower(X22,c_Groups_Oone__class_Oone(X22),X21) = c_Groups_Oone__class_Oone(X22) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2015])]) ).

fof(c_0_3187,plain,
    ! [X24,X25] :
      ( ~ class_RealVector_Oreal__normed__algebra(X25)
      | c_Groups_Otimes__class_Otimes(X25,X24,c_Groups_Ozero__class_Ozero(X25)) = c_Groups_Ozero__class_Ozero(X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2016])]) ).

fof(c_0_3188,plain,
    ! [X4,X5] :
      ( ~ class_RealVector_Oreal__normed__algebra(X5)
      | c_Groups_Otimes__class_Otimes(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2017])]) ).

fof(c_0_3189,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Ocomm__semiring__1(X5)
      | c_Groups_Otimes__class_Otimes(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2018])]) ).

fof(c_0_3190,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Omult__zero(X5)
      | c_Groups_Otimes__class_Otimes(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = c_Groups_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2019])]) ).

fof(c_0_3191,plain,
    ! [X23,X24] :
      ( ~ class_RealVector_Oreal__normed__algebra(X24)
      | c_Groups_Otimes__class_Otimes(X24,c_Groups_Ozero__class_Ozero(X24),X23) = c_Groups_Ozero__class_Ozero(X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2020])]) ).

fof(c_0_3192,plain,
    ! [X22,X23] :
      ( ~ class_RealVector_Oreal__normed__algebra(X23)
      | c_Groups_Otimes__class_Otimes(X23,c_Groups_Ozero__class_Ozero(X23),X22) = c_Groups_Ozero__class_Ozero(X23) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2021])]) ).

fof(c_0_3193,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Ocomm__semiring__1(X5)
      | c_Groups_Otimes__class_Otimes(X5,c_Groups_Ozero__class_Ozero(X5),X4) = c_Groups_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2022])]) ).

fof(c_0_3194,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Omult__zero(X5)
      | c_Groups_Otimes__class_Otimes(X5,c_Groups_Ozero__class_Ozero(X5),X4) = c_Groups_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2023])]) ).

fof(c_0_3195,plain,
    ! [X4,X5] :
      ( ~ class_Divides_Osemiring__div(X5)
      | X4 = c_Groups_Ozero__class_Ozero(X5)
      | c_Divides_Odiv__class_Odiv(X5,X4,X4) = c_Groups_Oone__class_Oone(X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2024])]) ).

fof(c_0_3196,plain,
    ! [X21] :
      ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X21)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2025])]) ).

fof(c_0_3197,plain,
    ! [X4,X5] :
      ( ~ class_Divides_Osemiring__div(X5)
      | c_Divides_Odiv__class_Odiv(X5,X4,c_Groups_Oone__class_Oone(X5)) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2026])]) ).

fof(c_0_3198,plain,
    ! [X4,X5] :
      ( ~ class_Divides_Osemiring__div(X5)
      | c_Divides_Odiv__class_Omod(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2027])]) ).

fof(c_0_3199,plain,
    ! [X4,X5] :
      ( ~ class_Power_Opower(X5)
      | c_Power_Opower__class_Opower(X5,X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2028])]) ).

fof(c_0_3200,plain,
    ! [X24,X25] :
      ( ~ class_Rings_Ocomm__semiring__1(X25)
      | c_Power_Opower__class_Opower(X25,X24,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X25) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2029])]) ).

fof(c_0_3201,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Ocomm__monoid__mult(X5)
      | c_Groups_Otimes__class_Otimes(X5,X4,c_Groups_Oone__class_Oone(X5)) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2030])]) ).

fof(c_0_3202,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Omonoid__mult(X5)
      | c_Groups_Otimes__class_Otimes(X5,X4,c_Groups_Oone__class_Oone(X5)) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2031])]) ).

fof(c_0_3203,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Ocomm__monoid__mult(X5)
      | c_Groups_Otimes__class_Otimes(X5,c_Groups_Oone__class_Oone(X5),X4) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2032])]) ).

fof(c_0_3204,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Omonoid__mult(X5)
      | c_Groups_Otimes__class_Otimes(X5,c_Groups_Oone__class_Oone(X5),X4) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2033])]) ).

fof(c_0_3205,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Ocomm__semiring__1(X5)
      | c_Groups_Otimes__class_Otimes(X5,X4,c_Groups_Oone__class_Oone(X5)) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2034])]) ).

fof(c_0_3206,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Ocomm__semiring__1(X5)
      | c_Groups_Otimes__class_Otimes(X5,c_Groups_Oone__class_Oone(X5),X4) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2035])]) ).

fof(c_0_3207,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Ogroup__add(X5)
      | c_Groups_Ominus__class_Ominus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2036])]) ).

fof(c_0_3208,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Ocomm__monoid__add(X5)
      | c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2037])]) ).

fof(c_0_3209,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Omonoid__add(X5)
      | c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2038])]) ).

fof(c_0_3210,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Ocomm__monoid__add(X5)
      | c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2039])]) ).

fof(c_0_3211,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Omonoid__add(X5)
      | c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2040])]) ).

fof(c_0_3212,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Ocomm__semiring__1(X5)
      | c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2041])]) ).

fof(c_0_3213,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Ocomm__semiring__1(X5)
      | c_Groups_Oplus__class_Oplus(X5,X4,c_Groups_Ozero__class_Ozero(X5)) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2042])]) ).

fof(c_0_3214,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Ocomm__semiring__1(X5)
      | c_Rings_Odvd__class_Odvd(X5,c_Groups_Oone__class_Oone(X5),X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2043])]) ).

fof(c_0_3215,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Ocomm__semiring__1(X5)
      | c_Rings_Odvd__class_Odvd(X5,X4,c_Groups_Ozero__class_Ozero(X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2044])]) ).

fof(c_0_3216,plain,
    ! [X20] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X20,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[c_0_2045]) ).

fof(c_0_3217,plain,
    ! [X4,X5] :
      ( ~ class_Divides_Osemiring__div(X5)
      | c_Divides_Odiv__class_Omod(X5,X4,X4) = c_Groups_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2046])]) ).

fof(c_0_3218,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Omonoid__mult(X5)
      | c_Power_Opower__class_Opower(X5,X4,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2047])]) ).

fof(c_0_3219,plain,
    ! [X24,X25] :
      ( ~ class_Rings_Ocomm__semiring__1(X25)
      | c_Power_Opower__class_Opower(X25,X24,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X24 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2048])]) ).

fof(c_0_3220,plain,
    ! [X4] :
      ( ~ class_Int_Onumber__ring(X4)
      | ~ c_Int_Oiszero(X4,c_Int_Onumber__class_Onumber__of(X4,c_Int_OMin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2049])]) ).

fof(c_0_3221,plain,
    ! [X4,X5] :
      ( ~ class_Groups_Ogroup__add(X5)
      | c_Groups_Ominus__class_Ominus(X5,X4,X4) = c_Groups_Ozero__class_Ozero(X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2050])]) ).

fof(c_0_3222,plain,
    ! [X8] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X8),
    inference(variable_rename,[status(thm)],[c_0_2051]) ).

fof(c_0_3223,plain,
    ! [X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X21),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X21,
    inference(variable_rename,[status(thm)],[c_0_2052]) ).

fof(c_0_3224,plain,
    ! [X21] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X21)),
    inference(variable_rename,[status(thm)],[c_0_2053]) ).

fof(c_0_3225,plain,
    ! [X4,X5] :
      ( ~ class_Rings_Ocomm__semiring__1(X5)
      | c_Rings_Odvd__class_Odvd(X5,X4,X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2054])]) ).

fof(c_0_3226,plain,
    ! [X16,X17,X18] :
      ( ( c_Int_Onumber__class_Onumber__of(X18,X17) != c_Int_Onumber__class_Onumber__of(X18,X16)
        | X17 = X16
        | ~ class_Int_Onumber__ring(X18)
        | ~ class_Int_Oring__char__0(X18) )
      & ( X17 != X16
        | c_Int_Onumber__class_Onumber__of(X18,X17) = c_Int_Onumber__class_Onumber__of(X18,X16)
        | ~ class_Int_Onumber__ring(X18)
        | ~ class_Int_Oring__char__0(X18) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2055])])]) ).

fof(c_0_3227,plain,
    ! [X21] : c_Nat_OSuc(X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X21),
    inference(variable_rename,[status(thm)],[c_0_2056]) ).

fof(c_0_3228,plain,
    ! [X21] : c_Nat_OSuc(X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[c_0_2057]) ).

fof(c_0_3229,plain,
    ! [X21] :
      ( X21 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2058])]) ).

fof(c_0_3230,plain,
    ! [X3] :
      ( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X3) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2059])]) ).

fof(c_0_3231,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    c_0_2060 ).

fof(c_0_3232,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    c_0_2061 ).

fof(c_0_3233,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    c_0_2062 ).

fof(c_0_3234,plain,
    ! [X21] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Nat_OSuc(X21)),
    inference(variable_rename,[status(thm)],[c_0_2063]) ).

fof(c_0_3235,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    c_0_2064 ).

fof(c_0_3236,plain,
    ! [X3,X4] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      & c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X4 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_2065])])]) ).

fof(c_0_3237,plain,
    ! [X22] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[c_0_2066]) ).

fof(c_0_3238,plain,
    ! [X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[c_0_2067]) ).

fof(c_0_3239,plain,
    ! [X21] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[c_0_2068]) ).

fof(c_0_3240,plain,
    ! [X20] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[c_0_2069]) ).

fof(c_0_3241,plain,
    ! [X21] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X21,
    inference(variable_rename,[status(thm)],[c_0_2070]) ).

fof(c_0_3242,plain,
    ! [X21] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X21) = X21,
    inference(variable_rename,[status(thm)],[c_0_2071]) ).

fof(c_0_3243,plain,
    ! [X11] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X11) = X11,
    inference(variable_rename,[status(thm)],[c_0_2072]) ).

fof(c_0_3244,plain,
    ! [X11] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X11) = X11,
    inference(variable_rename,[status(thm)],[c_0_2073]) ).

fof(c_0_3245,plain,
    ! [X11] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X11,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X11,
    inference(variable_rename,[status(thm)],[c_0_2074]) ).

fof(c_0_3246,plain,
    ! [X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X20,
    inference(variable_rename,[status(thm)],[c_0_2075]) ).

fof(c_0_3247,plain,
    ! [X8] : c_Int_OBit0(X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X8),
    inference(variable_rename,[status(thm)],[c_0_2076]) ).

fof(c_0_3248,plain,
    ! [X11] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X11,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X11,
    inference(variable_rename,[status(thm)],[c_0_2077]) ).

fof(c_0_3249,plain,
    ! [X11] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11) = X11,
    inference(variable_rename,[status(thm)],[c_0_2078]) ).

fof(c_0_3250,plain,
    ! [X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21) = X21,
    inference(variable_rename,[status(thm)],[c_0_2079]) ).

fof(c_0_3251,plain,
    ! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X20,
    inference(variable_rename,[status(thm)],[c_0_2080]) ).

fof(c_0_3252,plain,
    ! [X21,X22] :
      ( X22 != X21
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X22,X21) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2081])]) ).

fof(c_0_3253,plain,
    ! [X24,X25] :
      ( X25 != X24
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2082])]) ).

fof(c_0_3254,plain,
    ! [X24] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X24),
    inference(variable_rename,[status(thm)],[c_0_2083]) ).

fof(c_0_3255,plain,
    ! [X24] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[c_0_2084]) ).

fof(c_0_3256,plain,
    ! [X21] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21),
    inference(variable_rename,[status(thm)],[c_0_2085]) ).

fof(c_0_3257,plain,
    ! [X21] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X21),
    inference(variable_rename,[status(thm)],[c_0_2086]) ).

fof(c_0_3258,plain,
    ! [X3] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X3) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[c_0_2087]) ).

fof(c_0_3259,plain,
    ! [X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[c_0_2088]) ).

fof(c_0_3260,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    c_0_2089 ).

fof(c_0_3261,plain,
    ! [X21] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X21),
    inference(variable_rename,[status(thm)],[c_0_2090]) ).

fof(c_0_3262,plain,
    ! [X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X9),
    inference(variable_rename,[status(thm)],[c_0_2091]) ).

fof(c_0_3263,plain,
    ! [X9] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X9,X9),
    inference(variable_rename,[status(thm)],[c_0_2092]) ).

fof(c_0_3264,plain,
    ! [X24] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X24,X24),
    inference(variable_rename,[status(thm)],[c_0_2093]) ).

fof(c_0_3265,plain,
    ! [X8] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X8,c_Int_OPls) = X8,
    inference(variable_rename,[status(thm)],[c_0_2094]) ).

fof(c_0_3266,plain,
    ! [X8] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X8) = X8,
    inference(variable_rename,[status(thm)],[c_0_2095]) ).

fof(c_0_3267,plain,
    ! [X8] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Int_OPls) = X8,
    inference(variable_rename,[status(thm)],[c_0_2096]) ).

fof(c_0_3268,plain,
    ! [X9] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,X9) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[c_0_2097]) ).

fof(c_0_3269,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
    c_0_2098 ).

fof(c_0_3270,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    c_0_2099 ).

fof(c_0_3271,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
    c_0_2100 ).

fof(c_0_3272,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
    c_0_2101 ).

fof(c_0_3273,plain,
    ! [X16,X17] :
      ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X16))
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X16) )
      & ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
        | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X17)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2102])])])]) ).

fof(c_0_3274,plain,
    ! [X17,X18,X19] :
      ( ( c_Int_Onumber__class_Onumber__of(X19,X18) != X17
        | X17 = c_Int_Onumber__class_Onumber__of(X19,X18)
        | ~ class_Int_Onumber(X19) )
      & ( X17 != c_Int_Onumber__class_Onumber__of(X19,X18)
        | c_Int_Onumber__class_Onumber__of(X19,X18) = X17
        | ~ class_Int_Onumber(X19) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2103])])]) ).

fof(c_0_3275,plain,
    ! [X4] :
      ( ~ class_Int_Onumber__ring(X4)
      | c_Int_Oiszero(X4,c_Int_Onumber__class_Onumber__of(X4,c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2104])]) ).

fof(c_0_3276,axiom,
    c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    c_0_2105 ).

fof(c_0_3277,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    c_0_2106 ).

fof(c_0_3278,plain,
    ! [X4] :
      ( ~ class_Rings_Osemiring__1(X4)
      | ~ c_Int_Oiszero(X4,c_Groups_Oone__class_Oone(X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2107])]) ).

fof(c_0_3279,plain,
    ! [X47,X48] :
      ( ( ~ c_Int_Oiszero(X48,X47)
        | X47 = c_Groups_Ozero__class_Ozero(X48)
        | ~ class_Rings_Osemiring__1(X48) )
      & ( X47 != c_Groups_Ozero__class_Ozero(X48)
        | c_Int_Oiszero(X48,X47)
        | ~ class_Rings_Osemiring__1(X48) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2108])])]) ).

fof(c_0_3280,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),
    c_0_2109 ).

fof(c_0_3281,plain,
    ! [X4] :
      ( ~ class_Int_Onumber__ring(X4)
      | c_Int_Onumber__class_Onumber__of(X4,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2110])]) ).

fof(c_0_3282,plain,
    ! [X4] :
      ( ~ class_Int_Onumber__ring(X4)
      | c_Groups_Oone__class_Oone(X4) = c_Int_Onumber__class_Onumber__of(X4,c_Int_OBit1(c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2111])]) ).

fof(c_0_3283,plain,
    ! [X4] :
      ( ~ class_Rings_Osemiring__1(X4)
      | c_Int_Oiszero(X4,c_Groups_Ozero__class_Ozero(X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2112])]) ).

fof(c_0_3284,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    c_0_2113 ).

fof(c_0_3285,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    c_0_2114 ).

fof(c_0_3286,plain,
    ! [X4] :
      ( ~ class_Int_Onumber__ring(X4)
      | c_Groups_Ozero__class_Ozero(X4) = c_Int_Onumber__class_Onumber__of(X4,c_Int_OPls) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2115])]) ).

fof(c_0_3287,plain,
    ! [X4] :
      ( ~ class_Int_Onumber__ring(X4)
      | c_Int_Onumber__class_Onumber__of(X4,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2116])]) ).

fof(c_0_3288,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_2117 ).

fof(c_0_3289,plain,
    ! [X16,X17] :
      ( ( c_Groups_Oone__class_Oone(X17) != X16
        | X16 = c_Groups_Oone__class_Oone(X17)
        | ~ class_Groups_Oone(X17) )
      & ( X16 != c_Groups_Oone__class_Oone(X17)
        | c_Groups_Oone__class_Oone(X17) = X16
        | ~ class_Groups_Oone(X17) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2118])])]) ).

fof(c_0_3290,plain,
    ! [X16,X17] :
      ( ( c_Groups_Ozero__class_Ozero(X17) != X16
        | X16 = c_Groups_Ozero__class_Ozero(X17)
        | ~ class_Groups_Ozero(X17) )
      & ( X16 != c_Groups_Ozero__class_Ozero(X17)
        | c_Groups_Ozero__class_Ozero(X17) = X16
        | ~ class_Groups_Ozero(X17) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2119])])]) ).

fof(c_0_3291,plain,
    ! [X4] :
      ( ~ class_Rings_Ozero__neq__one(X4)
      | c_Groups_Oone__class_Oone(X4) != c_Groups_Ozero__class_Ozero(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2120])]) ).

fof(c_0_3292,plain,
    ! [X4] :
      ( ~ class_Rings_Ozero__neq__one(X4)
      | c_Groups_Ozero__class_Ozero(X4) != c_Groups_Oone__class_Oone(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2121])]) ).

fof(c_0_3293,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
    c_0_2122 ).

fof(c_0_3294,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    c_0_2123 ).

fof(c_0_3295,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
    c_0_2124 ).

fof(c_0_3296,axiom,
    c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    c_0_2125 ).

fof(c_0_3297,axiom,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_2126 ).

fof(c_0_3298,plain,
    ! [X24,X25] :
      ( c_Nat_OSuc(X25) != c_Nat_OSuc(X24)
      | X25 = X24 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2127])]) ).

fof(c_0_3299,plain,
    ! [X38,X39,X40,X41] :
      ( ( c_Nat_OSuc(X39) != c_Nat_OSuc(X38)
        | X39 = X38 )
      & ( X41 != X40
        | c_Nat_OSuc(X41) = c_Nat_OSuc(X40) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2128])])])]) ).

fof(c_0_3300,plain,
    ! [X6,X7,X8,X9] :
      ( ( c_Int_OBit0(X7) != c_Int_OBit0(X6)
        | X7 = X6 )
      & ( X9 != X8
        | c_Int_OBit0(X9) = c_Int_OBit0(X8) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2129])])])]) ).

fof(c_0_3301,plain,
    ! [X6,X7,X8,X9] :
      ( ( c_Int_OBit1(X7) != c_Int_OBit1(X6)
        | X7 = X6 )
      & ( X9 != X8
        | c_Int_OBit1(X9) = c_Int_OBit1(X8) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2130])])])]) ).

fof(c_0_3302,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
    c_0_2131 ).

fof(c_0_3303,plain,
    ! [X8] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8) = X8,
    inference(variable_rename,[status(thm)],[c_0_2132]) ).

fof(c_0_3304,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
    c_0_2133 ).

fof(c_0_3305,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_2134 ).

fof(c_0_3306,plain,
    ! [X8,X9] : c_Int_OBit1(X9) != c_Int_OBit0(X8),
    inference(variable_rename,[status(thm)],[c_0_2135]) ).

fof(c_0_3307,plain,
    ! [X8,X9] : c_Int_OBit0(X9) != c_Int_OBit1(X8),
    inference(variable_rename,[status(thm)],[c_0_2136]) ).

fof(c_0_3308,axiom,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    c_0_2137 ).

fof(c_0_3309,plain,
    ! [X20] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X20),
    inference(variable_rename,[status(thm)],[c_0_2138]) ).

fof(c_0_3310,plain,
    ! [X49] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X49),
    inference(variable_rename,[status(thm)],[c_0_2139]) ).

fof(c_0_3311,plain,
    ! [X20] : c_Nat_OSuc(X20) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[c_0_2140]) ).

fof(c_0_3312,plain,
    ! [X48] : c_Nat_OSuc(X48) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[c_0_2141]) ).

fof(c_0_3313,plain,
    ! [X20] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X20),
    inference(variable_rename,[status(thm)],[c_0_2142]) ).

fof(c_0_3314,plain,
    ! [X20] : c_Nat_OSuc(X20) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[c_0_2143]) ).

fof(c_0_3315,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_2144 ).

fof(c_0_3316,plain,
    ! [X6,X7] :
      ( ( c_Int_OBit1(X6) != c_Int_OMin
        | X6 = c_Int_OMin )
      & ( X7 != c_Int_OMin
        | c_Int_OBit1(X7) = c_Int_OMin ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2145])])])]) ).

fof(c_0_3317,plain,
    ! [X5,X6] :
      ( ( c_Int_OMin != c_Int_OBit1(X5)
        | c_Int_OMin = X5 )
      & ( c_Int_OMin != X6
        | c_Int_OMin = c_Int_OBit1(X6) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2146])])])]) ).

fof(c_0_3318,plain,
    ! [X6,X7] :
      ( ( c_Int_OBit0(X6) != c_Int_OPls
        | X6 = c_Int_OPls )
      & ( X7 != c_Int_OPls
        | c_Int_OBit0(X7) = c_Int_OPls ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2147])])])]) ).

fof(c_0_3319,plain,
    ! [X5,X6] :
      ( ( c_Int_OPls != c_Int_OBit0(X5)
        | c_Int_OPls = X5 )
      & ( c_Int_OPls != X6
        | c_Int_OPls = c_Int_OBit0(X6) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2148])])])]) ).

fof(c_0_3320,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    c_0_2149 ).

fof(c_0_3321,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    c_0_2150 ).

fof(c_0_3322,plain,
    ! [X21] : c_Nat_OSuc(X21) != X21,
    inference(variable_rename,[status(thm)],[c_0_2151]) ).

fof(c_0_3323,plain,
    ! [X21] : X21 != c_Nat_OSuc(X21),
    inference(variable_rename,[status(thm)],[c_0_2152]) ).

fof(c_0_3324,plain,
    ! [X8] : c_Int_OBit0(X8) != c_Int_OMin,
    inference(variable_rename,[status(thm)],[c_0_2153]) ).

fof(c_0_3325,plain,
    ! [X7] : c_Int_OMin != c_Int_OBit0(X7),
    inference(variable_rename,[status(thm)],[c_0_2154]) ).

fof(c_0_3326,plain,
    ! [X8] : c_Int_OBit1(X8) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[c_0_2155]) ).

fof(c_0_3327,plain,
    ! [X7] : c_Int_OPls != c_Int_OBit1(X7),
    inference(variable_rename,[status(thm)],[c_0_2156]) ).

fof(c_0_3328,axiom,
    v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_2157 ).

fof(c_0_3329,axiom,
    v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_2158 ).

fof(c_0_3330,axiom,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    c_0_2159 ).

fof(c_0_3331,axiom,
    class_Groups_Oone(tc_Complex_Ocomplex),
    c_0_2160 ).

fof(c_0_3332,axiom,
    class_Int_Onumber(tc_Complex_Ocomplex),
    c_0_2161 ).

fof(c_0_3333,axiom,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    c_0_2162 ).

fof(c_0_3334,axiom,
    class_Rings_Oring(tc_Complex_Ocomplex),
    c_0_2163 ).

fof(c_0_3335,axiom,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    c_0_2164 ).

fof(c_0_3336,axiom,
    class_Power_Opower(tc_Complex_Ocomplex),
    c_0_2165 ).

fof(c_0_3337,axiom,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    c_0_2166 ).

fof(c_0_3338,axiom,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    c_0_2167 ).

fof(c_0_3339,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    c_0_2168 ).

fof(c_0_3340,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    c_0_2169 ).

fof(c_0_3341,axiom,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    c_0_2170 ).

fof(c_0_3342,axiom,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    c_0_2171 ).

fof(c_0_3343,axiom,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    c_0_2172 ).

fof(c_0_3344,axiom,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    c_0_2173 ).

fof(c_0_3345,axiom,
    class_Rings_Osemiring__1(tc_Complex_Ocomplex),
    c_0_2174 ).

fof(c_0_3346,axiom,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    c_0_2175 ).

fof(c_0_3347,axiom,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    c_0_2176 ).

fof(c_0_3348,axiom,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    c_0_2177 ).

fof(c_0_3349,axiom,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    c_0_2178 ).

fof(c_0_3350,axiom,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    c_0_2179 ).

fof(c_0_3351,axiom,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    c_0_2180 ).

fof(c_0_3352,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    c_0_2181 ).

fof(c_0_3353,axiom,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    c_0_2182 ).

fof(c_0_3354,axiom,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    c_0_2183 ).

fof(c_0_3355,axiom,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    c_0_2184 ).

fof(c_0_3356,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    c_0_2185 ).

fof(c_0_3357,axiom,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    c_0_2186 ).

fof(c_0_3358,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    c_0_2187 ).

fof(c_0_3359,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    c_0_2188 ).

fof(c_0_3360,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    c_0_2189 ).

fof(c_0_3361,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    c_0_2190 ).

fof(c_0_3362,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    c_0_2191 ).

fof(c_0_3363,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    c_0_2192 ).

fof(c_0_3364,axiom,
    class_Rings_Odvd(tc_RealDef_Oreal),
    c_0_2193 ).

fof(c_0_3365,axiom,
    class_Groups_Oone(tc_RealDef_Oreal),
    c_0_2194 ).

fof(c_0_3366,axiom,
    class_Int_Onumber(tc_RealDef_Oreal),
    c_0_2195 ).

fof(c_0_3367,axiom,
    class_Rings_Oidom(tc_RealDef_Oreal),
    c_0_2196 ).

fof(c_0_3368,axiom,
    class_Rings_Oring(tc_RealDef_Oreal),
    c_0_2197 ).

fof(c_0_3369,axiom,
    class_Groups_Ozero(tc_RealDef_Oreal),
    c_0_2198 ).

fof(c_0_3370,axiom,
    class_Power_Opower(tc_RealDef_Oreal),
    c_0_2199 ).

fof(c_0_3371,axiom,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    c_0_2200 ).

fof(c_0_3372,axiom,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    c_0_2201 ).

fof(c_0_3373,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    c_0_2202 ).

fof(c_0_3374,axiom,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    c_0_2203 ).

fof(c_0_3375,axiom,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    c_0_2204 ).

fof(c_0_3376,axiom,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    c_0_2205 ).

fof(c_0_3377,axiom,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    c_0_2206 ).

fof(c_0_3378,axiom,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    c_0_2207 ).

fof(c_0_3379,axiom,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    c_0_2208 ).

fof(c_0_3380,axiom,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    c_0_2209 ).

fof(c_0_3381,axiom,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    c_0_2210 ).

fof(c_0_3382,axiom,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    c_0_2211 ).

fof(c_0_3383,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    c_0_2212 ).

fof(c_0_3384,axiom,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    c_0_2213 ).

fof(c_0_3385,axiom,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    c_0_2214 ).

fof(c_0_3386,axiom,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    c_0_2215 ).

fof(c_0_3387,axiom,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    c_0_2216 ).

fof(c_0_3388,axiom,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    c_0_2217 ).

fof(c_0_3389,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    c_0_2218 ).

fof(c_0_3390,axiom,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    c_0_2219 ).

fof(c_0_3391,axiom,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    c_0_2220 ).

fof(c_0_3392,axiom,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    c_0_2221 ).

fof(c_0_3393,axiom,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    c_0_2222 ).

fof(c_0_3394,axiom,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    c_0_2223 ).

fof(c_0_3395,axiom,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    c_0_2224 ).

fof(c_0_3396,axiom,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    c_0_2225 ).

fof(c_0_3397,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    c_0_2226 ).

fof(c_0_3398,axiom,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    c_0_2227 ).

fof(c_0_3399,axiom,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    c_0_2228 ).

fof(c_0_3400,axiom,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    c_0_2229 ).

fof(c_0_3401,axiom,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    c_0_2230 ).

fof(c_0_3402,axiom,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    c_0_2231 ).

fof(c_0_3403,axiom,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    c_0_2232 ).

fof(c_0_3404,axiom,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    c_0_2233 ).

fof(c_0_3405,axiom,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    c_0_2234 ).

fof(c_0_3406,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    c_0_2235 ).

fof(c_0_3407,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    c_0_2236 ).

fof(c_0_3408,axiom,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    c_0_2237 ).

fof(c_0_3409,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    c_0_2238 ).

fof(c_0_3410,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    c_0_2239 ).

fof(c_0_3411,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    c_0_2240 ).

fof(c_0_3412,axiom,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    c_0_2241 ).

fof(c_0_3413,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    c_0_2242 ).

fof(c_0_3414,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    c_0_2243 ).

fof(c_0_3415,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    c_0_2244 ).

fof(c_0_3416,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    c_0_2245 ).

fof(c_0_3417,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    c_0_2246 ).

fof(c_0_3418,axiom,
    class_Rings_Odvd(tc_Nat_Onat),
    c_0_2247 ).

fof(c_0_3419,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    c_0_2248 ).

fof(c_0_3420,axiom,
    class_Int_Onumber(tc_Nat_Onat),
    c_0_2249 ).

fof(c_0_3421,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    c_0_2250 ).

fof(c_0_3422,axiom,
    class_Power_Opower(tc_Nat_Onat),
    c_0_2251 ).

fof(c_0_3423,axiom,
    class_Rings_Osemiring(tc_Nat_Onat),
    c_0_2252 ).

fof(c_0_3424,axiom,
    class_Rings_Omult__zero(tc_Nat_Onat),
    c_0_2253 ).

fof(c_0_3425,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    c_0_2254 ).

fof(c_0_3426,axiom,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    c_0_2255 ).

fof(c_0_3427,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    c_0_2256 ).

fof(c_0_3428,axiom,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    c_0_2257 ).

fof(c_0_3429,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    c_0_2258 ).

fof(c_0_3430,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    c_0_2259 ).

fof(c_0_3431,axiom,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    c_0_2260 ).

fof(c_0_3432,axiom,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    c_0_2261 ).

fof(c_0_3433,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    c_0_2262 ).

fof(c_0_3434,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    c_0_2263 ).

fof(c_0_3435,axiom,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    c_0_2264 ).

fof(c_0_3436,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    c_0_2265 ).

fof(c_0_3437,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    c_0_2266 ).

fof(c_0_3438,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    c_0_2267 ).

fof(c_0_3439,axiom,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    c_0_2268 ).

fof(c_0_3440,axiom,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    c_0_2269 ).

fof(c_0_3441,axiom,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    c_0_2270 ).

fof(c_0_3442,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    c_0_2271 ).

fof(c_0_3443,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    c_0_2272 ).

fof(c_0_3444,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    c_0_2273 ).

fof(c_0_3445,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    c_0_2274 ).

fof(c_0_3446,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    c_0_2275 ).

fof(c_0_3447,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    c_0_2276 ).

fof(c_0_3448,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    c_0_2277 ).

fof(c_0_3449,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    c_0_2278 ).

fof(c_0_3450,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    c_0_2279 ).

fof(c_0_3451,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    c_0_2280 ).

fof(c_0_3452,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    c_0_2281 ).

fof(c_0_3453,axiom,
    class_Rings_Odvd(tc_Int_Oint),
    c_0_2282 ).

fof(c_0_3454,axiom,
    class_Groups_Oone(tc_Int_Oint),
    c_0_2283 ).

fof(c_0_3455,axiom,
    class_Int_Onumber(tc_Int_Oint),
    c_0_2284 ).

fof(c_0_3456,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    c_0_2285 ).

fof(c_0_3457,axiom,
    class_Rings_Oring(tc_Int_Oint),
    c_0_2286 ).

fof(c_0_3458,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    c_0_2287 ).

fof(c_0_3459,axiom,
    class_Power_Opower(tc_Int_Oint),
    c_0_2288 ).

fof(c_0_3460,axiom,
    class_Rings_Oring__1(tc_Int_Oint),
    c_0_2289 ).

fof(c_0_3461,axiom,
    class_Rings_Osemiring(tc_Int_Oint),
    c_0_2290 ).

fof(c_0_3462,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    c_0_2291 ).

fof(c_0_3463,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    c_0_2292 ).

fof(c_0_3464,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    c_0_2293 ).

fof(c_0_3465,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    c_0_2294 ).

fof(c_0_3466,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    c_0_2295 ).

fof(c_0_3467,axiom,
    class_Groups_Ogroup__add(tc_Int_Oint),
    c_0_2296 ).

fof(c_0_3468,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    c_0_2297 ).

fof(c_0_3469,axiom,
    class_Rings_Osemiring__1(tc_Int_Oint),
    c_0_2298 ).

fof(c_0_3470,axiom,
    class_Groups_Omonoid__add(tc_Int_Oint),
    c_0_2299 ).

fof(c_0_3471,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    c_0_2300 ).

fof(c_0_3472,axiom,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    c_0_2301 ).

fof(c_0_3473,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    c_0_2302 ).

fof(c_0_3474,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    c_0_2303 ).

fof(c_0_3475,axiom,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    c_0_2304 ).

fof(c_0_3476,axiom,
    class_Groups_Oab__group__add(tc_Int_Oint),
    c_0_2305 ).

fof(c_0_3477,axiom,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    c_0_2306 ).

fof(c_0_3478,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    c_0_2307 ).

fof(c_0_3479,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    c_0_2308 ).

fof(c_0_3480,axiom,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    c_0_2309 ).

fof(c_0_3481,axiom,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    c_0_2310 ).

fof(c_0_3482,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    c_0_2311 ).

fof(c_0_3483,axiom,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    c_0_2312 ).

fof(c_0_3484,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    c_0_2313 ).

fof(c_0_3485,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    c_0_2314 ).

fof(c_0_3486,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    c_0_2315 ).

fof(c_0_3487,axiom,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    c_0_2316 ).

fof(c_0_3488,axiom,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    c_0_2317 ).

fof(c_0_3489,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    c_0_2318 ).

fof(c_0_3490,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    c_0_2319 ).

fof(c_0_3491,axiom,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    c_0_2320 ).

fof(c_0_3492,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    c_0_2321 ).

fof(c_0_3493,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    c_0_2322 ).

fof(c_0_3494,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    c_0_2323 ).

fof(c_0_3495,axiom,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    c_0_2324 ).

fof(c_0_3496,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    c_0_2325 ).

fof(c_0_3497,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    c_0_2326 ).

fof(c_0_3498,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    c_0_2327 ).

fof(c_0_3499,axiom,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    c_0_2328 ).

fof(c_0_3500,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    c_0_2329 ).

fof(c_0_3501,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    c_0_2330 ).

fof(c_0_3502,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    c_0_2331 ).

fof(c_0_3503,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    c_0_2332 ).

fof(c_0_3504,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    c_0_2333 ).

fof(c_0_3505,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    c_0_2334 ).

fof(c_0_3506,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    c_0_2335 ).

fof(c_0_3507,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    c_0_2336 ).

fof(c_0_3508,axiom,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    c_0_2337 ).

fof(c_0_3509,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_2338 ).

fof(c_0_3510,axiom,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    c_0_2339 ).

fof(c_0_3511,axiom,
    c_Int_OPls != c_Int_OMin,
    c_0_2340 ).

fof(c_0_3512,axiom,
    c_Int_OMin != c_Int_OPls,
    c_0_2341 ).

cnf(c_0_3513,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(X1,X3,X5)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X5)),c_Groups_Otimes__class_Otimes(X1,X4,c_Groups_Ominus__class_Ominus(X1,X3,X5)))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2342]) ).

cnf(c_0_3514,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2343]) ).

cnf(c_0_3515,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2344]) ).

cnf(c_0_3516,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2345]) ).

cnf(c_0_3517,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2346]) ).

cnf(c_0_3518,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_2347]) ).

cnf(c_0_3519,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4),X6) ),
    inference(split_conjunct,[status(thm)],[c_0_2348]) ).

cnf(c_0_3520,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4),X6) ),
    inference(split_conjunct,[status(thm)],[c_0_2349]) ).

cnf(c_0_3521,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_2350]) ).

cnf(c_0_3522,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2343]) ).

cnf(c_0_3523,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2344]) ).

cnf(c_0_3524,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2345]) ).

cnf(c_0_3525,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2346]) ).

cnf(c_0_3526,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_2347]) ).

cnf(c_0_3527,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5),X6)
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_2348]) ).

cnf(c_0_3528,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5),X6)
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_2349]) ).

cnf(c_0_3529,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_2350]) ).

cnf(c_0_3530,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)),
    inference(split_conjunct,[status(thm)],[c_0_2351]) ).

cnf(c_0_3531,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2352]) ).

cnf(c_0_3532,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2353]) ).

cnf(c_0_3533,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2354]) ).

cnf(c_0_3534,plain,
    c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),X2)),
    inference(split_conjunct,[status(thm)],[c_0_2355]) ).

cnf(c_0_3535,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2356]) ).

cnf(c_0_3536,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(split_conjunct,[status(thm)],[c_0_2357]) ).

cnf(c_0_3537,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2358]) ).

cnf(c_0_3538,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2358]) ).

cnf(c_0_3539,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1),X2),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2359]) ).

cnf(c_0_3540,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4),X2),X3),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2360]) ).

cnf(c_0_3541,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2361]) ).

cnf(c_0_3542,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2362]) ).

cnf(c_0_3543,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2363]) ).

cnf(c_0_3544,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6) ),
    inference(split_conjunct,[status(thm)],[c_0_2364]) ).

cnf(c_0_3545,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2365]) ).

cnf(c_0_3546,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X2)),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2366]) ).

cnf(c_0_3547,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2))) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2367]) ).

cnf(c_0_3548,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2368]) ).

cnf(c_0_3549,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2369]) ).

cnf(c_0_3550,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2370]) ).

cnf(c_0_3551,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_2362]) ).

cnf(c_0_3552,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_2363]) ).

cnf(c_0_3553,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)),X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2371]) ).

cnf(c_0_3554,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2372]) ).

cnf(c_0_3555,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2)),X5))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_2366]) ).

cnf(c_0_3556,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2373]) ).

cnf(c_0_3557,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X3)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2374]) ).

cnf(c_0_3558,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2375]) ).

cnf(c_0_3559,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2376]) ).

cnf(c_0_3560,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2377]) ).

cnf(c_0_3561,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2378]) ).

cnf(c_0_3562,plain,
    ( epred1_3(X1,X2,X3)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk18_3(X3,X2,X1)),esk19_3(X3,X2,X1))
    | X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk20_3(X3,X2,X1)),esk21_3(X3,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3563,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2380]) ).

cnf(c_0_3564,plain,
    ( hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,esk8_3(X3,X2,X1))))
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(X2,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2381]) ).

cnf(c_0_3565,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2358]) ).

cnf(c_0_3566,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2357]) ).

cnf(c_0_3567,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2357]) ).

cnf(c_0_3568,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2382]) ).

cnf(c_0_3569,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X4 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2383]) ).

cnf(c_0_3570,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4) != X5 ),
    inference(split_conjunct,[status(thm)],[c_0_2384]) ).

cnf(c_0_3571,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X5)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X5))
    | ~ class_Rings_Oring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2385]) ).

cnf(c_0_3572,plain,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X3),c_Groups_Otimes__class_Otimes(X1,X2,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_2386]) ).

cnf(c_0_3573,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2387]) ).

cnf(c_0_3574,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2387]) ).

cnf(c_0_3575,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2388]) ).

cnf(c_0_3576,plain,
    ( X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2383]) ).

cnf(c_0_3577,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4) = X5
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2384]) ).

cnf(c_0_3578,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2389]) ).

cnf(c_0_3579,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)
    | ~ class_Rings_Oring(X1)
    | X4 != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6) ),
    inference(split_conjunct,[status(thm)],[c_0_2390]) ).

cnf(c_0_3580,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)
    | ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4) != X6 ),
    inference(split_conjunct,[status(thm)],[c_0_2391]) ).

cnf(c_0_3581,plain,
    ( epred1_3(X1,X2,X3)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk18_3(X3,X2,X1)),esk19_3(X3,X2,X1))
    | ~ hBOOL(hAPP(X1,esk21_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3582,plain,
    ( epred1_3(X1,X2,X3)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk20_3(X3,X2,X1)),esk21_3(X3,X2,X1))
    | ~ hBOOL(hAPP(X1,esk19_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3583,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2392]) ).

cnf(c_0_3584,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)),c_Groups_Ozero__class_Ozero(X2))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2393]) ).

cnf(c_0_3585,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2367]) ).

cnf(c_0_3586,plain,
    ( X2 = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6)
    | ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6) ),
    inference(split_conjunct,[status(thm)],[c_0_2390]) ).

cnf(c_0_3587,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5) = X6
    | ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6) ),
    inference(split_conjunct,[status(thm)],[c_0_2391]) ).

cnf(c_0_3588,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2394]) ).

cnf(c_0_3589,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2395]) ).

cnf(c_0_3590,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3),X5)
    | ~ class_Rings_Osemiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2396]) ).

cnf(c_0_3591,plain,
    ( X2 = X3
    | X4 = X5
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X5,X3)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X5,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2397]) ).

cnf(c_0_3592,plain,
    ( X3 = X5
    | X2 = X4
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2398]) ).

cnf(c_0_3593,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2),X4),
    inference(split_conjunct,[status(thm)],[c_0_2399]) ).

cnf(c_0_3594,plain,
    ( epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,esk19_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(X1,esk21_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3595,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2400]) ).

cnf(c_0_3596,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2401]) ).

cnf(c_0_3597,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,esk7_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_2381]) ).

cnf(c_0_3598,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2402]) ).

cnf(c_0_3599,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2403]) ).

cnf(c_0_3600,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2404]) ).

cnf(c_0_3601,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X3),X2),
    inference(split_conjunct,[status(thm)],[c_0_2405]) ).

cnf(c_0_3602,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2406]) ).

cnf(c_0_3603,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2406]) ).

cnf(c_0_3604,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[c_0_2407]) ).

cnf(c_0_3605,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[c_0_2407]) ).

cnf(c_0_3606,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X3,X2,X1))
    | X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk20_3(X3,X2,X1)),esk21_3(X3,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3607,plain,
    ( epred1_3(X1,X2,X3)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk18_3(X3,X2,X1)),esk19_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3608,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X3,X2,X1),X3)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk20_3(X3,X2,X1)),esk21_3(X3,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3609,plain,
    ( epred1_3(X1,X2,X3)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk18_3(X3,X2,X1)),esk19_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,esk21_3(X3,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3610,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2408]) ).

cnf(c_0_3611,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,esk15_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2409]) ).

cnf(c_0_3612,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,esk14_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2410]) ).

cnf(c_0_3613,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(X1,esk15_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2409]) ).

cnf(c_0_3614,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(X1,esk14_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2410]) ).

cnf(c_0_3615,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X5,X6),X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2411]) ).

cnf(c_0_3616,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X5,X6),X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2412]) ).

cnf(c_0_3617,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X5,X6),X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2413]) ).

cnf(c_0_3618,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(X1,X3,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2414]) ).

cnf(c_0_3619,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2415]) ).

cnf(c_0_3620,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2416]) ).

cnf(c_0_3621,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X5)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2417]) ).

cnf(c_0_3622,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,X4,c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2418]) ).

cnf(c_0_3623,plain,
    ( hBOOL(hAPP(X2,esk7_3(X3,X2,X1)))
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_2381]) ).

cnf(c_0_3624,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2419]) ).

cnf(c_0_3625,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2420]) ).

cnf(c_0_3626,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2421]) ).

cnf(c_0_3627,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2422]) ).

cnf(c_0_3628,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2423]) ).

cnf(c_0_3629,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2424]) ).

cnf(c_0_3630,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(split_conjunct,[status(thm)],[c_0_2425]) ).

cnf(c_0_3631,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2426]) ).

cnf(c_0_3632,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2427]) ).

cnf(c_0_3633,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2428]) ).

cnf(c_0_3634,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_2429]) ).

cnf(c_0_3635,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ epred1_3(X1,X2,X3)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3636,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ epred1_3(X1,X2,X3)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3637,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2387]) ).

cnf(c_0_3638,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X4)),c_Power_Opower__class_Opower(X1,X3,c_Nat_OSuc(X4)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2430]) ).

cnf(c_0_3639,plain,
    ( c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X2,X4),c_Divides_Odiv__class_Odiv(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2431]) ).

cnf(c_0_3640,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2386]) ).

cnf(c_0_3641,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2386]) ).

cnf(c_0_3642,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2432]) ).

cnf(c_0_3643,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X3,X2,X1))
    | ~ hBOOL(hAPP(X1,esk21_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3644,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ hBOOL(hAPP(X1,esk19_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3645,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X3,X2,X1),X3)
    | ~ hBOOL(hAPP(X1,esk21_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3646,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,esk21_3(X3,X2,X1))
    | ~ hBOOL(hAPP(X1,esk19_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3647,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk20_3(X3,X2,X1)),esk21_3(X3,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3648,plain,
    ( epred1_3(X1,X2,X3)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk18_3(X3,X2,X1)),esk19_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3649,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2433]) ).

cnf(c_0_3650,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2434]) ).

cnf(c_0_3651,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2435]) ).

cnf(c_0_3652,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2436]) ).

cnf(c_0_3653,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2437]) ).

cnf(c_0_3654,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2438]) ).

cnf(c_0_3655,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2439]) ).

cnf(c_0_3656,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2440]) ).

cnf(c_0_3657,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2441]) ).

cnf(c_0_3658,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2442]) ).

cnf(c_0_3659,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2443]) ).

cnf(c_0_3660,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2444]) ).

cnf(c_0_3661,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2445]) ).

cnf(c_0_3662,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
    | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2446]) ).

cnf(c_0_3663,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2447]) ).

cnf(c_0_3664,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
    | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2448]) ).

cnf(c_0_3665,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4)))
    | ~ class_Rings_Oring(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2449]) ).

cnf(c_0_3666,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4))
    | ~ class_Rings_Oring(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2450]) ).

cnf(c_0_3667,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4)))
    | ~ class_Rings_Osemiring(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2451]) ).

cnf(c_0_3668,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4))
    | ~ class_Rings_Osemiring(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2452]) ).

cnf(c_0_3669,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2453]) ).

cnf(c_0_3670,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2416]) ).

cnf(c_0_3671,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_2454]) ).

cnf(c_0_3672,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2455]) ).

cnf(c_0_3673,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2456]) ).

cnf(c_0_3674,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2457]) ).

cnf(c_0_3675,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2458]) ).

cnf(c_0_3676,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2459]) ).

cnf(c_0_3677,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2460]) ).

cnf(c_0_3678,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2461]) ).

cnf(c_0_3679,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2462]) ).

cnf(c_0_3680,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2463]) ).

cnf(c_0_3681,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2464]) ).

cnf(c_0_3682,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2465]) ).

cnf(c_0_3683,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2466]) ).

cnf(c_0_3684,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2467]) ).

cnf(c_0_3685,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2468]) ).

cnf(c_0_3686,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2469]) ).

cnf(c_0_3687,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 != X4 ),
    inference(split_conjunct,[status(thm)],[c_0_2397]) ).

cnf(c_0_3688,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != X5 ),
    inference(split_conjunct,[status(thm)],[c_0_2397]) ).

cnf(c_0_3689,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 != X4 ),
    inference(split_conjunct,[status(thm)],[c_0_2398]) ).

cnf(c_0_3690,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != X5 ),
    inference(split_conjunct,[status(thm)],[c_0_2398]) ).

cnf(c_0_3691,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2470]) ).

cnf(c_0_3692,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2468]) ).

cnf(c_0_3693,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2468]) ).

cnf(c_0_3694,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2469]) ).

cnf(c_0_3695,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2469]) ).

cnf(c_0_3696,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2471]) ).

cnf(c_0_3697,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2472]) ).

cnf(c_0_3698,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2473]) ).

cnf(c_0_3699,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2474]) ).

cnf(c_0_3700,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2475]) ).

cnf(c_0_3701,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2476]) ).

cnf(c_0_3702,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2477]) ).

cnf(c_0_3703,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2478]) ).

cnf(c_0_3704,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2479]) ).

cnf(c_0_3705,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2480]) ).

cnf(c_0_3706,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2481]) ).

cnf(c_0_3707,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2468]) ).

cnf(c_0_3708,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2469]) ).

cnf(c_0_3709,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2416]) ).

cnf(c_0_3710,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2482]) ).

cnf(c_0_3711,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2483]) ).

cnf(c_0_3712,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2484]) ).

cnf(c_0_3713,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2) = c_Power_Opower__class_Opower(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2485]) ).

cnf(c_0_3714,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2486]) ).

cnf(c_0_3715,plain,
    ( X4 = X6
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) != c_Groups_Oplus__class_Oplus(X1,X5,c_Groups_Otimes__class_Otimes(X1,X3,X6))
    | X2 != X5
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2487]) ).

cnf(c_0_3716,plain,
    ( c_Power_Opower__class_Opower(X1,c_Divides_Odiv__class_Odiv(X1,X2,X3),X4) = c_Divides_Odiv__class_Odiv(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2488]) ).

cnf(c_0_3717,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2489]) ).

cnf(c_0_3718,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2490]) ).

cnf(c_0_3719,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | c_Power_Opower__class_Opower(X3,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2491]) ).

cnf(c_0_3720,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3),
    inference(split_conjunct,[status(thm)],[c_0_2492]) ).

cnf(c_0_3721,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_2493]) ).

cnf(c_0_3722,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_2494]) ).

cnf(c_0_3723,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3),X2),
    inference(split_conjunct,[status(thm)],[c_0_2495]) ).

cnf(c_0_3724,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3),X2),
    inference(split_conjunct,[status(thm)],[c_0_2496]) ).

cnf(c_0_3725,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2497]) ).

cnf(c_0_3726,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2498]) ).

cnf(c_0_3727,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2426]) ).

cnf(c_0_3728,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2427]) ).

cnf(c_0_3729,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X5),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2499]) ).

cnf(c_0_3730,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2500]) ).

cnf(c_0_3731,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2501]) ).

cnf(c_0_3732,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2))) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2502]) ).

cnf(c_0_3733,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ hBOOL(hAPP(X1,esk21_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3734,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ hBOOL(hAPP(X1,esk19_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3735,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2409]) ).

cnf(c_0_3736,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2410]) ).

cnf(c_0_3737,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2409]) ).

cnf(c_0_3738,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2410]) ).

cnf(c_0_3739,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | X4 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2503]) ).

cnf(c_0_3740,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | X4 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2504]) ).

cnf(c_0_3741,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2505]) ).

cnf(c_0_3742,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2505]) ).

cnf(c_0_3743,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2406]) ).

cnf(c_0_3744,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2506]) ).

cnf(c_0_3745,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2507]) ).

cnf(c_0_3746,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2508]) ).

cnf(c_0_3747,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2509]) ).

cnf(c_0_3748,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2510]) ).

cnf(c_0_3749,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2511]) ).

cnf(c_0_3750,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2512]) ).

cnf(c_0_3751,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2513]) ).

cnf(c_0_3752,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_2514]) ).

cnf(c_0_3753,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2515]) ).

cnf(c_0_3754,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2516]) ).

cnf(c_0_3755,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2517]) ).

cnf(c_0_3756,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2518]) ).

cnf(c_0_3757,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)) = c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2519]) ).

cnf(c_0_3758,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2415]) ).

cnf(c_0_3759,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2520]) ).

cnf(c_0_3760,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2521]) ).

cnf(c_0_3761,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2522]) ).

cnf(c_0_3762,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X3),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2523]) ).

cnf(c_0_3763,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3),c_Power_Opower__class_Opower(tc_Int_Oint,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2524]) ).

cnf(c_0_3764,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X1),c_Power_Opower__class_Opower(tc_Int_Oint,X3,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2525]) ).

cnf(c_0_3765,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Oone__class_Oone(X1)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Oring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2526]) ).

cnf(c_0_3766,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2527]) ).

cnf(c_0_3767,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2528]) ).

cnf(c_0_3768,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2529]) ).

cnf(c_0_3769,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2530]) ).

cnf(c_0_3770,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2531]) ).

cnf(c_0_3771,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[c_0_2407]) ).

cnf(c_0_3772,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2532]) ).

cnf(c_0_3773,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2530]) ).

cnf(c_0_3774,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2531]) ).

cnf(c_0_3775,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2533]) ).

cnf(c_0_3776,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Rings_Olinordered__semidom(X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2534]) ).

cnf(c_0_3777,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2435]) ).

cnf(c_0_3778,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2436]) ).

cnf(c_0_3779,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2535]) ).

cnf(c_0_3780,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2536]) ).

cnf(c_0_3781,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2537]) ).

cnf(c_0_3782,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Oordered__comm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2538]) ).

cnf(c_0_3783,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2539]) ).

cnf(c_0_3784,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2540]) ).

cnf(c_0_3785,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2468]) ).

cnf(c_0_3786,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2468]) ).

cnf(c_0_3787,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2469]) ).

cnf(c_0_3788,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2469]) ).

cnf(c_0_3789,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2443]) ).

cnf(c_0_3790,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2444]) ).

cnf(c_0_3791,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2541]) ).

cnf(c_0_3792,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2542]) ).

cnf(c_0_3793,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2543]) ).

cnf(c_0_3794,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2544]) ).

cnf(c_0_3795,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2545]) ).

cnf(c_0_3796,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2546]) ).

cnf(c_0_3797,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2547]) ).

cnf(c_0_3798,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk15_3(X3,X2,X1))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[c_0_2409]) ).

cnf(c_0_3799,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk14_3(X3,X2,X1))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[c_0_2410]) ).

cnf(c_0_3800,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2445]) ).

cnf(c_0_3801,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2548]) ).

cnf(c_0_3802,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2447]) ).

cnf(c_0_3803,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2549]) ).

cnf(c_0_3804,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_2550]) ).

cnf(c_0_3805,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk15_3(X3,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2409]) ).

cnf(c_0_3806,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk14_3(X3,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2410]) ).

cnf(c_0_3807,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2416]) ).

cnf(c_0_3808,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2550]) ).

cnf(c_0_3809,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2551]) ).

cnf(c_0_3810,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2429]) ).

cnf(c_0_3811,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2552]) ).

cnf(c_0_3812,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2553]) ).

cnf(c_0_3813,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2554]) ).

cnf(c_0_3814,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2555]) ).

cnf(c_0_3815,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2556]) ).

cnf(c_0_3816,plain,
    ( c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Power_Opower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2557]) ).

cnf(c_0_3817,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2558]) ).

cnf(c_0_3818,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2559]) ).

cnf(c_0_3819,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2560]) ).

cnf(c_0_3820,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2560]) ).

cnf(c_0_3821,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2561]) ).

cnf(c_0_3822,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_2562]) ).

cnf(c_0_3823,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2563]) ).

cnf(c_0_3824,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2564]) ).

cnf(c_0_3825,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2565]) ).

cnf(c_0_3826,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2566]) ).

cnf(c_0_3827,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2567]) ).

cnf(c_0_3828,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2568]) ).

cnf(c_0_3829,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2569]) ).

cnf(c_0_3830,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2570]) ).

cnf(c_0_3831,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2571]) ).

cnf(c_0_3832,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2572]) ).

cnf(c_0_3833,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2573]) ).

cnf(c_0_3834,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2574]) ).

cnf(c_0_3835,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2575]) ).

cnf(c_0_3836,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2576]) ).

cnf(c_0_3837,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2577]) ).

cnf(c_0_3838,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2578]) ).

cnf(c_0_3839,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2579]) ).

cnf(c_0_3840,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2580]) ).

cnf(c_0_3841,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2561]) ).

cnf(c_0_3842,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2562]) ).

cnf(c_0_3843,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2581]) ).

cnf(c_0_3844,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2582]) ).

cnf(c_0_3845,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2583]) ).

cnf(c_0_3846,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2584]) ).

cnf(c_0_3847,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2456]) ).

cnf(c_0_3848,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2585]) ).

cnf(c_0_3849,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2459]) ).

cnf(c_0_3850,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2460]) ).

cnf(c_0_3851,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2461]) ).

cnf(c_0_3852,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2463]) ).

cnf(c_0_3853,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2586]) ).

cnf(c_0_3854,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2587]) ).

cnf(c_0_3855,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2464]) ).

cnf(c_0_3856,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2530]) ).

cnf(c_0_3857,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2531]) ).

cnf(c_0_3858,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2588]) ).

cnf(c_0_3859,plain,
    ( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2589]) ).

cnf(c_0_3860,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2590]) ).

cnf(c_0_3861,plain,
    ( epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_2591]) ).

cnf(c_0_3862,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2592]) ).

cnf(c_0_3863,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2593]) ).

cnf(c_0_3864,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2594]) ).

cnf(c_0_3865,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2595]) ).

cnf(c_0_3866,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2596]) ).

cnf(c_0_3867,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2597]) ).

cnf(c_0_3868,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(split_conjunct,[status(thm)],[c_0_2598]) ).

cnf(c_0_3869,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X3,X2))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2599]) ).

cnf(c_0_3870,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2600]) ).

cnf(c_0_3871,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2550]) ).

cnf(c_0_3872,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2550]) ).

cnf(c_0_3873,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2601]) ).

cnf(c_0_3874,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2602]) ).

cnf(c_0_3875,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2603]) ).

cnf(c_0_3876,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2))) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))),
    inference(split_conjunct,[status(thm)],[c_0_2604]) ).

cnf(c_0_3877,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[c_0_2605]) ).

cnf(c_0_3878,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[c_0_2605]) ).

cnf(c_0_3879,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2),
    inference(split_conjunct,[status(thm)],[c_0_2606]) ).

cnf(c_0_3880,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X3) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2607]) ).

cnf(c_0_3881,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2608]) ).

cnf(c_0_3882,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2609]) ).

cnf(c_0_3883,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2610]) ).

cnf(c_0_3884,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2611]) ).

cnf(c_0_3885,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2612]) ).

cnf(c_0_3886,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2613]) ).

cnf(c_0_3887,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2614]) ).

cnf(c_0_3888,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2615]) ).

cnf(c_0_3889,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2616]) ).

cnf(c_0_3890,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2617]) ).

cnf(c_0_3891,plain,
    c_Power_Opower__class_Opower(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2),c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2618]) ).

cnf(c_0_3892,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | X3 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2591]) ).

cnf(c_0_3893,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2561]) ).

cnf(c_0_3894,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2561]) ).

cnf(c_0_3895,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2619]) ).

cnf(c_0_3896,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2619]) ).

cnf(c_0_3897,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2620]) ).

cnf(c_0_3898,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2620]) ).

cnf(c_0_3899,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2621]) ).

cnf(c_0_3900,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2622]) ).

cnf(c_0_3901,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2623]) ).

cnf(c_0_3902,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2624]) ).

cnf(c_0_3903,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2621]) ).

cnf(c_0_3904,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2625]) ).

cnf(c_0_3905,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2626]) ).

cnf(c_0_3906,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2627]) ).

cnf(c_0_3907,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2628]) ).

cnf(c_0_3908,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2629]) ).

cnf(c_0_3909,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2630]) ).

cnf(c_0_3910,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2602]) ).

cnf(c_0_3911,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2631]) ).

cnf(c_0_3912,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_2632]) ).

cnf(c_0_3913,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2518]) ).

cnf(c_0_3914,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2518]) ).

cnf(c_0_3915,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2633]) ).

cnf(c_0_3916,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2602]) ).

cnf(c_0_3917,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2634]) ).

cnf(c_0_3918,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2634]) ).

cnf(c_0_3919,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2634]) ).

cnf(c_0_3920,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2634]) ).

cnf(c_0_3921,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2635]) ).

cnf(c_0_3922,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2635]) ).

cnf(c_0_3923,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2635]) ).

cnf(c_0_3924,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2635]) ).

cnf(c_0_3925,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | c_Power_Opower__class_Opower(X3,X1,c_Nat_OSuc(X4)) != c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X4))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2636]) ).

cnf(c_0_3926,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls))))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2637]) ).

cnf(c_0_3927,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2638]) ).

cnf(c_0_3928,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2639]) ).

cnf(c_0_3929,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2640]) ).

cnf(c_0_3930,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3931,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2641]) ).

cnf(c_0_3932,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,esk21_3(X3,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3933,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X3,X2,X1),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3934,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2642]) ).

cnf(c_0_3935,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2643]) ).

cnf(c_0_3936,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X3,X2,X1),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,esk21_3(X3,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_3937,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2644]) ).

cnf(c_0_3938,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2645]) ).

cnf(c_0_3939,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | ~ epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2591]) ).

cnf(c_0_3940,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2500]) ).

cnf(c_0_3941,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2501]) ).

cnf(c_0_3942,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2561]) ).

cnf(c_0_3943,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2561]) ).

cnf(c_0_3944,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2646]) ).

cnf(c_0_3945,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2647]) ).

cnf(c_0_3946,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2648]) ).

cnf(c_0_3947,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2649]) ).

cnf(c_0_3948,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2650]) ).

cnf(c_0_3949,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2651]) ).

cnf(c_0_3950,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2652]) ).

cnf(c_0_3951,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2634]) ).

cnf(c_0_3952,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2634]) ).

cnf(c_0_3953,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2635]) ).

cnf(c_0_3954,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2635]) ).

cnf(c_0_3955,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2653]) ).

cnf(c_0_3956,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2654]) ).

cnf(c_0_3957,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2655]) ).

cnf(c_0_3958,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2656]) ).

cnf(c_0_3959,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2657]) ).

cnf(c_0_3960,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2658]) ).

cnf(c_0_3961,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2658]) ).

cnf(c_0_3962,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2659]) ).

cnf(c_0_3963,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2659]) ).

cnf(c_0_3964,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2660]) ).

cnf(c_0_3965,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2661]) ).

cnf(c_0_3966,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2662]) ).

cnf(c_0_3967,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2663]) ).

cnf(c_0_3968,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2664]) ).

cnf(c_0_3969,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2665]) ).

cnf(c_0_3970,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2666]) ).

cnf(c_0_3971,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X1))),
    inference(split_conjunct,[status(thm)],[c_0_2667]) ).

cnf(c_0_3972,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2668]) ).

cnf(c_0_3973,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2669]) ).

cnf(c_0_3974,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2670]) ).

cnf(c_0_3975,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2507]) ).

cnf(c_0_3976,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2508]) ).

cnf(c_0_3977,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2671]) ).

cnf(c_0_3978,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2672]) ).

cnf(c_0_3979,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2673]) ).

cnf(c_0_3980,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2674]) ).

cnf(c_0_3981,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2675]) ).

cnf(c_0_3982,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2513]) ).

cnf(c_0_3983,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2514]) ).

cnf(c_0_3984,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2503]) ).

cnf(c_0_3985,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2504]) ).

cnf(c_0_3986,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2676]) ).

cnf(c_0_3987,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2677]) ).

cnf(c_0_3988,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2678]) ).

cnf(c_0_3989,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2679]) ).

cnf(c_0_3990,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2562]) ).

cnf(c_0_3991,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2550]) ).

cnf(c_0_3992,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2621]) ).

cnf(c_0_3993,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2680]) ).

cnf(c_0_3994,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2681]) ).

cnf(c_0_3995,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2682]) ).

cnf(c_0_3996,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2683]) ).

cnf(c_0_3997,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2684]) ).

cnf(c_0_3998,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ class_Int_Onumber(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2685]) ).

cnf(c_0_3999,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2686]) ).

cnf(c_0_4000,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2522]) ).

cnf(c_0_4001,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X1),c_Power_Opower__class_Opower(tc_Int_Oint,X3,X1))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2525]) ).

cnf(c_0_4002,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2528]) ).

cnf(c_0_4003,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2687]) ).

cnf(c_0_4004,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2688]) ).

cnf(c_0_4005,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2689]) ).

cnf(c_0_4006,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2690]) ).

cnf(c_0_4007,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2691]) ).

cnf(c_0_4008,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2692]) ).

cnf(c_0_4009,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2693]) ).

cnf(c_0_4010,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2457]) ).

cnf(c_0_4011,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2458]) ).

cnf(c_0_4012,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2694]) ).

cnf(c_0_4013,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2695]) ).

cnf(c_0_4014,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2696]) ).

cnf(c_0_4015,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2697]) ).

cnf(c_0_4016,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2532]) ).

cnf(c_0_4017,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2698]) ).

cnf(c_0_4018,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2533]) ).

cnf(c_0_4019,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2699]) ).

cnf(c_0_4020,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2700]) ).

cnf(c_0_4021,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2529]) ).

cnf(c_0_4022,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2686]) ).

cnf(c_0_4023,plain,
    ( X3 = X2
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2518]) ).

cnf(c_0_4024,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2701]) ).

cnf(c_0_4025,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X2)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1)),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2702]) ).

cnf(c_0_4026,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2703]) ).

cnf(c_0_4027,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X4,X3))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2623]) ).

cnf(c_0_4028,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2704]) ).

cnf(c_0_4029,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2705]) ).

cnf(c_0_4030,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2706]) ).

cnf(c_0_4031,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2707]) ).

cnf(c_0_4032,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2708]) ).

cnf(c_0_4033,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2630]) ).

cnf(c_0_4034,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2709]) ).

cnf(c_0_4035,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2631]) ).

cnf(c_0_4036,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2710]) ).

cnf(c_0_4037,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2711]) ).

cnf(c_0_4038,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2712]) ).

cnf(c_0_4039,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2713]) ).

cnf(c_0_4040,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2714]) ).

cnf(c_0_4041,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2715]) ).

cnf(c_0_4042,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2688]) ).

cnf(c_0_4043,plain,
    ( X2 = X3
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2716]) ).

cnf(c_0_4044,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2717]) ).

cnf(c_0_4045,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2718]) ).

cnf(c_0_4046,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2633]) ).

cnf(c_0_4047,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2719]) ).

cnf(c_0_4048,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2720]) ).

cnf(c_0_4049,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2721]) ).

cnf(c_0_4050,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2722]) ).

cnf(c_0_4051,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2723]) ).

cnf(c_0_4052,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2724]) ).

cnf(c_0_4053,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Nat_OSuc(X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
    inference(split_conjunct,[status(thm)],[c_0_2725]) ).

cnf(c_0_4054,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2642]) ).

cnf(c_0_4055,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2642]) ).

cnf(c_0_4056,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2726]) ).

cnf(c_0_4057,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oab__semigroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2727]) ).

cnf(c_0_4058,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Groups_Oab__semigroup__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2728]) ).

cnf(c_0_4059,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2729]) ).

cnf(c_0_4060,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2730]) ).

cnf(c_0_4061,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2731]) ).

cnf(c_0_4062,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2732]) ).

cnf(c_0_4063,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2733]) ).

cnf(c_0_4064,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2734]) ).

cnf(c_0_4065,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2735]) ).

cnf(c_0_4066,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2736]) ).

cnf(c_0_4067,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ epred1_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2591]) ).

cnf(c_0_4068,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2678]) ).

cnf(c_0_4069,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4)) = c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2737]) ).

cnf(c_0_4070,plain,
    ( c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2738]) ).

cnf(c_0_4071,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2739]) ).

cnf(c_0_4072,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2740]) ).

cnf(c_0_4073,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2),
    inference(split_conjunct,[status(thm)],[c_0_2741]) ).

cnf(c_0_4074,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),X2),
    inference(split_conjunct,[status(thm)],[c_0_2742]) ).

cnf(c_0_4075,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2743]) ).

cnf(c_0_4076,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2744]) ).

cnf(c_0_4077,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2679]) ).

cnf(c_0_4078,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2745]) ).

cnf(c_0_4079,plain,
    ( c_Orderings_Oord__class_Oless(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2746]) ).

cnf(c_0_4080,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2746]) ).

cnf(c_0_4081,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2747]) ).

cnf(c_0_4082,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_2747]) ).

cnf(c_0_4083,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_2748]) ).

cnf(c_0_4084,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2518]) ).

cnf(c_0_4085,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2457]) ).

cnf(c_0_4086,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2458]) ).

cnf(c_0_4087,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2749]) ).

cnf(c_0_4088,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2750]) ).

cnf(c_0_4089,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2),
    inference(split_conjunct,[status(thm)],[c_0_2751]) ).

cnf(c_0_4090,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),X3) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2752]) ).

cnf(c_0_4091,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),
    inference(split_conjunct,[status(thm)],[c_0_2753]) ).

cnf(c_0_4092,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_2754]) ).

cnf(c_0_4093,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2755]) ).

cnf(c_0_4094,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2756]) ).

cnf(c_0_4095,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2757]) ).

cnf(c_0_4096,plain,
    c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2),X3) = c_Power_Opower__class_Opower(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2758]) ).

cnf(c_0_4097,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2759]) ).

cnf(c_0_4098,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2760]) ).

cnf(c_0_4099,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2761]) ).

cnf(c_0_4100,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_2762]) ).

cnf(c_0_4101,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[c_0_2763]) ).

cnf(c_0_4102,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2764]) ).

cnf(c_0_4103,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2765]) ).

cnf(c_0_4104,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[c_0_2766]) ).

cnf(c_0_4105,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2767]) ).

cnf(c_0_4106,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[c_0_2768]) ).

cnf(c_0_4107,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_2454]) ).

cnf(c_0_4108,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2769]) ).

cnf(c_0_4109,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2715]) ).

cnf(c_0_4110,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2715]) ).

cnf(c_0_4111,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2686]) ).

cnf(c_0_4112,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2770]) ).

cnf(c_0_4113,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2771]) ).

cnf(c_0_4114,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(split_conjunct,[status(thm)],[c_0_2772]) ).

cnf(c_0_4115,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2773]) ).

cnf(c_0_4116,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2774]) ).

cnf(c_0_4117,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2688]) ).

cnf(c_0_4118,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2689]) ).

cnf(c_0_4119,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2775]) ).

cnf(c_0_4120,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2686]) ).

cnf(c_0_4121,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2776]) ).

cnf(c_0_4122,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2561]) ).

cnf(c_0_4123,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2777]) ).

cnf(c_0_4124,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2777]) ).

cnf(c_0_4125,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2778]) ).

cnf(c_0_4126,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2779]) ).

cnf(c_0_4127,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2780]) ).

cnf(c_0_4128,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2781]) ).

cnf(c_0_4129,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2782]) ).

cnf(c_0_4130,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2688]) ).

cnf(c_0_4131,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2783]) ).

cnf(c_0_4132,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2783]) ).

cnf(c_0_4133,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2560]) ).

cnf(c_0_4134,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2784]) ).

cnf(c_0_4135,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2632]) ).

cnf(c_0_4136,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2785]) ).

cnf(c_0_4137,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Int_Onumber(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2784]) ).

cnf(c_0_4138,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2786]) ).

cnf(c_0_4139,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2723]) ).

cnf(c_0_4140,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2688]) ).

cnf(c_0_4141,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2787]) ).

cnf(c_0_4142,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2788]) ).

cnf(c_0_4143,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Oidom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2503]) ).

cnf(c_0_4144,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Oidom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2504]) ).

cnf(c_0_4145,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2689]) ).

cnf(c_0_4146,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2691]) ).

cnf(c_0_4147,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2686]) ).

cnf(c_0_4148,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2723]) ).

cnf(c_0_4149,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2789]) ).

cnf(c_0_4150,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2550]) ).

cnf(c_0_4151,plain,
    ( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk12_1(X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2601]) ).

cnf(c_0_4152,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2790]) ).

cnf(c_0_4153,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2791]) ).

cnf(c_0_4154,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2716]) ).

cnf(c_0_4155,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2562]) ).

cnf(c_0_4156,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2688]) ).

cnf(c_0_4157,plain,
    ( X3 = X4
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Power_Opower__class_Opower(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2792]) ).

cnf(c_0_4158,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2))
    | c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_2793]) ).

cnf(c_0_4159,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[c_0_2605]) ).

cnf(c_0_4160,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2598]) ).

cnf(c_0_4161,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_4162,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_4163,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2794]) ).

cnf(c_0_4164,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2795]) ).

cnf(c_0_4165,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2773]) ).

cnf(c_0_4166,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2796]) ).

cnf(c_0_4167,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2797]) ).

cnf(c_0_4168,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2774]) ).

cnf(c_0_4169,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2783]) ).

cnf(c_0_4170,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2798]) ).

cnf(c_0_4171,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,esk21_3(X3,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_4172,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X3,X2,X1),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_4173,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2690]) ).

cnf(c_0_4174,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2799]) ).

cnf(c_0_4175,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2719]) ).

cnf(c_0_4176,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2720]) ).

cnf(c_0_4177,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2800]) ).

cnf(c_0_4178,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2721]) ).

cnf(c_0_4179,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2722]) ).

cnf(c_0_4180,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2801]) ).

cnf(c_0_4181,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2802]) ).

cnf(c_0_4182,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2724]) ).

cnf(c_0_4183,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2803]) ).

cnf(c_0_4184,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2804]) ).

cnf(c_0_4185,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2804]) ).

cnf(c_0_4186,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2804]) ).

cnf(c_0_4187,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2804]) ).

cnf(c_0_4188,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2805]) ).

cnf(c_0_4189,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2518]) ).

cnf(c_0_4190,plain,
    ( X3 = X2
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2518]) ).

cnf(c_0_4191,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
    inference(split_conjunct,[status(thm)],[c_0_2806]) ).

cnf(c_0_4192,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
    inference(split_conjunct,[status(thm)],[c_0_2807]) ).

cnf(c_0_4193,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_2808]) ).

cnf(c_0_4194,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2529]) ).

cnf(c_0_4195,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2786]) ).

cnf(c_0_4196,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2809]) ).

cnf(c_0_4197,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2810]) ).

cnf(c_0_4198,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2739]) ).

cnf(c_0_4199,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2740]) ).

cnf(c_0_4200,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2811]) ).

cnf(c_0_4201,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_2812]) ).

cnf(c_0_4202,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2813]) ).

cnf(c_0_4203,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2814]) ).

cnf(c_0_4204,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1))
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(split_conjunct,[status(thm)],[c_0_2815]) ).

cnf(c_0_4205,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2816]) ).

cnf(c_0_4206,plain,
    ( X2 = X3
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2817]) ).

cnf(c_0_4207,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2813]) ).

cnf(c_0_4208,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2818]) ).

cnf(c_0_4209,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2819]) ).

cnf(c_0_4210,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Odiv(X1,X3,X2)) = X3
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2820]) ).

cnf(c_0_4211,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2821]) ).

cnf(c_0_4212,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2822]) ).

cnf(c_0_4213,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2823]) ).

cnf(c_0_4214,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),
    inference(split_conjunct,[status(thm)],[c_0_2824]) ).

cnf(c_0_4215,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2825]) ).

cnf(c_0_4216,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2707]) ).

cnf(c_0_4217,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2708]) ).

cnf(c_0_4218,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2826]) ).

cnf(c_0_4219,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2827]) ).

cnf(c_0_4220,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2828]) ).

cnf(c_0_4221,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2829]) ).

cnf(c_0_4222,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2830]) ).

cnf(c_0_4223,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2831]) ).

cnf(c_0_4224,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2668]) ).

cnf(c_0_4225,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2668]) ).

cnf(c_0_4226,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2764]) ).

cnf(c_0_4227,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2765]) ).

cnf(c_0_4228,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber(X1)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2832]) ).

cnf(c_0_4229,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2833]) ).

cnf(c_0_4230,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2763]) ).

cnf(c_0_4231,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2766]) ).

cnf(c_0_4232,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2767]) ).

cnf(c_0_4233,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2834]) ).

cnf(c_0_4234,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2768]) ).

cnf(c_0_4235,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_2835]) ).

cnf(c_0_4236,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_2836]) ).

cnf(c_0_4237,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2837]) ).

cnf(c_0_4238,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2838]) ).

cnf(c_0_4239,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2828]) ).

cnf(c_0_4240,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2830]) ).

cnf(c_0_4241,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2839]) ).

cnf(c_0_4242,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2840]) ).

cnf(c_0_4243,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2841]) ).

cnf(c_0_4244,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk11_2(X1,X2)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2842]) ).

cnf(c_0_4245,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_2748]) ).

cnf(c_0_4246,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2550]) ).

cnf(c_0_4247,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2770]) ).

cnf(c_0_4248,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2771]) ).

cnf(c_0_4249,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2772]) ).

cnf(c_0_4250,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2843]) ).

cnf(c_0_4251,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2844]) ).

cnf(c_0_4252,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2845]) ).

cnf(c_0_4253,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2846]) ).

cnf(c_0_4254,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2847]) ).

cnf(c_0_4255,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2848]) ).

cnf(c_0_4256,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2849]) ).

cnf(c_0_4257,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2850]) ).

cnf(c_0_4258,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2781]) ).

cnf(c_0_4259,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2851]) ).

cnf(c_0_4260,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2852]) ).

cnf(c_0_4261,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2786]) ).

cnf(c_0_4262,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2853]) ).

cnf(c_0_4263,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2854]) ).

cnf(c_0_4264,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2855]) ).

cnf(c_0_4265,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_2793]) ).

cnf(c_0_4266,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2856]) ).

cnf(c_0_4267,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2857]) ).

cnf(c_0_4268,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2858]) ).

cnf(c_0_4269,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2859]) ).

cnf(c_0_4270,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2860]) ).

cnf(c_0_4271,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2632]) ).

cnf(c_0_4272,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2861]) ).

cnf(c_0_4273,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Power_Opower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2862]) ).

cnf(c_0_4274,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2863]) ).

cnf(c_0_4275,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2864]) ).

cnf(c_0_4276,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2865]) ).

cnf(c_0_4277,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2866]) ).

cnf(c_0_4278,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk3_1(X1)))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2706]) ).

cnf(c_0_4279,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2867]) ).

cnf(c_0_4280,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2867]) ).

cnf(c_0_4281,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2868]) ).

cnf(c_0_4282,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2869]) ).

cnf(c_0_4283,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2685]) ).

cnf(c_0_4284,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2870]) ).

cnf(c_0_4285,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2871]) ).

cnf(c_0_4286,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2872]) ).

cnf(c_0_4287,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2873]) ).

cnf(c_0_4288,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2874]) ).

cnf(c_0_4289,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2851]) ).

cnf(c_0_4290,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_2842]) ).

cnf(c_0_4291,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X3
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2875]) ).

cnf(c_0_4292,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2876]) ).

cnf(c_0_4293,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2776]) ).

cnf(c_0_4294,plain,
    ( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2877]) ).

cnf(c_0_4295,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2877]) ).

cnf(c_0_4296,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2878]) ).

cnf(c_0_4297,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X2) = c_Divides_Odiv__class_Omod(X1,X3,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2879]) ).

cnf(c_0_4298,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2880]) ).

cnf(c_0_4299,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2881]) ).

cnf(c_0_4300,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),
    inference(split_conjunct,[status(thm)],[c_0_2882]) ).

cnf(c_0_4301,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2883]) ).

cnf(c_0_4302,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2884]) ).

cnf(c_0_4303,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2885]) ).

cnf(c_0_4304,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2886]) ).

cnf(c_0_4305,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2887]) ).

cnf(c_0_4306,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2888]) ).

cnf(c_0_4307,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2889]) ).

cnf(c_0_4308,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2890]) ).

cnf(c_0_4309,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2890]) ).

cnf(c_0_4310,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2890]) ).

cnf(c_0_4311,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2890]) ).

cnf(c_0_4312,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2891]) ).

cnf(c_0_4313,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2892]) ).

cnf(c_0_4314,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2893]) ).

cnf(c_0_4315,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2893]) ).

cnf(c_0_4316,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2893]) ).

cnf(c_0_4317,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2893]) ).

cnf(c_0_4318,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2894]) ).

cnf(c_0_4319,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2894]) ).

cnf(c_0_4320,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2895]) ).

cnf(c_0_4321,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2895]) ).

cnf(c_0_4322,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2896]) ).

cnf(c_0_4323,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2896]) ).

cnf(c_0_4324,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2896]) ).

cnf(c_0_4325,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2896]) ).

cnf(c_0_4326,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2897]) ).

cnf(c_0_4327,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2897]) ).

cnf(c_0_4328,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2898]) ).

cnf(c_0_4329,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2899]) ).

cnf(c_0_4330,plain,
    ( c_Power_Opower__class_Opower(X1,X2,X3) = c_Power_Opower__class_Opower(X1,X2,X4)
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | X3 != X4 ),
    inference(split_conjunct,[status(thm)],[c_0_2792]) ).

cnf(c_0_4331,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2900]) ).

cnf(c_0_4332,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2901]) ).

cnf(c_0_4333,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2902]) ).

cnf(c_0_4334,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2903]) ).

cnf(c_0_4335,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2904]) ).

cnf(c_0_4336,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2905]) ).

cnf(c_0_4337,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2906]) ).

cnf(c_0_4338,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2786]) ).

cnf(c_0_4339,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2907]) ).

cnf(c_0_4340,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2688]) ).

cnf(c_0_4341,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2908]) ).

cnf(c_0_4342,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2909]) ).

cnf(c_0_4343,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2910]) ).

cnf(c_0_4344,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2911]) ).

cnf(c_0_4345,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2745]) ).

cnf(c_0_4346,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2853]) ).

cnf(c_0_4347,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2854]) ).

cnf(c_0_4348,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2867]) ).

cnf(c_0_4349,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2912]) ).

cnf(c_0_4350,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2913]) ).

cnf(c_0_4351,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2914]) ).

cnf(c_0_4352,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2915]) ).

cnf(c_0_4353,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2916]) ).

cnf(c_0_4354,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2917]) ).

cnf(c_0_4355,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__ring(X1)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2918]) ).

cnf(c_0_4356,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2867]) ).

cnf(c_0_4357,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2867]) ).

cnf(c_0_4358,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2686]) ).

cnf(c_0_4359,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2804]) ).

cnf(c_0_4360,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2919]) ).

cnf(c_0_4361,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2817]) ).

cnf(c_0_4362,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2867]) ).

cnf(c_0_4363,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2851]) ).

cnf(c_0_4364,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2920]) ).

cnf(c_0_4365,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2921]) ).

cnf(c_0_4366,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2689]) ).

cnf(c_0_4367,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2690]) ).

cnf(c_0_4368,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk5_1(X1)))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2787]) ).

cnf(c_0_4369,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2875]) ).

cnf(c_0_4370,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2876]) ).

cnf(c_0_4371,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_2748]) ).

cnf(c_0_4372,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2518]) ).

cnf(c_0_4373,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2922]) ).

cnf(c_0_4374,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2923]) ).

cnf(c_0_4375,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2924]) ).

cnf(c_0_4376,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[c_0_2908]) ).

cnf(c_0_4377,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2909]) ).

cnf(c_0_4378,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2910]) ).

cnf(c_0_4379,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[c_0_2911]) ).

cnf(c_0_4380,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2920]) ).

cnf(c_0_4381,plain,
    ( X1 = X2
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2925]) ).

cnf(c_0_4382,plain,
    ( X4 = X5
    | ~ class_Groups_Oab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2926]) ).

cnf(c_0_4383,plain,
    ( X2 = X3
    | ~ class_Groups_Oab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | X4 != X5 ),
    inference(split_conjunct,[status(thm)],[c_0_2926]) ).

cnf(c_0_4384,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2906]) ).

cnf(c_0_4385,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2811]) ).

cnf(c_0_4386,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2907]) ).

cnf(c_0_4387,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_2808]) ).

cnf(c_0_4388,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_2914]) ).

cnf(c_0_4389,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2915]) ).

cnf(c_0_4390,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_2916]) ).

cnf(c_0_4391,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2917]) ).

cnf(c_0_4392,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2927]) ).

cnf(c_0_4393,plain,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2928]) ).

cnf(c_0_4394,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2686]) ).

cnf(c_0_4395,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(X3,X1,X4) != c_Groups_Oplus__class_Oplus(X3,X2,X4)
    | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2929]) ).

cnf(c_0_4396,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
    | ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2930]) ).

cnf(c_0_4397,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
    | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2931]) ).

cnf(c_0_4398,plain,
    ( X2 = X3
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oplus__class_Oplus(X1,X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_2932]) ).

cnf(c_0_4399,plain,
    ( X2 = X3
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X4,X2) != c_Groups_Oplus__class_Oplus(X1,X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2933]) ).

cnf(c_0_4400,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_2811]) ).

cnf(c_0_4401,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2934]) ).

cnf(c_0_4402,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2934]) ).

cnf(c_0_4403,plain,
    ( X2 = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2935]) ).

cnf(c_0_4404,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2936]) ).

cnf(c_0_4405,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2937]) ).

cnf(c_0_4406,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2938]) ).

cnf(c_0_4407,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | X2 != c_Groups_Oone__class_Oone(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2816]) ).

cnf(c_0_4408,plain,
    ( X1 = X2
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2939]) ).

cnf(c_0_4409,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk9_2(X2,X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2940]) ).

cnf(c_0_4410,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2941]) ).

cnf(c_0_4411,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X2))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2942]) ).

cnf(c_0_4412,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2943]) ).

cnf(c_0_4413,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2944]) ).

cnf(c_0_4414,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2945]) ).

cnf(c_0_4415,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2946]) ).

cnf(c_0_4416,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2947]) ).

cnf(c_0_4417,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2948]) ).

cnf(c_0_4418,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2949]) ).

cnf(c_0_4419,plain,
    ( c_Divides_Odiv__class_Odiv(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2950]) ).

cnf(c_0_4420,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2951]) ).

cnf(c_0_4421,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2952]) ).

cnf(c_0_4422,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2953]) ).

cnf(c_0_4423,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2954]) ).

cnf(c_0_4424,plain,
    ( X1 = X2
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2955]) ).

cnf(c_0_4425,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2956]) ).

cnf(c_0_4426,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2957]) ).

cnf(c_0_4427,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2958]) ).

cnf(c_0_4428,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2959]) ).

cnf(c_0_4429,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2960]) ).

cnf(c_0_4430,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2961]) ).

cnf(c_0_4431,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(split_conjunct,[status(thm)],[c_0_2962]) ).

cnf(c_0_4432,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2963]) ).

cnf(c_0_4433,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2964]) ).

cnf(c_0_4434,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2965]) ).

cnf(c_0_4435,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2966]) ).

cnf(c_0_4436,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2967]) ).

cnf(c_0_4437,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2968]) ).

cnf(c_0_4438,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2969]) ).

cnf(c_0_4439,plain,
    ( X2 = X1
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2970]) ).

cnf(c_0_4440,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2971]) ).

cnf(c_0_4441,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2923]) ).

cnf(c_0_4442,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2924]) ).

cnf(c_0_4443,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2972]) ).

cnf(c_0_4444,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2973]) ).

cnf(c_0_4445,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2974]) ).

cnf(c_0_4446,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X2))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2975]) ).

cnf(c_0_4447,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2976]) ).

cnf(c_0_4448,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2977]) ).

cnf(c_0_4449,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2978]) ).

cnf(c_0_4450,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_2379]) ).

cnf(c_0_4451,plain,
    ( X1 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,esk17_2(X2,X1))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2979]) ).

cnf(c_0_4452,plain,
    ( X1 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_2(X2,X1))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2980]) ).

cnf(c_0_4453,plain,
    c_Int_OBit1(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_2981]) ).

cnf(c_0_4454,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2982]) ).

cnf(c_0_4455,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2983]) ).

cnf(c_0_4456,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X1),X2) = c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_2984]) ).

cnf(c_0_4457,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_2763]) ).

cnf(c_0_4458,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2985]) ).

cnf(c_0_4459,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2986]) ).

cnf(c_0_4460,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2764]) ).

cnf(c_0_4461,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2765]) ).

cnf(c_0_4462,plain,
    ( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk13_2(X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2987]) ).

cnf(c_0_4463,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_2815]) ).

cnf(c_0_4464,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X2) = c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2988]) ).

cnf(c_0_4465,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,X2,X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2989]) ).

cnf(c_0_4466,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Nat_OSuc(X1)),
    inference(split_conjunct,[status(thm)],[c_0_2990]) ).

cnf(c_0_4467,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_2991]) ).

cnf(c_0_4468,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X1)),
    inference(split_conjunct,[status(thm)],[c_0_2992]) ).

cnf(c_0_4469,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)),
    inference(split_conjunct,[status(thm)],[c_0_2993]) ).

cnf(c_0_4470,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)),
    inference(split_conjunct,[status(thm)],[c_0_2994]) ).

cnf(c_0_4471,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)),
    inference(split_conjunct,[status(thm)],[c_0_2995]) ).

cnf(c_0_4472,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2928]) ).

cnf(c_0_4473,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2941]) ).

cnf(c_0_4474,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_2996]) ).

cnf(c_0_4475,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_2997]) ).

cnf(c_0_4476,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
    inference(split_conjunct,[status(thm)],[c_0_2998]) ).

cnf(c_0_4477,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_2999]) ).

cnf(c_0_4478,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2890]) ).

cnf(c_0_4479,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2804]) ).

cnf(c_0_4480,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3000]) ).

cnf(c_0_4481,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2893]) ).

cnf(c_0_4482,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2894]) ).

cnf(c_0_4483,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2895]) ).

cnf(c_0_4484,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2896]) ).

cnf(c_0_4485,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_3001]) ).

cnf(c_0_4486,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_3002]) ).

cnf(c_0_4487,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X1)),
    inference(split_conjunct,[status(thm)],[c_0_3003]) ).

cnf(c_0_4488,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_3004]) ).

cnf(c_0_4489,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_3005]) ).

cnf(c_0_4490,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3006]) ).

cnf(c_0_4491,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3007]) ).

cnf(c_0_4492,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3008]) ).

cnf(c_0_4493,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3009]) ).

cnf(c_0_4494,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3010]) ).

cnf(c_0_4495,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3011]) ).

cnf(c_0_4496,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3012]) ).

cnf(c_0_4497,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3013]) ).

cnf(c_0_4498,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3014]) ).

cnf(c_0_4499,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3015]) ).

cnf(c_0_4500,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3016]) ).

cnf(c_0_4501,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3017]) ).

cnf(c_0_4502,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3018]) ).

cnf(c_0_4503,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3019]) ).

cnf(c_0_4504,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3020]) ).

cnf(c_0_4505,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3021]) ).

cnf(c_0_4506,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3022]) ).

cnf(c_0_4507,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3023]) ).

cnf(c_0_4508,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3024]) ).

cnf(c_0_4509,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2934]) ).

cnf(c_0_4510,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_3025]) ).

cnf(c_0_4511,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_3026]) ).

cnf(c_0_4512,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3027]) ).

cnf(c_0_4513,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_3028]) ).

cnf(c_0_4514,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_3029]) ).

cnf(c_0_4515,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3030]) ).

cnf(c_0_4516,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3027]) ).

cnf(c_0_4517,plain,
    ( X1 = c_Nat_OSuc(X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3031]) ).

cnf(c_0_4518,plain,
    ( X1 = c_Nat_OSuc(X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3032]) ).

cnf(c_0_4519,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | X1 != c_Nat_OSuc(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2940]) ).

cnf(c_0_4520,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_3025]) ).

cnf(c_0_4521,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(split_conjunct,[status(thm)],[c_0_3026]) ).

cnf(c_0_4522,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | X3 != c_Groups_Otimes__class_Otimes(X1,X2,X4)
    | ~ class_Rings_Odvd(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3033]) ).

cnf(c_0_4523,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3006]) ).

cnf(c_0_4524,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3007]) ).

cnf(c_0_4525,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3008]) ).

cnf(c_0_4526,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3009]) ).

cnf(c_0_4527,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3010]) ).

cnf(c_0_4528,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3011]) ).

cnf(c_0_4529,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3012]) ).

cnf(c_0_4530,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3013]) ).

cnf(c_0_4531,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3014]) ).

cnf(c_0_4532,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3015]) ).

cnf(c_0_4533,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3016]) ).

cnf(c_0_4534,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3017]) ).

cnf(c_0_4535,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3034]) ).

cnf(c_0_4536,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3019]) ).

cnf(c_0_4537,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3020]) ).

cnf(c_0_4538,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3021]) ).

cnf(c_0_4539,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3022]) ).

cnf(c_0_4540,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3023]) ).

cnf(c_0_4541,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3024]) ).

cnf(c_0_4542,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3035]) ).

cnf(c_0_4543,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3036]) ).

cnf(c_0_4544,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_3037]) ).

cnf(c_0_4545,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3038]) ).

cnf(c_0_4546,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Nat_OSuc(X1) = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3039]) ).

cnf(c_0_4547,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3040]) ).

cnf(c_0_4548,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_2935]) ).

cnf(c_0_4549,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3041]) ).

cnf(c_0_4550,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3042]) ).

cnf(c_0_4551,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3043]) ).

cnf(c_0_4552,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3044]) ).

cnf(c_0_4553,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3045]) ).

cnf(c_0_4554,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3046]) ).

cnf(c_0_4555,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3047]) ).

cnf(c_0_4556,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3048]) ).

cnf(c_0_4557,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3048]) ).

cnf(c_0_4558,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_3049]) ).

cnf(c_0_4559,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3050]) ).

cnf(c_0_4560,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3051]) ).

cnf(c_0_4561,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3042]) ).

cnf(c_0_4562,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3043]) ).

cnf(c_0_4563,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3044]) ).

cnf(c_0_4564,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3052]) ).

cnf(c_0_4565,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3032]) ).

cnf(c_0_4566,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3035]) ).

cnf(c_0_4567,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3053]) ).

cnf(c_0_4568,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_3054]) ).

cnf(c_0_4569,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_3055]) ).

cnf(c_0_4570,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_3056]) ).

cnf(c_0_4571,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_3057]) ).

cnf(c_0_4572,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_3058]) ).

cnf(c_0_4573,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_3059]) ).

cnf(c_0_4574,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_3060]) ).

cnf(c_0_4575,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin) ),
    inference(split_conjunct,[status(thm)],[c_0_3061]) ).

cnf(c_0_4576,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin) ),
    inference(split_conjunct,[status(thm)],[c_0_3062]) ).

cnf(c_0_4577,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_3063]) ).

cnf(c_0_4578,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin) ),
    inference(split_conjunct,[status(thm)],[c_0_3064]) ).

cnf(c_0_4579,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_3065]) ).

cnf(c_0_4580,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin) ),
    inference(split_conjunct,[status(thm)],[c_0_3066]) ).

cnf(c_0_4581,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_3067]) ).

cnf(c_0_4582,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_3068]) ).

cnf(c_0_4583,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_3069]) ).

cnf(c_0_4584,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2890]) ).

cnf(c_0_4585,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2804]) ).

cnf(c_0_4586,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3070]) ).

cnf(c_0_4587,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2893]) ).

cnf(c_0_4588,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2894]) ).

cnf(c_0_4589,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2895]) ).

cnf(c_0_4590,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2896]) ).

cnf(c_0_4591,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3071]) ).

cnf(c_0_4592,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2920]) ).

cnf(c_0_4593,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3072]) ).

cnf(c_0_4594,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3073]) ).

cnf(c_0_4595,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3074]) ).

cnf(c_0_4596,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X3 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_3075]) ).

cnf(c_0_4597,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | X1 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_3076]) ).

cnf(c_0_4598,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_2970]) ).

cnf(c_0_4599,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_2923]) ).

cnf(c_0_4600,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2979]) ).

cnf(c_0_4601,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2980]) ).

cnf(c_0_4602,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3077]) ).

cnf(c_0_4603,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3071]) ).

cnf(c_0_4604,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3078]) ).

cnf(c_0_4605,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3079]) ).

cnf(c_0_4606,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3080]) ).

cnf(c_0_4607,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3081]) ).

cnf(c_0_4608,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3082]) ).

cnf(c_0_4609,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3083]) ).

cnf(c_0_4610,plain,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2968]) ).

cnf(c_0_4611,plain,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2969]) ).

cnf(c_0_4612,plain,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2971]) ).

cnf(c_0_4613,plain,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2923]) ).

cnf(c_0_4614,plain,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2924]) ).

cnf(c_0_4615,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_3054]) ).

cnf(c_0_4616,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3055]) ).

cnf(c_0_4617,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_3056]) ).

cnf(c_0_4618,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3057]) ).

cnf(c_0_4619,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3058]) ).

cnf(c_0_4620,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3059]) ).

cnf(c_0_4621,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3060]) ).

cnf(c_0_4622,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OMin) ),
    inference(split_conjunct,[status(thm)],[c_0_3061]) ).

cnf(c_0_4623,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
    inference(split_conjunct,[status(thm)],[c_0_3062]) ).

cnf(c_0_4624,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3063]) ).

cnf(c_0_4625,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
    inference(split_conjunct,[status(thm)],[c_0_3064]) ).

cnf(c_0_4626,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3065]) ).

cnf(c_0_4627,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
    inference(split_conjunct,[status(thm)],[c_0_3066]) ).

cnf(c_0_4628,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_3067]) ).

cnf(c_0_4629,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3068]) ).

cnf(c_0_4630,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_3069]) ).

cnf(c_0_4631,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_2987]) ).

cnf(c_0_4632,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2809]) ).

cnf(c_0_4633,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3084]) ).

cnf(c_0_4634,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_3085]) ).

cnf(c_0_4635,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3077]) ).

cnf(c_0_4636,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3086]) ).

cnf(c_0_4637,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3087]) ).

cnf(c_0_4638,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3080]) ).

cnf(c_0_4639,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3081]) ).

cnf(c_0_4640,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3082]) ).

cnf(c_0_4641,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3083]) ).

cnf(c_0_4642,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2903]) ).

cnf(c_0_4643,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2903]) ).

cnf(c_0_4644,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3088]) ).

cnf(c_0_4645,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3089]) ).

cnf(c_0_4646,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2905]) ).

cnf(c_0_4647,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_2905]) ).

cnf(c_0_4648,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2928]) ).

cnf(c_0_4649,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)))
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_3085]) ).

cnf(c_0_4650,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(esk9_2(X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_2940]) ).

cnf(c_0_4651,plain,
    ( X1 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk4_1(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2958]) ).

cnf(c_0_4652,plain,
    ( X1 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk2_1(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2959]) ).

cnf(c_0_4653,plain,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3090]) ).

cnf(c_0_4654,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3090]) ).

cnf(c_0_4655,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3091]) ).

cnf(c_0_4656,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2943]) ).

cnf(c_0_4657,plain,
    c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X1))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X1),
    inference(split_conjunct,[status(thm)],[c_0_3092]) ).

cnf(c_0_4658,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2925]) ).

cnf(c_0_4659,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2936]) ).

cnf(c_0_4660,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2960]) ).

cnf(c_0_4661,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2961]) ).

cnf(c_0_4662,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X4,X3)
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 != X4 ),
    inference(split_conjunct,[status(thm)],[c_0_2932]) ).

cnf(c_0_4663,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,X4)
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | X3 != X4 ),
    inference(split_conjunct,[status(thm)],[c_0_2933]) ).

cnf(c_0_4664,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3093]) ).

cnf(c_0_4665,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3094]) ).

cnf(c_0_4666,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(X1,X3,X2)
    | X3 = X2
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3095]) ).

cnf(c_0_4667,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_3096]) ).

cnf(c_0_4668,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
    inference(split_conjunct,[status(thm)],[c_0_3097]) ).

cnf(c_0_4669,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Ozero__class_Ozero(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3091]) ).

cnf(c_0_4670,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3036]) ).

cnf(c_0_4671,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3098]) ).

cnf(c_0_4672,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Otimes__class_Otimes(X1,X3,X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3099]) ).

cnf(c_0_4673,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2953]) ).

cnf(c_0_4674,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2954]) ).

cnf(c_0_4675,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2937]) ).

cnf(c_0_4676,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2938]) ).

cnf(c_0_4677,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3100]) ).

cnf(c_0_4678,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3101]) ).

cnf(c_0_4679,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2955]) ).

cnf(c_0_4680,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2956]) ).

cnf(c_0_4681,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2957]) ).

cnf(c_0_4682,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3102]) ).

cnf(c_0_4683,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3103]) ).

cnf(c_0_4684,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[c_0_3104]) ).

cnf(c_0_4685,plain,
    ( X1 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk6_1(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3047]) ).

cnf(c_0_4686,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) = c_Nat_OSuc(c_Nat_OSuc(X1)),
    inference(split_conjunct,[status(thm)],[c_0_3105]) ).

cnf(c_0_4687,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X1)),
    inference(split_conjunct,[status(thm)],[c_0_3106]) ).

cnf(c_0_4688,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3107]) ).

cnf(c_0_4689,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3108]) ).

cnf(c_0_4690,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X3 = c_Groups_Ozero__class_Ozero(X2)
    | c_Groups_Otimes__class_Otimes(X2,X3,X1) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Ono__zero__divisors(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3109]) ).

cnf(c_0_4691,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3110]) ).

cnf(c_0_4692,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3111]) ).

cnf(c_0_4693,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
    | X1 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2977]) ).

cnf(c_0_4694,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2978]) ).

cnf(c_0_4695,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2955]) ).

cnf(c_0_4696,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2956]) ).

cnf(c_0_4697,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)
    | X1 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_2957]) ).

cnf(c_0_4698,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3108]) ).

cnf(c_0_4699,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3112]) ).

cnf(c_0_4700,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X2 = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_3113]) ).

cnf(c_0_4701,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X2 = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_3114]) ).

cnf(c_0_4702,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X2 = X1
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3115]) ).

cnf(c_0_4703,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ozero__class_Ozero(X2),X1)
    | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3116]) ).

cnf(c_0_4704,plain,
    c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3117]) ).

cnf(c_0_4705,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3118]) ).

cnf(c_0_4706,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[c_0_3119]) ).

cnf(c_0_4707,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3102]) ).

cnf(c_0_4708,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3102]) ).

cnf(c_0_4709,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3103]) ).

cnf(c_0_4710,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3103]) ).

cnf(c_0_4711,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3120]) ).

cnf(c_0_4712,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3121]) ).

cnf(c_0_4713,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3122]) ).

cnf(c_0_4714,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3040]) ).

cnf(c_0_4715,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3123]) ).

cnf(c_0_4716,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_3124]) ).

cnf(c_0_4717,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_3125]) ).

cnf(c_0_4718,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_3126]) ).

cnf(c_0_4719,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_3127]) ).

cnf(c_0_4720,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_3128]) ).

cnf(c_0_4721,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3129]) ).

cnf(c_0_4722,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oplus__class_Oplus(X1,X2,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3130]) ).

cnf(c_0_4723,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3131]) ).

cnf(c_0_4724,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_2991]) ).

cnf(c_0_4725,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3132]) ).

cnf(c_0_4726,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(split_conjunct,[status(thm)],[c_0_3133]) ).

cnf(c_0_4727,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(split_conjunct,[status(thm)],[c_0_3134]) ).

cnf(c_0_4728,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(split_conjunct,[status(thm)],[c_0_3135]) ).

cnf(c_0_4729,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_3136]) ).

cnf(c_0_4730,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_3136]) ).

cnf(c_0_4731,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_3136]) ).

cnf(c_0_4732,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_3136]) ).

cnf(c_0_4733,plain,
    ( X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_3137]) ).

cnf(c_0_4734,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3138]) ).

cnf(c_0_4735,plain,
    ( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3138]) ).

cnf(c_0_4736,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3102]) ).

cnf(c_0_4737,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3103]) ).

cnf(c_0_4738,plain,
    ( X2 = X3
    | ~ class_Groups_Oab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3139]) ).

cnf(c_0_4739,plain,
    ( X2 = X3
    | ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3140]) ).

cnf(c_0_4740,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3141]) ).

cnf(c_0_4741,plain,
    ( X1 = c_Nat_OSuc(esk10_1(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3142]) ).

cnf(c_0_4742,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != c_Groups_Oplus__class_Oplus(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3143]) ).

cnf(c_0_4743,plain,
    ( c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3090]) ).

cnf(c_0_4744,plain,
    v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_3144]) ).

cnf(c_0_4745,plain,
    ( ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2)))
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3145]) ).

cnf(c_0_4746,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_3146]) ).

cnf(c_0_4747,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(split_conjunct,[status(thm)],[c_0_3147]) ).

cnf(c_0_4748,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3148]) ).

cnf(c_0_4749,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)),X2) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3149]) ).

cnf(c_0_4750,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3150]) ).

cnf(c_0_4751,plain,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3151]) ).

cnf(c_0_4752,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X1 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ),
    inference(split_conjunct,[status(thm)],[c_0_3136]) ).

cnf(c_0_4753,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_3152]) ).

cnf(c_0_4754,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3153]) ).

cnf(c_0_4755,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3154]) ).

cnf(c_0_4756,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3155]) ).

cnf(c_0_4757,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3156]) ).

cnf(c_0_4758,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3156]) ).

cnf(c_0_4759,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3157]) ).

cnf(c_0_4760,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3157]) ).

cnf(c_0_4761,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3158]) ).

cnf(c_0_4762,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3158]) ).

cnf(c_0_4763,plain,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3159]) ).

cnf(c_0_4764,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3160]) ).

cnf(c_0_4765,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[c_0_3161]) ).

cnf(c_0_4766,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[c_0_3162]) ).

cnf(c_0_4767,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[c_0_3163]) ).

cnf(c_0_4768,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3077]) ).

cnf(c_0_4769,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3164]) ).

cnf(c_0_4770,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3165]) ).

cnf(c_0_4771,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3081]) ).

cnf(c_0_4772,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3114]) ).

cnf(c_0_4773,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3114]) ).

cnf(c_0_4774,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3082]) ).

cnf(c_0_4775,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3138]) ).

cnf(c_0_4776,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_3166]) ).

cnf(c_0_4777,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X2) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3167]) ).

cnf(c_0_4778,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3168]) ).

cnf(c_0_4779,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Nat_OSuc(X2)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3169]) ).

cnf(c_0_4780,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3170]) ).

cnf(c_0_4781,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[c_0_3171]) ).

cnf(c_0_4782,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_3172]) ).

cnf(c_0_4783,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_3173]) ).

cnf(c_0_4784,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3170]) ).

cnf(c_0_4785,plain,
    ( ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3174]) ).

cnf(c_0_4786,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3102]) ).

cnf(c_0_4787,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3102]) ).

cnf(c_0_4788,plain,
    ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3103]) ).

cnf(c_0_4789,plain,
    ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3103]) ).

cnf(c_0_4790,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
    inference(split_conjunct,[status(thm)],[c_0_3175]) ).

cnf(c_0_4791,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
    inference(split_conjunct,[status(thm)],[c_0_3176]) ).

cnf(c_0_4792,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
    inference(split_conjunct,[status(thm)],[c_0_3177]) ).

cnf(c_0_4793,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(split_conjunct,[status(thm)],[c_0_3178]) ).

cnf(c_0_4794,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3104]) ).

cnf(c_0_4795,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[c_0_3179]) ).

cnf(c_0_4796,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3146]) ).

cnf(c_0_4797,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3147]) ).

cnf(c_0_4798,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3180]) ).

cnf(c_0_4799,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3181]) ).

cnf(c_0_4800,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3182]) ).

cnf(c_0_4801,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3130]) ).

cnf(c_0_4802,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3131]) ).

cnf(c_0_4803,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3111]) ).

cnf(c_0_4804,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3111]) ).

cnf(c_0_4805,plain,
    ( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[c_0_3118]) ).

cnf(c_0_4806,plain,
    c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[c_0_3183]) ).

cnf(c_0_4807,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3184]) ).

cnf(c_0_4808,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3185]) ).

cnf(c_0_4809,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3186]) ).

cnf(c_0_4810,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3187]) ).

cnf(c_0_4811,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3188]) ).

cnf(c_0_4812,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3189]) ).

cnf(c_0_4813,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3190]) ).

cnf(c_0_4814,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3191]) ).

cnf(c_0_4815,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3192]) ).

cnf(c_0_4816,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3193]) ).

cnf(c_0_4817,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3194]) ).

cnf(c_0_4818,plain,
    ( c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2557]) ).

cnf(c_0_4819,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3119]) ).

cnf(c_0_4820,plain,
    ( c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3195]) ).

cnf(c_0_4821,plain,
    ( X2 = c_Groups_Oplus__class_Oplus(X1,X2,X3)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3143]) ).

cnf(c_0_4822,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oab__group__add(X1)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_3139]) ).

cnf(c_0_4823,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_3140]) ).

cnf(c_0_4824,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3196]) ).

cnf(c_0_4825,plain,
    ( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3197]) ).

cnf(c_0_4826,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3198]) ).

cnf(c_0_4827,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3199]) ).

cnf(c_0_4828,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3200]) ).

cnf(c_0_4829,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3201]) ).

cnf(c_0_4830,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3202]) ).

cnf(c_0_4831,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3203]) ).

cnf(c_0_4832,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3204]) ).

cnf(c_0_4833,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3205]) ).

cnf(c_0_4834,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3206]) ).

cnf(c_0_4835,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3207]) ).

cnf(c_0_4836,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3208]) ).

cnf(c_0_4837,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3209]) ).

cnf(c_0_4838,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3210]) ).

cnf(c_0_4839,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3211]) ).

cnf(c_0_4840,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3212]) ).

cnf(c_0_4841,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3213]) ).

cnf(c_0_4842,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3214]) ).

cnf(c_0_4843,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3215]) ).

cnf(c_0_4844,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3216]) ).

cnf(c_0_4845,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != c_Nat_OSuc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3032]) ).

cnf(c_0_4846,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3156]) ).

cnf(c_0_4847,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3157]) ).

cnf(c_0_4848,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_3136]) ).

cnf(c_0_4849,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3158]) ).

cnf(c_0_4850,plain,
    ( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3118]) ).

cnf(c_0_4851,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3217]) ).

cnf(c_0_4852,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3218]) ).

cnf(c_0_4853,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3219]) ).

cnf(c_0_4854,plain,
    ( ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3220]) ).

cnf(c_0_4855,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3221]) ).

cnf(c_0_4856,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
    inference(split_conjunct,[status(thm)],[c_0_3222]) ).

cnf(c_0_4857,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2940]) ).

cnf(c_0_4858,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X1 != c_Nat_OSuc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3142]) ).

cnf(c_0_4859,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3223]) ).

cnf(c_0_4860,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3035]) ).

cnf(c_0_4861,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X1)),
    inference(split_conjunct,[status(thm)],[c_0_3224]) ).

cnf(c_0_4862,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3154]) ).

cnf(c_0_4863,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3155]) ).

cnf(c_0_4864,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3225]) ).

cnf(c_0_4865,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_2867]) ).

cnf(c_0_4866,plain,
    ( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2589]) ).

cnf(c_0_4867,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2590]) ).

cnf(c_0_4868,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3148]) ).

cnf(c_0_4869,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3148]) ).

cnf(c_0_4870,plain,
    ( X2 = X3
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_Int_Onumber__class_Onumber__of(X1,X2) != c_Int_Onumber__class_Onumber__of(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_3226]) ).

cnf(c_0_4871,plain,
    c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
    inference(split_conjunct,[status(thm)],[c_0_3227]) ).

cnf(c_0_4872,plain,
    c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[c_0_3228]) ).

cnf(c_0_4873,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3229]) ).

cnf(c_0_4874,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_3151]) ).

cnf(c_0_4875,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X2
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[c_0_2638]) ).

cnf(c_0_4876,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[c_0_3230]) ).

cnf(c_0_4877,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_3231]) ).

cnf(c_0_4878,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_3232]) ).

cnf(c_0_4879,plain,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_3233]) ).

cnf(c_0_4880,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1)),
    inference(split_conjunct,[status(thm)],[c_0_3234]) ).

cnf(c_0_4881,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(split_conjunct,[status(thm)],[c_0_3235]) ).

cnf(c_0_4882,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3236]) ).

cnf(c_0_4883,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3237]) ).

cnf(c_0_4884,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3238]) ).

cnf(c_0_4885,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3239]) ).

cnf(c_0_4886,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3240]) ).

cnf(c_0_4887,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3236]) ).

cnf(c_0_4888,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3241]) ).

cnf(c_0_4889,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3242]) ).

cnf(c_0_4890,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3243]) ).

cnf(c_0_4891,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3244]) ).

cnf(c_0_4892,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3245]) ).

cnf(c_0_4893,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3246]) ).

cnf(c_0_4894,plain,
    c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_3247]) ).

cnf(c_0_4895,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3248]) ).

cnf(c_0_4896,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3249]) ).

cnf(c_0_4897,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3250]) ).

cnf(c_0_4898,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3251]) ).

cnf(c_0_4899,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3252]) ).

cnf(c_0_4900,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3086]) ).

cnf(c_0_4901,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3080]) ).

cnf(c_0_4902,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3083]) ).

cnf(c_0_4903,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3253]) ).

cnf(c_0_4904,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_2924]) ).

cnf(c_0_4905,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_2972]) ).

cnf(c_0_4906,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_2972]) ).

cnf(c_0_4907,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
    inference(split_conjunct,[status(thm)],[c_0_3254]) ).

cnf(c_0_4908,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[c_0_3255]) ).

cnf(c_0_4909,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
    inference(split_conjunct,[status(thm)],[c_0_3256]) ).

cnf(c_0_4910,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
    inference(split_conjunct,[status(thm)],[c_0_3257]) ).

cnf(c_0_4911,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3258]) ).

cnf(c_0_4912,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3259]) ).

cnf(c_0_4913,plain,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_3260]) ).

cnf(c_0_4914,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_3261]) ).

cnf(c_0_4915,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_3262]) ).

cnf(c_0_4916,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_3263]) ).

cnf(c_0_4917,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_3264]) ).

cnf(c_0_4918,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3265]) ).

cnf(c_0_4919,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3266]) ).

cnf(c_0_4920,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3267]) ).

cnf(c_0_4921,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,X1) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[c_0_3268]) ).

cnf(c_0_4922,plain,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
    inference(split_conjunct,[status(thm)],[c_0_3269]) ).

cnf(c_0_4923,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(split_conjunct,[status(thm)],[c_0_3270]) ).

cnf(c_0_4924,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
    inference(split_conjunct,[status(thm)],[c_0_3271]) ).

cnf(c_0_4925,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
    inference(split_conjunct,[status(thm)],[c_0_3272]) ).

cnf(c_0_4926,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_3273]) ).

cnf(c_0_4927,plain,
    ( X2 = c_Int_Onumber__class_Onumber__of(X1,X3)
    | ~ class_Int_Onumber(X1)
    | c_Int_Onumber__class_Onumber__of(X1,X3) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3274]) ).

cnf(c_0_4928,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) = X3
    | ~ class_Int_Onumber(X1)
    | X3 != c_Int_Onumber__class_Onumber__of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3274]) ).

cnf(c_0_4929,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Int_Onumber__class_Onumber__of(X1,X3)
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_3226]) ).

cnf(c_0_4930,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3275]) ).

cnf(c_0_4931,plain,
    c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[c_0_3276]) ).

cnf(c_0_4932,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(split_conjunct,[status(thm)],[c_0_3277]) ).

cnf(c_0_4933,plain,
    ( ~ c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3278]) ).

cnf(c_0_4934,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__1(X1)
    | ~ c_Int_Oiszero(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3279]) ).

cnf(c_0_4935,plain,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),
    inference(split_conjunct,[status(thm)],[c_0_3280]) ).

cnf(c_0_4936,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3273]) ).

cnf(c_0_4937,plain,
    ( c_Int_Oiszero(X1,X2)
    | ~ class_Rings_Osemiring__1(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3279]) ).

cnf(c_0_4938,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3281]) ).

cnf(c_0_4939,plain,
    ( c_Groups_Oone__class_Oone(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3282]) ).

cnf(c_0_4940,plain,
    ( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3283]) ).

cnf(c_0_4941,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[c_0_3284]) ).

cnf(c_0_4942,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_3285]) ).

cnf(c_0_4943,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3286]) ).

cnf(c_0_4944,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3287]) ).

cnf(c_0_4945,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[c_0_3288]) ).

cnf(c_0_4946,plain,
    ( X2 = c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Oone(X1)
    | c_Groups_Oone__class_Oone(X1) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3289]) ).

cnf(c_0_4947,plain,
    ( c_Groups_Oone__class_Oone(X1) = X2
    | ~ class_Groups_Oone(X1)
    | X2 != c_Groups_Oone__class_Oone(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3289]) ).

cnf(c_0_4948,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ozero(X1)
    | c_Groups_Ozero__class_Ozero(X1) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3290]) ).

cnf(c_0_4949,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = X2
    | ~ class_Groups_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3290]) ).

cnf(c_0_4950,plain,
    ( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3291]) ).

cnf(c_0_4951,plain,
    ( c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Ozero__neq__one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3292]) ).

cnf(c_0_4952,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[c_0_3293]) ).

cnf(c_0_4953,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3294]) ).

cnf(c_0_4954,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
    inference(split_conjunct,[status(thm)],[c_0_3295]) ).

cnf(c_0_4955,plain,
    c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(split_conjunct,[status(thm)],[c_0_3296]) ).

cnf(c_0_4956,plain,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[c_0_3297]) ).

cnf(c_0_4957,plain,
    ( X1 = X2
    | c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3298]) ).

cnf(c_0_4958,plain,
    ( X1 = X2
    | c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3299]) ).

cnf(c_0_4959,plain,
    ( X1 = X2
    | c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3300]) ).

cnf(c_0_4960,plain,
    ( X1 = X2
    | c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_3301]) ).

cnf(c_0_4961,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
    inference(split_conjunct,[status(thm)],[c_0_3302]) ).

cnf(c_0_4962,plain,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_3303]) ).

cnf(c_0_4963,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
    inference(split_conjunct,[status(thm)],[c_0_3304]) ).

cnf(c_0_4964,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3305]) ).

cnf(c_0_4965,plain,
    c_Int_OBit1(X1) != c_Int_OBit0(X2),
    inference(split_conjunct,[status(thm)],[c_0_3306]) ).

cnf(c_0_4966,plain,
    c_Int_OBit0(X1) != c_Int_OBit1(X2),
    inference(split_conjunct,[status(thm)],[c_0_3307]) ).

cnf(c_0_4967,plain,
    ( c_Nat_OSuc(X1) = c_Nat_OSuc(X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3299]) ).

cnf(c_0_4968,plain,
    ( c_Int_OBit0(X1) = c_Int_OBit0(X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3300]) ).

cnf(c_0_4969,plain,
    ( c_Int_OBit1(X1) = c_Int_OBit1(X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_3301]) ).

cnf(c_0_4970,plain,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    inference(split_conjunct,[status(thm)],[c_0_3308]) ).

cnf(c_0_4971,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
    inference(split_conjunct,[status(thm)],[c_0_3309]) ).

cnf(c_0_4972,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
    inference(split_conjunct,[status(thm)],[c_0_3310]) ).

cnf(c_0_4973,plain,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3311]) ).

cnf(c_0_4974,plain,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3312]) ).

cnf(c_0_4975,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
    inference(split_conjunct,[status(thm)],[c_0_3313]) ).

cnf(c_0_4976,plain,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3314]) ).

cnf(c_0_4977,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[c_0_3315]) ).

cnf(c_0_4978,plain,
    ( X1 = c_Int_OMin
    | c_Int_OBit1(X1) != c_Int_OMin ),
    inference(split_conjunct,[status(thm)],[c_0_3316]) ).

cnf(c_0_4979,plain,
    ( c_Int_OMin = X1
    | c_Int_OMin != c_Int_OBit1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3317]) ).

cnf(c_0_4980,plain,
    ( X1 = c_Int_OPls
    | c_Int_OBit0(X1) != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[c_0_3318]) ).

cnf(c_0_4981,plain,
    ( c_Int_OPls = X1
    | c_Int_OPls != c_Int_OBit0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_3319]) ).

cnf(c_0_4982,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3320]) ).

cnf(c_0_4983,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3321]) ).

cnf(c_0_4984,plain,
    c_Nat_OSuc(X1) != X1,
    inference(split_conjunct,[status(thm)],[c_0_3322]) ).

cnf(c_0_4985,plain,
    X1 != c_Nat_OSuc(X1),
    inference(split_conjunct,[status(thm)],[c_0_3323]) ).

cnf(c_0_4986,plain,
    c_Int_OBit0(X1) != c_Int_OMin,
    inference(split_conjunct,[status(thm)],[c_0_3324]) ).

cnf(c_0_4987,plain,
    c_Int_OMin != c_Int_OBit0(X1),
    inference(split_conjunct,[status(thm)],[c_0_3325]) ).

cnf(c_0_4988,plain,
    c_Int_OBit1(X1) != c_Int_OPls,
    inference(split_conjunct,[status(thm)],[c_0_3326]) ).

cnf(c_0_4989,plain,
    c_Int_OPls != c_Int_OBit1(X1),
    inference(split_conjunct,[status(thm)],[c_0_3327]) ).

cnf(c_0_4990,plain,
    ( c_Int_OBit1(X1) = c_Int_OMin
    | X1 != c_Int_OMin ),
    inference(split_conjunct,[status(thm)],[c_0_3316]) ).

cnf(c_0_4991,plain,
    ( c_Int_OMin = c_Int_OBit1(X1)
    | c_Int_OMin != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_3317]) ).

cnf(c_0_4992,plain,
    ( c_Int_OBit0(X1) = c_Int_OPls
    | X1 != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[c_0_3318]) ).

cnf(c_0_4993,plain,
    ( c_Int_OPls = c_Int_OBit0(X1)
    | c_Int_OPls != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_3319]) ).

cnf(c_0_4994,plain,
    v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3328]) ).

cnf(c_0_4995,plain,
    v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3329]) ).

cnf(c_0_4996,plain,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3330]) ).

cnf(c_0_4997,plain,
    class_Groups_Oone(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3331]) ).

cnf(c_0_4998,plain,
    class_Int_Onumber(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3332]) ).

cnf(c_0_4999,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3333]) ).

cnf(c_0_5000,plain,
    class_Rings_Oring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3334]) ).

cnf(c_0_5001,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3335]) ).

cnf(c_0_5002,plain,
    class_Power_Opower(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3336]) ).

cnf(c_0_5003,plain,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3337]) ).

cnf(c_0_5004,plain,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3338]) ).

cnf(c_0_5005,plain,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3339]) ).

cnf(c_0_5006,plain,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3340]) ).

cnf(c_0_5007,plain,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3341]) ).

cnf(c_0_5008,plain,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3342]) ).

cnf(c_0_5009,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3343]) ).

cnf(c_0_5010,plain,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3344]) ).

cnf(c_0_5011,plain,
    class_Rings_Osemiring__1(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3345]) ).

cnf(c_0_5012,plain,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3346]) ).

cnf(c_0_5013,plain,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3347]) ).

cnf(c_0_5014,plain,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3348]) ).

cnf(c_0_5015,plain,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3349]) ).

cnf(c_0_5016,plain,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3350]) ).

cnf(c_0_5017,plain,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3351]) ).

cnf(c_0_5018,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3352]) ).

cnf(c_0_5019,plain,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3353]) ).

cnf(c_0_5020,plain,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3354]) ).

cnf(c_0_5021,plain,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3355]) ).

cnf(c_0_5022,plain,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3356]) ).

cnf(c_0_5023,plain,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3357]) ).

cnf(c_0_5024,plain,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3358]) ).

cnf(c_0_5025,plain,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3359]) ).

cnf(c_0_5026,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3360]) ).

cnf(c_0_5027,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3361]) ).

cnf(c_0_5028,plain,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3362]) ).

cnf(c_0_5029,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[c_0_3363]) ).

cnf(c_0_5030,plain,
    class_Rings_Odvd(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3364]) ).

cnf(c_0_5031,plain,
    class_Groups_Oone(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3365]) ).

cnf(c_0_5032,plain,
    class_Int_Onumber(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3366]) ).

cnf(c_0_5033,plain,
    class_Rings_Oidom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3367]) ).

cnf(c_0_5034,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3368]) ).

cnf(c_0_5035,plain,
    class_Groups_Ozero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3369]) ).

cnf(c_0_5036,plain,
    class_Power_Opower(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3370]) ).

cnf(c_0_5037,plain,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3371]) ).

cnf(c_0_5038,plain,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3372]) ).

cnf(c_0_5039,plain,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3373]) ).

cnf(c_0_5040,plain,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3374]) ).

cnf(c_0_5041,plain,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3375]) ).

cnf(c_0_5042,plain,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3376]) ).

cnf(c_0_5043,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3377]) ).

cnf(c_0_5044,plain,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3378]) ).

cnf(c_0_5045,plain,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3379]) ).

cnf(c_0_5046,plain,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3380]) ).

cnf(c_0_5047,plain,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3381]) ).

cnf(c_0_5048,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3382]) ).

cnf(c_0_5049,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3383]) ).

cnf(c_0_5050,plain,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3384]) ).

cnf(c_0_5051,plain,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3385]) ).

cnf(c_0_5052,plain,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3386]) ).

cnf(c_0_5053,plain,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3387]) ).

cnf(c_0_5054,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3388]) ).

cnf(c_0_5055,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3389]) ).

cnf(c_0_5056,plain,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3390]) ).

cnf(c_0_5057,plain,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3391]) ).

cnf(c_0_5058,plain,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3392]) ).

cnf(c_0_5059,plain,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3393]) ).

cnf(c_0_5060,plain,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3394]) ).

cnf(c_0_5061,plain,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3395]) ).

cnf(c_0_5062,plain,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3396]) ).

cnf(c_0_5063,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3397]) ).

cnf(c_0_5064,plain,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3398]) ).

cnf(c_0_5065,plain,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3399]) ).

cnf(c_0_5066,plain,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3400]) ).

cnf(c_0_5067,plain,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3401]) ).

cnf(c_0_5068,plain,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3402]) ).

cnf(c_0_5069,plain,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3403]) ).

cnf(c_0_5070,plain,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3404]) ).

cnf(c_0_5071,plain,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3405]) ).

cnf(c_0_5072,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3406]) ).

cnf(c_0_5073,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3407]) ).

cnf(c_0_5074,plain,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3408]) ).

cnf(c_0_5075,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3409]) ).

cnf(c_0_5076,plain,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3410]) ).

cnf(c_0_5077,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3411]) ).

cnf(c_0_5078,plain,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3412]) ).

cnf(c_0_5079,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3413]) ).

cnf(c_0_5080,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3414]) ).

cnf(c_0_5081,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3415]) ).

cnf(c_0_5082,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3416]) ).

cnf(c_0_5083,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[c_0_3417]) ).

cnf(c_0_5084,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3418]) ).

cnf(c_0_5085,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3419]) ).

cnf(c_0_5086,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3420]) ).

cnf(c_0_5087,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3421]) ).

cnf(c_0_5088,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3422]) ).

cnf(c_0_5089,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3423]) ).

cnf(c_0_5090,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3424]) ).

cnf(c_0_5091,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3425]) ).

cnf(c_0_5092,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3426]) ).

cnf(c_0_5093,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3427]) ).

cnf(c_0_5094,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3428]) ).

cnf(c_0_5095,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3429]) ).

cnf(c_0_5096,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3430]) ).

cnf(c_0_5097,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3431]) ).

cnf(c_0_5098,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3432]) ).

cnf(c_0_5099,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3433]) ).

cnf(c_0_5100,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3434]) ).

cnf(c_0_5101,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3435]) ).

cnf(c_0_5102,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3436]) ).

cnf(c_0_5103,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3437]) ).

cnf(c_0_5104,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3438]) ).

cnf(c_0_5105,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3439]) ).

cnf(c_0_5106,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3440]) ).

cnf(c_0_5107,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3441]) ).

cnf(c_0_5108,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3442]) ).

cnf(c_0_5109,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3443]) ).

cnf(c_0_5110,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3444]) ).

cnf(c_0_5111,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3445]) ).

cnf(c_0_5112,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3446]) ).

cnf(c_0_5113,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3447]) ).

cnf(c_0_5114,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3448]) ).

cnf(c_0_5115,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3449]) ).

cnf(c_0_5116,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3450]) ).

cnf(c_0_5117,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3451]) ).

cnf(c_0_5118,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[c_0_3452]) ).

cnf(c_0_5119,plain,
    class_Rings_Odvd(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3453]) ).

cnf(c_0_5120,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3454]) ).

cnf(c_0_5121,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3455]) ).

cnf(c_0_5122,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3456]) ).

cnf(c_0_5123,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3457]) ).

cnf(c_0_5124,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3458]) ).

cnf(c_0_5125,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3459]) ).

cnf(c_0_5126,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3460]) ).

cnf(c_0_5127,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3461]) ).

cnf(c_0_5128,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3462]) ).

cnf(c_0_5129,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3463]) ).

cnf(c_0_5130,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3464]) ).

cnf(c_0_5131,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3465]) ).

cnf(c_0_5132,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3466]) ).

cnf(c_0_5133,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3467]) ).

cnf(c_0_5134,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3468]) ).

cnf(c_0_5135,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3469]) ).

cnf(c_0_5136,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3470]) ).

cnf(c_0_5137,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3471]) ).

cnf(c_0_5138,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3472]) ).

cnf(c_0_5139,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3473]) ).

cnf(c_0_5140,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3474]) ).

cnf(c_0_5141,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3475]) ).

cnf(c_0_5142,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3476]) ).

cnf(c_0_5143,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3477]) ).

cnf(c_0_5144,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3478]) ).

cnf(c_0_5145,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3479]) ).

cnf(c_0_5146,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3480]) ).

cnf(c_0_5147,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3481]) ).

cnf(c_0_5148,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3482]) ).

cnf(c_0_5149,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3483]) ).

cnf(c_0_5150,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3484]) ).

cnf(c_0_5151,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3485]) ).

cnf(c_0_5152,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3486]) ).

cnf(c_0_5153,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3487]) ).

cnf(c_0_5154,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3488]) ).

cnf(c_0_5155,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3489]) ).

cnf(c_0_5156,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3490]) ).

cnf(c_0_5157,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3491]) ).

cnf(c_0_5158,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3492]) ).

cnf(c_0_5159,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3493]) ).

cnf(c_0_5160,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3494]) ).

cnf(c_0_5161,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3495]) ).

cnf(c_0_5162,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3496]) ).

cnf(c_0_5163,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3497]) ).

cnf(c_0_5164,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3498]) ).

cnf(c_0_5165,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3499]) ).

cnf(c_0_5166,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3500]) ).

cnf(c_0_5167,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3501]) ).

cnf(c_0_5168,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3502]) ).

cnf(c_0_5169,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3503]) ).

cnf(c_0_5170,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3504]) ).

cnf(c_0_5171,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3505]) ).

cnf(c_0_5172,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3506]) ).

cnf(c_0_5173,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3507]) ).

cnf(c_0_5174,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(split_conjunct,[status(thm)],[c_0_3508]) ).

cnf(c_0_5175,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[c_0_3509]) ).

cnf(c_0_5176,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[c_0_3510]) ).

cnf(c_0_5177,plain,
    c_Int_OPls != c_Int_OMin,
    inference(split_conjunct,[status(thm)],[c_0_3511]) ).

cnf(c_0_5178,plain,
    c_Int_OMin != c_Int_OPls,
    inference(split_conjunct,[status(thm)],[c_0_3512]) ).

cnf(c_0_5179,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(X1,X3,X5)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X5)),c_Groups_Otimes__class_Otimes(X1,X4,c_Groups_Ominus__class_Ominus(X1,X3,X5))) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_3513,
    [final] ).

cnf(c_0_5180,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5)) ),
    c_0_3514,
    [final] ).

cnf(c_0_5181,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5) ),
    c_0_3515,
    [final] ).

cnf(c_0_5182,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5)) ),
    c_0_3516,
    [final] ).

cnf(c_0_5183,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5) ),
    c_0_3517,
    [final] ).

cnf(c_0_5184,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6)) ),
    c_0_3518,
    [final] ).

cnf(c_0_5185,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4),X6) ),
    c_0_3519,
    [final] ).

cnf(c_0_5186,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4),X6) ),
    c_0_3520,
    [final] ).

cnf(c_0_5187,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6)) ),
    c_0_3521,
    [final] ).

cnf(c_0_5188,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5)) ),
    c_0_3522,
    [final] ).

cnf(c_0_5189,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)) ),
    c_0_3523,
    [final] ).

cnf(c_0_5190,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5)) ),
    c_0_3524,
    [final] ).

cnf(c_0_5191,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)) ),
    c_0_3525,
    [final] ).

cnf(c_0_5192,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6)) ),
    c_0_3526,
    [final] ).

cnf(c_0_5193,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5),X6)
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6)) ),
    c_0_3527,
    [final] ).

cnf(c_0_5194,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5),X6)
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6)) ),
    c_0_3528,
    [final] ).

cnf(c_0_5195,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6)) ),
    c_0_3529,
    [final] ).

cnf(c_0_5196,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3),
    c_0_3530,
    [final] ).

cnf(c_0_5197,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_3531,
    [final] ).

cnf(c_0_5198,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),X3)) = c_Power_Opower__class_Opower(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_3532,
    [final] ).

cnf(c_0_5199,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),X3)) = c_Power_Opower__class_Opower(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_3533,
    [final] ).

cnf(c_0_5200,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),X2)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    c_0_3534,
    [final] ).

cnf(c_0_5201,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_3535,
    [final] ).

cnf(c_0_5202,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    c_0_3536,
    [final] ).

cnf(c_0_5203,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3537,
    [final] ).

cnf(c_0_5204,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3538,
    [final] ).

cnf(c_0_5205,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1),X2),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
    c_0_3539,
    [final] ).

cnf(c_0_5206,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4),X2),X3),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
    c_0_3540,
    [final] ).

cnf(c_0_5207,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_3541,
    [final] ).

cnf(c_0_5208,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5)) ),
    c_0_3542,
    [final] ).

cnf(c_0_5209,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5)) ),
    c_0_3543,
    [final] ).

cnf(c_0_5210,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6) ),
    c_0_3544,
    [final] ).

cnf(c_0_5211,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5) ),
    c_0_3545,
    [final] ).

cnf(c_0_5212,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X2)),X4)) ),
    c_0_3546,
    [final] ).

cnf(c_0_5213,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2)))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    c_0_3547,
    [final] ).

cnf(c_0_5214,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X3)) ),
    c_0_3548,
    [final] ).

cnf(c_0_5215,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5)) ),
    c_0_3549,
    [final] ).

cnf(c_0_5216,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    c_0_3550,
    [final] ).

cnf(c_0_5217,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
    c_0_3551,
    [final] ).

cnf(c_0_5218,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
    c_0_3552,
    [final] ).

cnf(c_0_5219,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)),X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    c_0_3553,
    [final] ).

cnf(c_0_5220,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    c_0_3554,
    [final] ).

cnf(c_0_5221,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2)),X5))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X5)) ),
    c_0_3555,
    [final] ).

cnf(c_0_5222,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_3556,
    [final] ).

cnf(c_0_5223,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X3))) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3557,
    [final] ).

cnf(c_0_5224,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
    c_0_3558,
    [final] ).

cnf(c_0_5225,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1(X1) ),
    c_0_3559,
    [final] ).

cnf(c_0_5226,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    c_0_3560,
    [final] ).

cnf(c_0_5227,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    c_0_3561,
    [final] ).

cnf(c_0_5228,plain,
    ( epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk18_3(X3,X2,X1)),esk19_3(X3,X2,X1)) = X2
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk20_3(X3,X2,X1)),esk21_3(X3,X2,X1)) = X2 ),
    c_0_3562,
    [final] ).

cnf(c_0_5229,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_3563,
    [final] ).

cnf(c_0_5230,plain,
    ( hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,esk8_3(X3,X2,X1))))
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(X2,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1))) ),
    c_0_3564,
    [final] ).

cnf(c_0_5231,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_3565,
    [final] ).

cnf(c_0_5232,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_3566,
    [final] ).

cnf(c_0_5233,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_3567,
    [final] ).

cnf(c_0_5234,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_3568,
    [final] ).

cnf(c_0_5235,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X4 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5) ),
    c_0_3569,
    [final] ).

cnf(c_0_5236,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4) != X5 ),
    c_0_3570,
    [final] ).

cnf(c_0_5237,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X5)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X5)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ class_Rings_Oring(X1) ),
    c_0_3571,
    [final] ).

cnf(c_0_5238,plain,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X3),c_Groups_Otimes__class_Otimes(X1,X2,X2))) ),
    c_0_3572,
    [final] ).

cnf(c_0_5239,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3573,
    [final] ).

cnf(c_0_5240,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3574,
    [final] ).

cnf(c_0_5241,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring(X1) ),
    c_0_3575,
    [final] ).

cnf(c_0_5242,plain,
    ( X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5) ),
    c_0_3576,
    [final] ).

cnf(c_0_5243,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4) = X5
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5) ),
    c_0_3577,
    [final] ).

cnf(c_0_5244,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)))
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_3578,
    [final] ).

cnf(c_0_5245,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)
    | ~ class_Rings_Oring(X1)
    | X4 != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6) ),
    c_0_3579,
    [final] ).

cnf(c_0_5246,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)
    | ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4) != X6 ),
    c_0_3580,
    [final] ).

cnf(c_0_5247,plain,
    ( epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk18_3(X3,X2,X1)),esk19_3(X3,X2,X1)) = X2
    | ~ hBOOL(hAPP(X1,esk21_3(X3,X2,X1))) ),
    c_0_3581,
    [final] ).

cnf(c_0_5248,plain,
    ( epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk20_3(X3,X2,X1)),esk21_3(X3,X2,X1)) = X2
    | ~ hBOOL(hAPP(X1,esk19_3(X3,X2,X1))) ),
    c_0_3582,
    [final] ).

cnf(c_0_5249,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    c_0_3583,
    [final] ).

cnf(c_0_5250,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)),c_Groups_Ozero__class_Ozero(X2))
    | ~ class_Rings_Olinordered__idom(X2) ),
    c_0_3584,
    [final] ).

cnf(c_0_5251,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    c_0_3585,
    [final] ).

cnf(c_0_5252,plain,
    ( X2 = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6)
    | ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6) ),
    c_0_3586,
    [final] ).

cnf(c_0_5253,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5) = X6
    | ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6) ),
    c_0_3587,
    [final] ).

cnf(c_0_5254,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3588,
    [final] ).

cnf(c_0_5255,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3589,
    [final] ).

cnf(c_0_5256,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3),X5)
    | ~ class_Rings_Osemiring(X1) ),
    c_0_3590,
    [final] ).

cnf(c_0_5257,plain,
    ( X2 = X3
    | X4 = X5
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X5,X3)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X5,X2)) ),
    c_0_3591,
    [final] ).

cnf(c_0_5258,plain,
    ( X3 = X5
    | X2 = X4
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    c_0_3592,
    [final] ).

cnf(c_0_5259,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2),X4),
    c_0_3593,
    [final] ).

cnf(c_0_5260,plain,
    ( epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,esk19_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(X1,esk21_3(X3,X2,X1))) ),
    c_0_3594,
    [final] ).

cnf(c_0_5261,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_3595,
    [final] ).

cnf(c_0_5262,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),X3)) ),
    c_0_3596,
    [final] ).

cnf(c_0_5263,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,esk7_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))) ),
    c_0_3597,
    [final] ).

cnf(c_0_5264,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3598,
    [final] ).

cnf(c_0_5265,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ class_Divides_Oring__div(X1) ),
    c_0_3599,
    [final] ).

cnf(c_0_5266,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3600,
    [final] ).

cnf(c_0_5267,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X3),X2),
    c_0_3601,
    [final] ).

cnf(c_0_5268,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_3602,
    [final] ).

cnf(c_0_5269,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_3603,
    [final] ).

cnf(c_0_5270,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    c_0_3604,
    [final] ).

cnf(c_0_5271,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    c_0_3605,
    [final] ).

cnf(c_0_5272,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X3,X2,X1))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk20_3(X3,X2,X1)),esk21_3(X3,X2,X1)) = X2 ),
    c_0_3606,
    [final] ).

cnf(c_0_5273,plain,
    ( epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk18_3(X3,X2,X1)),esk19_3(X3,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_3607,
    [final] ).

cnf(c_0_5274,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X3,X2,X1),X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk20_3(X3,X2,X1)),esk21_3(X3,X2,X1)) = X2 ),
    c_0_3608,
    [final] ).

cnf(c_0_5275,plain,
    ( epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk18_3(X3,X2,X1)),esk19_3(X3,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,esk21_3(X3,X2,X1)) ),
    c_0_3609,
    [final] ).

cnf(c_0_5276,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3610,
    [final] ).

cnf(c_0_5277,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,esk15_3(X3,X2,X1))) ),
    c_0_3611,
    [final] ).

cnf(c_0_5278,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,esk14_3(X3,X2,X1))) ),
    c_0_3612,
    [final] ).

cnf(c_0_5279,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(X1,esk15_3(X3,X2,X1))) ),
    c_0_3613,
    [final] ).

cnf(c_0_5280,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(X1,esk14_3(X3,X2,X1))) ),
    c_0_3614,
    [final] ).

cnf(c_0_5281,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X5,X6),X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3615,
    [final] ).

cnf(c_0_5282,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X5,X6),X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | ~ class_Divides_Oring__div(X1) ),
    c_0_3616,
    [final] ).

cnf(c_0_5283,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X5,X6),X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3617,
    [final] ).

cnf(c_0_5284,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(X1,X3,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    c_0_3618,
    [final] ).

cnf(c_0_5285,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_3619,
    [final] ).

cnf(c_0_5286,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    c_0_3620,
    [final] ).

cnf(c_0_5287,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X5)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3621,
    [final] ).

cnf(c_0_5288,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,X4,c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3622,
    [final] ).

cnf(c_0_5289,plain,
    ( hBOOL(hAPP(X2,esk7_3(X3,X2,X1)))
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))) ),
    c_0_3623,
    [final] ).

cnf(c_0_5290,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3624,
    [final] ).

cnf(c_0_5291,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3625,
    [final] ).

cnf(c_0_5292,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3626,
    [final] ).

cnf(c_0_5293,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3627,
    [final] ).

cnf(c_0_5294,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    c_0_3628,
    [final] ).

cnf(c_0_5295,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    c_0_3629,
    [final] ).

cnf(c_0_5296,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    c_0_3630,
    [final] ).

cnf(c_0_5297,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
    c_0_3631,
    [final] ).

cnf(c_0_5298,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
    c_0_3632,
    [final] ).

cnf(c_0_5299,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_3633,
    [final] ).

cnf(c_0_5300,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))) ),
    c_0_3634,
    [final] ).

cnf(c_0_5301,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ epred1_3(X1,X2,X3)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    c_0_3635,
    [final] ).

cnf(c_0_5302,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ epred1_3(X1,X2,X3)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_3636,
    [final] ).

cnf(c_0_5303,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_3637,
    [final] ).

cnf(c_0_5304,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X4)),c_Power_Opower__class_Opower(X1,X3,c_Nat_OSuc(X4)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3638,
    [final] ).

cnf(c_0_5305,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X2,X4),c_Divides_Odiv__class_Odiv(X1,X3,X4)) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3639,
    [final] ).

cnf(c_0_5306,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    c_0_3640,
    [final] ).

cnf(c_0_5307,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    c_0_3641,
    [final] ).

cnf(c_0_5308,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
    | ~ class_Rings_Olinordered__ring(X1) ),
    c_0_3642,
    [final] ).

cnf(c_0_5309,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X3,X2,X1))
    | ~ hBOOL(hAPP(X1,esk21_3(X3,X2,X1))) ),
    c_0_3643,
    [final] ).

cnf(c_0_5310,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ hBOOL(hAPP(X1,esk19_3(X3,X2,X1))) ),
    c_0_3644,
    [final] ).

cnf(c_0_5311,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X3,X2,X1),X3)
    | ~ hBOOL(hAPP(X1,esk21_3(X3,X2,X1))) ),
    c_0_3645,
    [final] ).

cnf(c_0_5312,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,esk21_3(X3,X2,X1))
    | ~ hBOOL(hAPP(X1,esk19_3(X3,X2,X1))) ),
    c_0_3646,
    [final] ).

cnf(c_0_5313,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk20_3(X3,X2,X1)),esk21_3(X3,X2,X1)) = X2 ),
    c_0_3647,
    [final] ).

cnf(c_0_5314,plain,
    ( epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk18_3(X3,X2,X1)),esk19_3(X3,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_3648,
    [final] ).

cnf(c_0_5315,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3649,
    [final] ).

cnf(c_0_5316,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3650,
    [final] ).

cnf(c_0_5317,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    c_0_3651,
    [final] ).

cnf(c_0_5318,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    c_0_3652,
    [final] ).

cnf(c_0_5319,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring(X1) ),
    c_0_3653,
    [final] ).

cnf(c_0_5320,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3654,
    [final] ).

cnf(c_0_5321,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring(X1) ),
    c_0_3655,
    [final] ).

cnf(c_0_5322,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3656,
    [final] ).

cnf(c_0_5323,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3657,
    [final] ).

cnf(c_0_5324,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3658,
    [final] ).

cnf(c_0_5325,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    c_0_3659,
    [final] ).

cnf(c_0_5326,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    c_0_3660,
    [final] ).

cnf(c_0_5327,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    c_0_3661,
    [final] ).

cnf(c_0_5328,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
    | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
    | ~ class_Rings_Olinordered__semidom(X3) ),
    c_0_3662,
    [final] ).

cnf(c_0_5329,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    c_0_3663,
    [final] ).

cnf(c_0_5330,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
    | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
    | ~ class_Rings_Olinordered__semidom(X3) ),
    c_0_3664,
    [final] ).

cnf(c_0_5331,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4))
    | ~ class_Rings_Oring(X1)
    | ~ class_Int_Onumber(X1) ),
    c_0_3665,
    [final] ).

cnf(c_0_5332,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,X3,X4))
    | ~ class_Rings_Oring(X1)
    | ~ class_Int_Onumber(X1) ),
    c_0_3666,
    [final] ).

cnf(c_0_5333,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4))
    | ~ class_Rings_Osemiring(X1)
    | ~ class_Int_Onumber(X1) ),
    c_0_3667,
    [final] ).

cnf(c_0_5334,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Rings_Osemiring(X1)
    | ~ class_Int_Onumber(X1) ),
    c_0_3668,
    [final] ).

cnf(c_0_5335,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_3669,
    [final] ).

cnf(c_0_5336,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    c_0_3670,
    [final] ).

cnf(c_0_5337,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    c_0_3671,
    [final] ).

cnf(c_0_5338,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X2)) ),
    c_0_3672,
    [final] ).

cnf(c_0_5339,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)) ),
    c_0_3673,
    [final] ).

cnf(c_0_5340,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    c_0_3674,
    [final] ).

cnf(c_0_5341,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)) ),
    c_0_3675,
    [final] ).

cnf(c_0_5342,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    c_0_3676,
    [final] ).

cnf(c_0_5343,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3)) ),
    c_0_3677,
    [final] ).

cnf(c_0_5344,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)) ),
    c_0_3678,
    [final] ).

cnf(c_0_5345,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    c_0_3679,
    [final] ).

cnf(c_0_5346,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    c_0_3680,
    [final] ).

cnf(c_0_5347,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    c_0_3681,
    [final] ).

cnf(c_0_5348,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
    c_0_3682,
    [final] ).

cnf(c_0_5349,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3683,
    [final] ).

cnf(c_0_5350,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3684,
    [final] ).

cnf(c_0_5351,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    c_0_3685,
    [final] ).

cnf(c_0_5352,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    c_0_3686,
    [final] ).

cnf(c_0_5353,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 != X4 ),
    c_0_3687,
    [final] ).

cnf(c_0_5354,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != X5 ),
    c_0_3688,
    [final] ).

cnf(c_0_5355,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 != X4 ),
    c_0_3689,
    [final] ).

cnf(c_0_5356,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != X5 ),
    c_0_3690,
    [final] ).

cnf(c_0_5357,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3691,
    [final] ).

cnf(c_0_5358,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    c_0_3692,
    [final] ).

cnf(c_0_5359,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    c_0_3693,
    [final] ).

cnf(c_0_5360,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    c_0_3694,
    [final] ).

cnf(c_0_5361,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    c_0_3695,
    [final] ).

cnf(c_0_5362,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3696,
    [final] ).

cnf(c_0_5363,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3697,
    [final] ).

cnf(c_0_5364,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3698,
    [final] ).

cnf(c_0_5365,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ class_Divides_Oring__div(X1) ),
    c_0_3699,
    [final] ).

cnf(c_0_5366,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ class_Divides_Oring__div(X1) ),
    c_0_3700,
    [final] ).

cnf(c_0_5367,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3701,
    [final] ).

cnf(c_0_5368,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3702,
    [final] ).

cnf(c_0_5369,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3703,
    [final] ).

cnf(c_0_5370,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3704,
    [final] ).

cnf(c_0_5371,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3705,
    [final] ).

cnf(c_0_5372,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3706,
    [final] ).

cnf(c_0_5373,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    c_0_3707,
    [final] ).

cnf(c_0_5374,plain,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    c_0_3708,
    [final] ).

cnf(c_0_5375,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    c_0_3709,
    [final] ).

cnf(c_0_5376,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_3710,
    [final] ).

cnf(c_0_5377,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_3711,
    [final] ).

cnf(c_0_5378,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_3712,
    [final] ).

cnf(c_0_5379,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2) = c_Power_Opower__class_Opower(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_3713,
    [final] ).

cnf(c_0_5380,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3714,
    [final] ).

cnf(c_0_5381,plain,
    ( X4 = X6
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) != c_Groups_Oplus__class_Oplus(X1,X5,c_Groups_Otimes__class_Otimes(X1,X3,X6))
    | X2 != X5
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    c_0_3715,
    [final] ).

cnf(c_0_5382,plain,
    ( c_Divides_Odiv__class_Odiv(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4)) = c_Power_Opower__class_Opower(X1,c_Divides_Odiv__class_Odiv(X1,X2,X3),X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3716,
    [final] ).

cnf(c_0_5383,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_3717,
    [final] ).

cnf(c_0_5384,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_3718,
    [final] ).

cnf(c_0_5385,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | c_Power_Opower__class_Opower(X3,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    c_0_3719,
    [final] ).

cnf(c_0_5386,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3),
    c_0_3720,
    [final] ).

cnf(c_0_5387,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3),
    c_0_3721,
    [final] ).

cnf(c_0_5388,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),X3),
    c_0_3722,
    [final] ).

cnf(c_0_5389,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3),X2),
    c_0_3723,
    [final] ).

cnf(c_0_5390,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3),X2),
    c_0_3724,
    [final] ).

cnf(c_0_5391,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    c_0_3725,
    [final] ).

cnf(c_0_5392,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    c_0_3726,
    [final] ).

cnf(c_0_5393,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    c_0_3727,
    [final] ).

cnf(c_0_5394,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    c_0_3728,
    [final] ).

cnf(c_0_5395,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X5),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3729,
    [final] ).

cnf(c_0_5396,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2)) ),
    c_0_3730,
    [final] ).

cnf(c_0_5397,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2)) ),
    c_0_3731,
    [final] ).

cnf(c_0_5398,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2))) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_3732,
    [final] ).

cnf(c_0_5399,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ hBOOL(hAPP(X1,esk21_3(X3,X2,X1))) ),
    c_0_3733,
    [final] ).

cnf(c_0_5400,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ hBOOL(hAPP(X1,esk19_3(X3,X2,X1))) ),
    c_0_3734,
    [final] ).

cnf(c_0_5401,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    c_0_3735,
    [final] ).

cnf(c_0_5402,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    c_0_3736,
    [final] ).

cnf(c_0_5403,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
    c_0_3737,
    [final] ).

cnf(c_0_5404,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
    c_0_3738,
    [final] ).

cnf(c_0_5405,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | X4 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) ),
    c_0_3739,
    [final] ).

cnf(c_0_5406,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | X4 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    c_0_3740,
    [final] ).

cnf(c_0_5407,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
    c_0_3741,
    [final] ).

cnf(c_0_5408,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
    c_0_3742,
    [final] ).

cnf(c_0_5409,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_3743,
    [final] ).

cnf(c_0_5410,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3744,
    [final] ).

cnf(c_0_5411,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    c_0_3745,
    [final] ).

cnf(c_0_5412,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    c_0_3746,
    [final] ).

cnf(c_0_5413,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    c_0_3747,
    [final] ).

cnf(c_0_5414,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    c_0_3748,
    [final] ).

cnf(c_0_5415,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    c_0_3749,
    [final] ).

cnf(c_0_5416,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    c_0_3750,
    [final] ).

cnf(c_0_5417,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    c_0_3751,
    [final] ).

cnf(c_0_5418,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    c_0_3752,
    [final] ).

cnf(c_0_5419,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1)) != X3
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    c_0_3753,
    [final] ).

cnf(c_0_5420,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    c_0_3754,
    [final] ).

cnf(c_0_5421,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1)) != X3
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    c_0_3755,
    [final] ).

cnf(c_0_5422,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    c_0_3756,
    [final] ).

cnf(c_0_5423,plain,
    ( c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_3757,
    [final] ).

cnf(c_0_5424,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_3758,
    [final] ).

cnf(c_0_5425,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
    c_0_3759,
    [final] ).

cnf(c_0_5426,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
    c_0_3760,
    [final] ).

cnf(c_0_5427,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1)) ),
    c_0_3761,
    [final] ).

cnf(c_0_5428,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X3),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X3)) ),
    c_0_3762,
    [final] ).

cnf(c_0_5429,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3),c_Power_Opower__class_Opower(tc_Int_Oint,X2,X3)) ),
    c_0_3763,
    [final] ).

cnf(c_0_5430,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X1),c_Power_Opower__class_Opower(tc_Int_Oint,X3,X1)) ),
    c_0_3764,
    [final] ).

cnf(c_0_5431,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1))) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Oring__1(X1) ),
    c_0_3765,
    [final] ).

cnf(c_0_5432,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2)) ),
    c_0_3766,
    [final] ).

cnf(c_0_5433,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)) ),
    c_0_3767,
    [final] ).

cnf(c_0_5434,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    c_0_3768,
    [final] ).

cnf(c_0_5435,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    c_0_3769,
    [final] ).

cnf(c_0_5436,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    c_0_3770,
    [final] ).

cnf(c_0_5437,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    c_0_3771,
    [final] ).

cnf(c_0_5438,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
    c_0_3772,
    [final] ).

cnf(c_0_5439,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    c_0_3773,
    [final] ).

cnf(c_0_5440,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    c_0_3774,
    [final] ).

cnf(c_0_5441,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
    c_0_3775,
    [final] ).

cnf(c_0_5442,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Rings_Olinordered__semidom(X4) ),
    c_0_3776,
    [final] ).

cnf(c_0_5443,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
    c_0_3777,
    [final] ).

cnf(c_0_5444,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
    c_0_3778,
    [final] ).

cnf(c_0_5445,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3779,
    [final] ).

cnf(c_0_5446,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    c_0_3780,
    [final] ).

cnf(c_0_5447,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    c_0_3781,
    [final] ).

cnf(c_0_5448,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Oordered__comm__semiring(X1) ),
    c_0_3782,
    [final] ).

cnf(c_0_5449,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
    | ~ class_Rings_Oordered__ring(X1) ),
    c_0_3783,
    [final] ).

cnf(c_0_5450,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
    | ~ class_Rings_Oordered__ring(X1) ),
    c_0_3784,
    [final] ).

cnf(c_0_5451,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    c_0_3785,
    [final] ).

cnf(c_0_5452,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3786,
    [final] ).

cnf(c_0_5453,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    c_0_3787,
    [final] ).

cnf(c_0_5454,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3788,
    [final] ).

cnf(c_0_5455,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    c_0_3789,
    [final] ).

cnf(c_0_5456,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3) ),
    c_0_3790,
    [final] ).

cnf(c_0_5457,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3791,
    [final] ).

cnf(c_0_5458,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3792,
    [final] ).

cnf(c_0_5459,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1) ),
    c_0_3793,
    [final] ).

cnf(c_0_5460,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    c_0_3794,
    [final] ).

cnf(c_0_5461,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    c_0_3795,
    [final] ).

cnf(c_0_5462,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_3796,
    [final] ).

cnf(c_0_5463,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_3797,
    [final] ).

cnf(c_0_5464,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk15_3(X3,X2,X1)) = X2
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    c_0_3798,
    [final] ).

cnf(c_0_5465,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk14_3(X3,X2,X1)) = X2
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    c_0_3799,
    [final] ).

cnf(c_0_5466,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) ),
    c_0_3800,
    [final] ).

cnf(c_0_5467,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3801,
    [final] ).

cnf(c_0_5468,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
    c_0_3802,
    [final] ).

cnf(c_0_5469,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3803,
    [final] ).

cnf(c_0_5470,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    c_0_3804,
    [final] ).

cnf(c_0_5471,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk15_3(X3,X2,X1)) = X2 ),
    c_0_3805,
    [final] ).

cnf(c_0_5472,plain,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,esk14_3(X3,X2,X1)) = X2 ),
    c_0_3806,
    [final] ).

cnf(c_0_5473,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    c_0_3807,
    [final] ).

cnf(c_0_5474,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    c_0_3808,
    [final] ).

cnf(c_0_5475,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    c_0_3809,
    [final] ).

cnf(c_0_5476,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    c_0_3810,
    [final] ).

cnf(c_0_5477,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_3811,
    [final] ).

cnf(c_0_5478,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_3812,
    [final] ).

cnf(c_0_5479,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    c_0_3813,
    [final] ).

cnf(c_0_5480,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_3814,
    [final] ).

cnf(c_0_5481,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3815,
    [final] ).

cnf(c_0_5482,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(X1,X2,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Power_Opower(X1) ),
    c_0_3816,
    [final] ).

cnf(c_0_5483,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_3817,
    [final] ).

cnf(c_0_5484,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3818,
    [final] ).

cnf(c_0_5485,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_3819,
    [final] ).

cnf(c_0_5486,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_3820,
    [final] ).

cnf(c_0_5487,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3821,
    [final] ).

cnf(c_0_5488,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    c_0_3822,
    [final] ).

cnf(c_0_5489,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3823,
    [final] ).

cnf(c_0_5490,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3824,
    [final] ).

cnf(c_0_5491,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3825,
    [final] ).

cnf(c_0_5492,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3826,
    [final] ).

cnf(c_0_5493,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_3827,
    [final] ).

cnf(c_0_5494,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_3828,
    [final] ).

cnf(c_0_5495,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_3829,
    [final] ).

cnf(c_0_5496,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_3830,
    [final] ).

cnf(c_0_5497,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4)) = c_Power_Opower__class_Opower(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    c_0_3831,
    [final] ).

cnf(c_0_5498,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3832,
    [final] ).

cnf(c_0_5499,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_3833,
    [final] ).

cnf(c_0_5500,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_3834,
    [final] ).

cnf(c_0_5501,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3835,
    [final] ).

cnf(c_0_5502,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Rings_Ocomm__semiring(X1) ),
    c_0_3836,
    [final] ).

cnf(c_0_5503,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_3837,
    [final] ).

cnf(c_0_5504,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3838,
    [final] ).

cnf(c_0_5505,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_3839,
    [final] ).

cnf(c_0_5506,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4)) = c_Power_Opower__class_Opower(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3840,
    [final] ).

cnf(c_0_5507,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    c_0_3841,
    [final] ).

cnf(c_0_5508,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    c_0_3842,
    [final] ).

cnf(c_0_5509,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_3843,
    [final] ).

cnf(c_0_5510,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3844,
    [final] ).

cnf(c_0_5511,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
    c_0_3845,
    [final] ).

cnf(c_0_5512,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1) ),
    c_0_3846,
    [final] ).

cnf(c_0_5513,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
    c_0_3847,
    [final] ).

cnf(c_0_5514,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    c_0_3848,
    [final] ).

cnf(c_0_5515,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    c_0_3849,
    [final] ).

cnf(c_0_5516,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    c_0_3850,
    [final] ).

cnf(c_0_5517,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    c_0_3851,
    [final] ).

cnf(c_0_5518,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    c_0_3852,
    [final] ).

cnf(c_0_5519,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    c_0_3853,
    [final] ).

cnf(c_0_5520,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    c_0_3854,
    [final] ).

cnf(c_0_5521,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    c_0_3855,
    [final] ).

cnf(c_0_5522,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    c_0_3856,
    [final] ).

cnf(c_0_5523,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_3857,
    [final] ).

cnf(c_0_5524,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
    c_0_3858,
    [final] ).

cnf(c_0_5525,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_3859,
    [final] ).

cnf(c_0_5526,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_3860,
    [final] ).

cnf(c_0_5527,plain,
    ( epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))) ),
    c_0_3861,
    [final] ).

cnf(c_0_5528,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
    c_0_3862,
    [final] ).

cnf(c_0_5529,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    c_0_3863,
    [final] ).

cnf(c_0_5530,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    c_0_3864,
    [final] ).

cnf(c_0_5531,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
    c_0_3865,
    [final] ).

cnf(c_0_5532,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    c_0_3866,
    [final] ).

cnf(c_0_5533,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    c_0_3867,
    [final] ).

cnf(c_0_5534,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    c_0_3868,
    [final] ).

cnf(c_0_5535,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X3,X2))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3869,
    [final] ).

cnf(c_0_5536,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3870,
    [final] ).

cnf(c_0_5537,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_3871,
    [final] ).

cnf(c_0_5538,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    c_0_3872,
    [final] ).

cnf(c_0_5539,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    c_0_3873,
    [final] ).

cnf(c_0_5540,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    c_0_3874,
    [final] ).

cnf(c_0_5541,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_3875,
    [final] ).

cnf(c_0_5542,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2))),
    c_0_3876,
    [final] ).

cnf(c_0_5543,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    c_0_3877,
    [final] ).

cnf(c_0_5544,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    c_0_3878,
    [final] ).

cnf(c_0_5545,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2),
    c_0_3879,
    [final] ).

cnf(c_0_5546,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X3),
    c_0_3880,
    [final] ).

cnf(c_0_5547,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)),
    c_0_3881,
    [final] ).

cnf(c_0_5548,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3),
    c_0_3882,
    [final] ).

cnf(c_0_5549,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
    c_0_3883,
    [final] ).

cnf(c_0_5550,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),
    c_0_3884,
    [final] ).

cnf(c_0_5551,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)),
    c_0_3885,
    [final] ).

cnf(c_0_5552,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),X3),
    c_0_3886,
    [final] ).

cnf(c_0_5553,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3),
    c_0_3887,
    [final] ).

cnf(c_0_5554,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
    c_0_3888,
    [final] ).

cnf(c_0_5555,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),
    c_0_3889,
    [final] ).

cnf(c_0_5556,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    c_0_3890,
    [final] ).

cnf(c_0_5557,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2),c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3)) = c_Power_Opower__class_Opower(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    c_0_3891,
    [final] ).

cnf(c_0_5558,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | X3 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_3892,
    [final] ).

cnf(c_0_5559,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3893,
    [final] ).

cnf(c_0_5560,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    c_0_3894,
    [final] ).

cnf(c_0_5561,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
    c_0_3895,
    [final] ).

cnf(c_0_5562,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
    c_0_3896,
    [final] ).

cnf(c_0_5563,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2) ),
    c_0_3897,
    [final] ).

cnf(c_0_5564,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
    c_0_3898,
    [final] ).

cnf(c_0_5565,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3899,
    [final] ).

cnf(c_0_5566,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_3900,
    [final] ).

cnf(c_0_5567,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X4,X3)) ),
    c_0_3901,
    [final] ).

cnf(c_0_5568,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X3) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    c_0_3902,
    [final] ).

cnf(c_0_5569,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    c_0_3903,
    [final] ).

cnf(c_0_5570,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    c_0_3904,
    [final] ).

cnf(c_0_5571,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    c_0_3905,
    [final] ).

cnf(c_0_5572,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    c_0_3906,
    [final] ).

cnf(c_0_5573,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    c_0_3907,
    [final] ).

cnf(c_0_5574,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
    c_0_3908,
    [final] ).

cnf(c_0_5575,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    c_0_3909,
    [final] ).

cnf(c_0_5576,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)) ),
    c_0_3910,
    [final] ).

cnf(c_0_5577,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    c_0_3911,
    [final] ).

cnf(c_0_5578,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))) ),
    c_0_3912,
    [final] ).

cnf(c_0_5579,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    c_0_3913,
    [final] ).

cnf(c_0_5580,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    c_0_3914,
    [final] ).

cnf(c_0_5581,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    c_0_3915,
    [final] ).

cnf(c_0_5582,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)) ),
    c_0_3916,
    [final] ).

cnf(c_0_5583,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    c_0_3917,
    [final] ).

cnf(c_0_5584,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    c_0_3918,
    [final] ).

cnf(c_0_5585,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    c_0_3919,
    [final] ).

cnf(c_0_5586,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    c_0_3920,
    [final] ).

cnf(c_0_5587,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3921,
    [final] ).

cnf(c_0_5588,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3922,
    [final] ).

cnf(c_0_5589,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3923,
    [final] ).

cnf(c_0_5590,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3924,
    [final] ).

cnf(c_0_5591,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | c_Power_Opower__class_Opower(X3,X1,c_Nat_OSuc(X4)) != c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X4))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    c_0_3925,
    [final] ).

cnf(c_0_5592,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X2) ),
    c_0_3926,
    [final] ).

cnf(c_0_5593,plain,
    ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_3927,
    [final] ).

cnf(c_0_5594,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)) ),
    c_0_3928,
    [final] ).

cnf(c_0_5595,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) ),
    c_0_3929,
    [final] ).

cnf(c_0_5596,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_3930,
    [final] ).

cnf(c_0_5597,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3931,
    [final] ).

cnf(c_0_5598,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,esk21_3(X3,X2,X1)) ),
    c_0_3932,
    [final] ).

cnf(c_0_5599,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X3,X2,X1),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_3933,
    [final] ).

cnf(c_0_5600,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    c_0_3934,
    [final] ).

cnf(c_0_5601,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
    c_0_3935,
    [final] ).

cnf(c_0_5602,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X3,X2,X1),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,esk21_3(X3,X2,X1)) ),
    c_0_3936,
    [final] ).

cnf(c_0_5603,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_3937,
    [final] ).

cnf(c_0_5604,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3938,
    [final] ).

cnf(c_0_5605,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | ~ epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,X2)) ),
    c_0_3939,
    [final] ).

cnf(c_0_5606,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    c_0_3940,
    [final] ).

cnf(c_0_5607,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    c_0_3941,
    [final] ).

cnf(c_0_5608,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3942,
    [final] ).

cnf(c_0_5609,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_3943,
    [final] ).

cnf(c_0_5610,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    c_0_3944,
    [final] ).

cnf(c_0_5611,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    c_0_3945,
    [final] ).

cnf(c_0_5612,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    c_0_3946,
    [final] ).

cnf(c_0_5613,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    c_0_3947,
    [final] ).

cnf(c_0_5614,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3948,
    [final] ).

cnf(c_0_5615,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    c_0_3949,
    [final] ).

cnf(c_0_5616,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    c_0_3950,
    [final] ).

cnf(c_0_5617,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    c_0_3951,
    [final] ).

cnf(c_0_5618,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3952,
    [final] ).

cnf(c_0_5619,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    c_0_3953,
    [final] ).

cnf(c_0_5620,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3954,
    [final] ).

cnf(c_0_5621,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    c_0_3955,
    [final] ).

cnf(c_0_5622,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    c_0_3956,
    [final] ).

cnf(c_0_5623,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    c_0_3957,
    [final] ).

cnf(c_0_5624,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    c_0_3958,
    [final] ).

cnf(c_0_5625,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__ring(X1) ),
    c_0_3959,
    [final] ).

cnf(c_0_5626,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    c_0_3960,
    [final] ).

cnf(c_0_5627,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3961,
    [final] ).

cnf(c_0_5628,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    c_0_3962,
    [final] ).

cnf(c_0_5629,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3963,
    [final] ).

cnf(c_0_5630,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    c_0_3964,
    [final] ).

cnf(c_0_5631,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    c_0_3965,
    [final] ).

cnf(c_0_5632,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3966,
    [final] ).

cnf(c_0_5633,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3967,
    [final] ).

cnf(c_0_5634,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3968,
    [final] ).

cnf(c_0_5635,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    c_0_3969,
    [final] ).

cnf(c_0_5636,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    c_0_3970,
    [final] ).

cnf(c_0_5637,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X1))),
    c_0_3971,
    [final] ).

cnf(c_0_5638,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
    c_0_3972,
    [final] ).

cnf(c_0_5639,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    c_0_3973,
    [final] ).

cnf(c_0_5640,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    c_0_3974,
    [final] ).

cnf(c_0_5641,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
    c_0_3975,
    [final] ).

cnf(c_0_5642,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
    c_0_3976,
    [final] ).

cnf(c_0_5643,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    c_0_3977,
    [final] ).

cnf(c_0_5644,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    c_0_3978,
    [final] ).

cnf(c_0_5645,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3979,
    [final] ).

cnf(c_0_5646,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_3980,
    [final] ).

cnf(c_0_5647,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    c_0_3981,
    [final] ).

cnf(c_0_5648,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    c_0_3982,
    [final] ).

cnf(c_0_5649,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
    c_0_3983,
    [final] ).

cnf(c_0_5650,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
    c_0_3984,
    [final] ).

cnf(c_0_5651,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
    c_0_3985,
    [final] ).

cnf(c_0_5652,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3986,
    [final] ).

cnf(c_0_5653,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_3987,
    [final] ).

cnf(c_0_5654,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    c_0_3988,
    [final] ).

cnf(c_0_5655,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3)) ),
    c_0_3989,
    [final] ).

cnf(c_0_5656,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    c_0_3990,
    [final] ).

cnf(c_0_5657,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    c_0_3991,
    [final] ).

cnf(c_0_5658,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_3992,
    [final] ).

cnf(c_0_5659,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    c_0_3993,
    [final] ).

cnf(c_0_5660,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    c_0_3994,
    [final] ).

cnf(c_0_5661,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    c_0_3995,
    [final] ).

cnf(c_0_5662,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    c_0_3996,
    [final] ).

cnf(c_0_5663,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_3997,
    [final] ).

cnf(c_0_5664,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ class_Int_Onumber(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    c_0_3998,
    [final] ).

cnf(c_0_5665,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    c_0_3999,
    [final] ).

cnf(c_0_5666,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    c_0_4000,
    [final] ).

cnf(c_0_5667,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X1),c_Power_Opower__class_Opower(tc_Int_Oint,X3,X1))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
    c_0_4001,
    [final] ).

cnf(c_0_5668,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
    c_0_4002,
    [final] ).

cnf(c_0_5669,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4003,
    [final] ).

cnf(c_0_5670,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4004,
    [final] ).

cnf(c_0_5671,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    c_0_4005,
    [final] ).

cnf(c_0_5672,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2)) ),
    c_0_4006,
    [final] ).

cnf(c_0_5673,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2)) ),
    c_0_4007,
    [final] ).

cnf(c_0_5674,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    c_0_4008,
    [final] ).

cnf(c_0_5675,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    c_0_4009,
    [final] ).

cnf(c_0_5676,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    c_0_4010,
    [final] ).

cnf(c_0_5677,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    c_0_4011,
    [final] ).

cnf(c_0_5678,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
    c_0_4012,
    [final] ).

cnf(c_0_5679,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    c_0_4013,
    [final] ).

cnf(c_0_5680,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    c_0_4014,
    [final] ).

cnf(c_0_5681,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    c_0_4015,
    [final] ).

cnf(c_0_5682,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    c_0_4016,
    [final] ).

cnf(c_0_5683,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    c_0_4017,
    [final] ).

cnf(c_0_5684,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    c_0_4018,
    [final] ).

cnf(c_0_5685,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    c_0_4019,
    [final] ).

cnf(c_0_5686,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
    c_0_4020,
    [final] ).

cnf(c_0_5687,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    c_0_4021,
    [final] ).

cnf(c_0_5688,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4022,
    [final] ).

cnf(c_0_5689,plain,
    ( X3 = X2
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    c_0_4023,
    [final] ).

cnf(c_0_5690,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4024,
    [final] ).

cnf(c_0_5691,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X2)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1)),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4025,
    [final] ).

cnf(c_0_5692,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4026,
    [final] ).

cnf(c_0_5693,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X4,X3))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
    c_0_4027,
    [final] ).

cnf(c_0_5694,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    c_0_4028,
    [final] ).

cnf(c_0_5695,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4029,
    [final] ).

cnf(c_0_5696,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) ),
    c_0_4030,
    [final] ).

cnf(c_0_5697,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),X1) ),
    c_0_4031,
    [final] ).

cnf(c_0_5698,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X1) ),
    c_0_4032,
    [final] ).

cnf(c_0_5699,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    c_0_4033,
    [final] ).

cnf(c_0_5700,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4034,
    [final] ).

cnf(c_0_5701,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4035,
    [final] ).

cnf(c_0_5702,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4036,
    [final] ).

cnf(c_0_5703,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4037,
    [final] ).

cnf(c_0_5704,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4038,
    [final] ).

cnf(c_0_5705,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4039,
    [final] ).

cnf(c_0_5706,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    c_0_4040,
    [final] ).

cnf(c_0_5707,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4041,
    [final] ).

cnf(c_0_5708,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4042,
    [final] ).

cnf(c_0_5709,plain,
    ( X2 = X3
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1) ),
    c_0_4043,
    [final] ).

cnf(c_0_5710,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4044,
    [final] ).

cnf(c_0_5711,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    c_0_4045,
    [final] ).

cnf(c_0_5712,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4046,
    [final] ).

cnf(c_0_5713,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4047,
    [final] ).

cnf(c_0_5714,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
    c_0_4048,
    [final] ).

cnf(c_0_5715,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4049,
    [final] ).

cnf(c_0_5716,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
    c_0_4050,
    [final] ).

cnf(c_0_5717,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4051,
    [final] ).

cnf(c_0_5718,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4052,
    [final] ).

cnf(c_0_5719,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Nat_OSuc(X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
    c_0_4053,
    [final] ).

cnf(c_0_5720,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    c_0_4054,
    [final] ).

cnf(c_0_5721,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    c_0_4055,
    [final] ).

cnf(c_0_5722,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_4056,
    [final] ).

cnf(c_0_5723,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oab__semigroup__add(X1) ),
    c_0_4057,
    [final] ).

cnf(c_0_5724,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Groups_Oab__semigroup__mult(X1) ),
    c_0_4058,
    [final] ).

cnf(c_0_5725,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4059,
    [final] ).

cnf(c_0_5726,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4060,
    [final] ).

cnf(c_0_5727,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4061,
    [final] ).

cnf(c_0_5728,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4062,
    [final] ).

cnf(c_0_5729,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4063,
    [final] ).

cnf(c_0_5730,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4064,
    [final] ).

cnf(c_0_5731,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4065,
    [final] ).

cnf(c_0_5732,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4066,
    [final] ).

cnf(c_0_5733,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ epred1_3(X1,X2,X3) ),
    c_0_4067,
    [final] ).

cnf(c_0_5734,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    c_0_4068,
    [final] ).

cnf(c_0_5735,plain,
    ( c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4))
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_4069,
    [final] ).

cnf(c_0_5736,plain,
    ( c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4070,
    [final] ).

cnf(c_0_5737,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4071,
    [final] ).

cnf(c_0_5738,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4072,
    [final] ).

cnf(c_0_5739,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2),
    c_0_4073,
    [final] ).

cnf(c_0_5740,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),X2) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X1),X2),
    c_0_4074,
    [final] ).

cnf(c_0_5741,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    c_0_4075,
    [final] ).

cnf(c_0_5742,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4076,
    [final] ).

cnf(c_0_5743,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) ),
    c_0_4077,
    [final] ).

cnf(c_0_5744,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    c_0_4078,
    [final] ).

cnf(c_0_5745,plain,
    ( c_Orderings_Oord__class_Oless(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    c_0_4079,
    [final] ).

cnf(c_0_5746,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
    c_0_4080,
    [final] ).

cnf(c_0_5747,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    c_0_4081,
    [final] ).

cnf(c_0_5748,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
    c_0_4082,
    [final] ).

cnf(c_0_5749,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    c_0_4083,
    [final] ).

cnf(c_0_5750,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    c_0_4084,
    [final] ).

cnf(c_0_5751,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4085,
    [final] ).

cnf(c_0_5752,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    c_0_4086,
    [final] ).

cnf(c_0_5753,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4087,
    [final] ).

cnf(c_0_5754,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4088,
    [final] ).

cnf(c_0_5755,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2),
    c_0_4089,
    [final] ).

cnf(c_0_5756,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),X3) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3)),
    c_0_4090,
    [final] ).

cnf(c_0_5757,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),
    c_0_4091,
    [final] ).

cnf(c_0_5758,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),
    c_0_4092,
    [final] ).

cnf(c_0_5759,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    c_0_4093,
    [final] ).

cnf(c_0_5760,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
    c_0_4094,
    [final] ).

cnf(c_0_5761,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)),
    c_0_4095,
    [final] ).

cnf(c_0_5762,plain,
    c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2),X3) = c_Power_Opower__class_Opower(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
    c_0_4096,
    [final] ).

cnf(c_0_5763,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    c_0_4097,
    [final] ).

cnf(c_0_5764,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
    c_0_4098,
    [final] ).

cnf(c_0_5765,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
    c_0_4099,
    [final] ).

cnf(c_0_5766,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),
    c_0_4100,
    [final] ).

cnf(c_0_5767,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    c_0_4101,
    [final] ).

cnf(c_0_5768,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    c_0_4102,
    [final] ).

cnf(c_0_5769,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1)) ),
    c_0_4103,
    [final] ).

cnf(c_0_5770,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    c_0_4104,
    [final] ).

cnf(c_0_5771,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
    c_0_4105,
    [final] ).

cnf(c_0_5772,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    c_0_4106,
    [final] ).

cnf(c_0_5773,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    c_0_4107,
    [final] ).

cnf(c_0_5774,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4108,
    [final] ).

cnf(c_0_5775,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    c_0_4109,
    [final] ).

cnf(c_0_5776,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    c_0_4110,
    [final] ).

cnf(c_0_5777,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    c_0_4111,
    [final] ).

cnf(c_0_5778,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4112,
    [final] ).

cnf(c_0_5779,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
    c_0_4113,
    [final] ).

cnf(c_0_5780,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    c_0_4114,
    [final] ).

cnf(c_0_5781,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    c_0_4115,
    [final] ).

cnf(c_0_5782,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
    c_0_4116,
    [final] ).

cnf(c_0_5783,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    c_0_4117,
    [final] ).

cnf(c_0_5784,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    c_0_4118,
    [final] ).

cnf(c_0_5785,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ),
    c_0_4119,
    [final] ).

cnf(c_0_5786,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    c_0_4120,
    [final] ).

cnf(c_0_5787,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4121,
    [final] ).

cnf(c_0_5788,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    c_0_4122,
    [final] ).

cnf(c_0_5789,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
    c_0_4123,
    [final] ).

cnf(c_0_5790,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
    c_0_4124,
    [final] ).

cnf(c_0_5791,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
    c_0_4125,
    [final] ).

cnf(c_0_5792,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
    c_0_4126,
    [final] ).

cnf(c_0_5793,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
    c_0_4127,
    [final] ).

cnf(c_0_5794,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
    c_0_4128,
    [final] ).

cnf(c_0_5795,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
    c_0_4129,
    [final] ).

cnf(c_0_5796,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    c_0_4130,
    [final] ).

cnf(c_0_5797,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4131,
    [final] ).

cnf(c_0_5798,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4132,
    [final] ).

cnf(c_0_5799,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4133,
    [final] ).

cnf(c_0_5800,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4134,
    [final] ).

cnf(c_0_5801,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4135,
    [final] ).

cnf(c_0_5802,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    c_0_4136,
    [final] ).

cnf(c_0_5803,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Int_Onumber(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    c_0_4137,
    [final] ).

cnf(c_0_5804,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4138,
    [final] ).

cnf(c_0_5805,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    c_0_4139,
    [final] ).

cnf(c_0_5806,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4140,
    [final] ).

cnf(c_0_5807,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    c_0_4141,
    [final] ).

cnf(c_0_5808,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4142,
    [final] ).

cnf(c_0_5809,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Oidom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4143,
    [final] ).

cnf(c_0_5810,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Oidom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4144,
    [final] ).

cnf(c_0_5811,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    c_0_4145,
    [final] ).

cnf(c_0_5812,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    c_0_4146,
    [final] ).

cnf(c_0_5813,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    c_0_4147,
    [final] ).

cnf(c_0_5814,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4148,
    [final] ).

cnf(c_0_5815,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_4149,
    [final] ).

cnf(c_0_5816,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    c_0_4150,
    [final] ).

cnf(c_0_5817,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk12_1(X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4151,
    [final] ).

cnf(c_0_5818,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4152,
    [final] ).

cnf(c_0_5819,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4153,
    [final] ).

cnf(c_0_5820,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    c_0_4154,
    [final] ).

cnf(c_0_5821,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    c_0_4155,
    [final] ).

cnf(c_0_5822,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4156,
    [final] ).

cnf(c_0_5823,plain,
    ( X3 = X4
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Power_Opower__class_Opower(X1,X2,X4) ),
    c_0_4157,
    [final] ).

cnf(c_0_5824,plain,
    ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = X2 ),
    c_0_4158,
    [final] ).

cnf(c_0_5825,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    c_0_4159,
    [final] ).

cnf(c_0_5826,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_4160,
    [final] ).

cnf(c_0_5827,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4161,
    [final] ).

cnf(c_0_5828,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4162,
    [final] ).

cnf(c_0_5829,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4163,
    [final] ).

cnf(c_0_5830,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4164,
    [final] ).

cnf(c_0_5831,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    c_0_4165,
    [final] ).

cnf(c_0_5832,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4166,
    [final] ).

cnf(c_0_5833,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4167,
    [final] ).

cnf(c_0_5834,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    c_0_4168,
    [final] ).

cnf(c_0_5835,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4169,
    [final] ).

cnf(c_0_5836,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    c_0_4170,
    [final] ).

cnf(c_0_5837,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,esk21_3(X3,X2,X1)) ),
    c_0_4171,
    [final] ).

cnf(c_0_5838,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X3,X2,X1),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4172,
    [final] ).

cnf(c_0_5839,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    c_0_4173,
    [final] ).

cnf(c_0_5840,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_4174,
    [final] ).

cnf(c_0_5841,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4175,
    [final] ).

cnf(c_0_5842,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    c_0_4176,
    [final] ).

cnf(c_0_5843,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_4177,
    [final] ).

cnf(c_0_5844,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4178,
    [final] ).

cnf(c_0_5845,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    c_0_4179,
    [final] ).

cnf(c_0_5846,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_4180,
    [final] ).

cnf(c_0_5847,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring(X1) ),
    c_0_4181,
    [final] ).

cnf(c_0_5848,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4182,
    [final] ).

cnf(c_0_5849,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_4183,
    [final] ).

cnf(c_0_5850,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4184,
    [final] ).

cnf(c_0_5851,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    c_0_4185,
    [final] ).

cnf(c_0_5852,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4186,
    [final] ).

cnf(c_0_5853,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    c_0_4187,
    [final] ).

cnf(c_0_5854,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_4188,
    [final] ).

cnf(c_0_5855,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    c_0_4189,
    [final] ).

cnf(c_0_5856,plain,
    ( X3 = X2
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    c_0_4190,
    [final] ).

cnf(c_0_5857,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
    c_0_4191,
    [final] ).

cnf(c_0_5858,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
    c_0_4192,
    [final] ).

cnf(c_0_5859,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    c_0_4193,
    [final] ).

cnf(c_0_5860,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4194,
    [final] ).

cnf(c_0_5861,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2) ),
    c_0_4195,
    [final] ).

cnf(c_0_5862,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4196,
    [final] ).

cnf(c_0_5863,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4197,
    [final] ).

cnf(c_0_5864,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    c_0_4198,
    [final] ).

cnf(c_0_5865,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    c_0_4199,
    [final] ).

cnf(c_0_5866,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
    c_0_4200,
    [final] ).

cnf(c_0_5867,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_4201,
    [final] ).

cnf(c_0_5868,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_4202,
    [final] ).

cnf(c_0_5869,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4203,
    [final] ).

cnf(c_0_5870,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1))
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    c_0_4204,
    [final] ).

cnf(c_0_5871,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
    c_0_4205,
    [final] ).

cnf(c_0_5872,plain,
    ( X2 = X3
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    c_0_4206,
    [final] ).

cnf(c_0_5873,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
    c_0_4207,
    [final] ).

cnf(c_0_5874,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    c_0_4208,
    [final] ).

cnf(c_0_5875,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    c_0_4209,
    [final] ).

cnf(c_0_5876,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Odiv(X1,X3,X2)) = X3
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4210,
    [final] ).

cnf(c_0_5877,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4211,
    [final] ).

cnf(c_0_5878,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4212,
    [final] ).

cnf(c_0_5879,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4213,
    [final] ).

cnf(c_0_5880,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),
    c_0_4214,
    [final] ).

cnf(c_0_5881,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4215,
    [final] ).

cnf(c_0_5882,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    c_0_4216,
    [final] ).

cnf(c_0_5883,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    c_0_4217,
    [final] ).

cnf(c_0_5884,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    c_0_4218,
    [final] ).

cnf(c_0_5885,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    c_0_4219,
    [final] ).

cnf(c_0_5886,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4220,
    [final] ).

cnf(c_0_5887,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4221,
    [final] ).

cnf(c_0_5888,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4222,
    [final] ).

cnf(c_0_5889,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4223,
    [final] ).

cnf(c_0_5890,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4224,
    [final] ).

cnf(c_0_5891,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    c_0_4225,
    [final] ).

cnf(c_0_5892,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4226,
    [final] ).

cnf(c_0_5893,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4227,
    [final] ).

cnf(c_0_5894,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber(X1)
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_4228,
    [final] ).

cnf(c_0_5895,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4229,
    [final] ).

cnf(c_0_5896,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4230,
    [final] ).

cnf(c_0_5897,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4231,
    [final] ).

cnf(c_0_5898,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4232,
    [final] ).

cnf(c_0_5899,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4233,
    [final] ).

cnf(c_0_5900,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4234,
    [final] ).

cnf(c_0_5901,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
    c_0_4235,
    [final] ).

cnf(c_0_5902,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
    c_0_4236,
    [final] ).

cnf(c_0_5903,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    c_0_4237,
    [final] ).

cnf(c_0_5904,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    c_0_4238,
    [final] ).

cnf(c_0_5905,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4239,
    [final] ).

cnf(c_0_5906,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4240,
    [final] ).

cnf(c_0_5907,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    c_0_4241,
    [final] ).

cnf(c_0_5908,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4242,
    [final] ).

cnf(c_0_5909,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4243,
    [final] ).

cnf(c_0_5910,plain,
    ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk11_2(X1,X2))) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    c_0_4244,
    [final] ).

cnf(c_0_5911,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    c_0_4245,
    [final] ).

cnf(c_0_5912,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4246,
    [final] ).

cnf(c_0_5913,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4247,
    [final] ).

cnf(c_0_5914,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    c_0_4248,
    [final] ).

cnf(c_0_5915,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    c_0_4249,
    [final] ).

cnf(c_0_5916,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    c_0_4250,
    [final] ).

cnf(c_0_5917,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4251,
    [final] ).

cnf(c_0_5918,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    c_0_4252,
    [final] ).

cnf(c_0_5919,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    c_0_4253,
    [final] ).

cnf(c_0_5920,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4254,
    [final] ).

cnf(c_0_5921,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    c_0_4255,
    [final] ).

cnf(c_0_5922,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4256,
    [final] ).

cnf(c_0_5923,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    c_0_4257,
    [final] ).

cnf(c_0_5924,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4258,
    [final] ).

cnf(c_0_5925,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    c_0_4259,
    [final] ).

cnf(c_0_5926,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4260,
    [final] ).

cnf(c_0_5927,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4261,
    [final] ).

cnf(c_0_5928,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    c_0_4262,
    [final] ).

cnf(c_0_5929,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    c_0_4263,
    [final] ).

cnf(c_0_5930,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4264,
    [final] ).

cnf(c_0_5931,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) != X2 ),
    c_0_4265,
    [final] ).

cnf(c_0_5932,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4266,
    [final] ).

cnf(c_0_5933,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4267,
    [final] ).

cnf(c_0_5934,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4268,
    [final] ).

cnf(c_0_5935,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4269,
    [final] ).

cnf(c_0_5936,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4270,
    [final] ).

cnf(c_0_5937,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4271,
    [final] ).

cnf(c_0_5938,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_4272,
    [final] ).

cnf(c_0_5939,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
    | ~ class_Power_Opower(X1) ),
    c_0_4273,
    [final] ).

cnf(c_0_5940,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4274,
    [final] ).

cnf(c_0_5941,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4275,
    [final] ).

cnf(c_0_5942,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4276,
    [final] ).

cnf(c_0_5943,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    c_0_4277,
    [final] ).

cnf(c_0_5944,plain,
    ( c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk3_1(X1))) = X1
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4278,
    [final] ).

cnf(c_0_5945,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4279,
    [final] ).

cnf(c_0_5946,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4280,
    [final] ).

cnf(c_0_5947,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4281,
    [final] ).

cnf(c_0_5948,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4282,
    [final] ).

cnf(c_0_5949,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ class_Int_Onumber(X1) ),
    c_0_4283,
    [final] ).

cnf(c_0_5950,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    c_0_4284,
    [final] ).

cnf(c_0_5951,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4285,
    [final] ).

cnf(c_0_5952,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4286,
    [final] ).

cnf(c_0_5953,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    c_0_4287,
    [final] ).

cnf(c_0_5954,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4288,
    [final] ).

cnf(c_0_5955,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4289,
    [final] ).

cnf(c_0_5956,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
    c_0_4290,
    [final] ).

cnf(c_0_5957,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X3
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    c_0_4291,
    [final] ).

cnf(c_0_5958,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
    c_0_4292,
    [final] ).

cnf(c_0_5959,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4293,
    [final] ).

cnf(c_0_5960,plain,
    ( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != X3 ),
    c_0_4294,
    [final] ).

cnf(c_0_5961,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) ),
    c_0_4295,
    [final] ).

cnf(c_0_5962,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4296,
    [final] ).

cnf(c_0_5963,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X2) = c_Divides_Odiv__class_Omod(X1,X3,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4297,
    [final] ).

cnf(c_0_5964,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4298,
    [final] ).

cnf(c_0_5965,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4299,
    [final] ).

cnf(c_0_5966,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
    c_0_4300,
    [final] ).

cnf(c_0_5967,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    c_0_4301,
    [final] ).

cnf(c_0_5968,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
    c_0_4302,
    [final] ).

cnf(c_0_5969,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
    c_0_4303,
    [final] ).

cnf(c_0_5970,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    c_0_4304,
    [final] ).

cnf(c_0_5971,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4305,
    [final] ).

cnf(c_0_5972,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4306,
    [final] ).

cnf(c_0_5973,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4307,
    [final] ).

cnf(c_0_5974,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4308,
    [final] ).

cnf(c_0_5975,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    c_0_4309,
    [final] ).

cnf(c_0_5976,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4310,
    [final] ).

cnf(c_0_5977,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    c_0_4311,
    [final] ).

cnf(c_0_5978,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    c_0_4312,
    [final] ).

cnf(c_0_5979,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4313,
    [final] ).

cnf(c_0_5980,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4314,
    [final] ).

cnf(c_0_5981,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    c_0_4315,
    [final] ).

cnf(c_0_5982,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4316,
    [final] ).

cnf(c_0_5983,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    c_0_4317,
    [final] ).

cnf(c_0_5984,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4318,
    [final] ).

cnf(c_0_5985,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    c_0_4319,
    [final] ).

cnf(c_0_5986,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4320,
    [final] ).

cnf(c_0_5987,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    c_0_4321,
    [final] ).

cnf(c_0_5988,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4322,
    [final] ).

cnf(c_0_5989,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    c_0_4323,
    [final] ).

cnf(c_0_5990,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4324,
    [final] ).

cnf(c_0_5991,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    c_0_4325,
    [final] ).

cnf(c_0_5992,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
    c_0_4326,
    [final] ).

cnf(c_0_5993,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
    c_0_4327,
    [final] ).

cnf(c_0_5994,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),
    c_0_4328,
    [final] ).

cnf(c_0_5995,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
    c_0_4329,
    [final] ).

cnf(c_0_5996,plain,
    ( c_Power_Opower__class_Opower(X1,X2,X3) = c_Power_Opower__class_Opower(X1,X2,X4)
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | X3 != X4 ),
    c_0_4330,
    [final] ).

cnf(c_0_5997,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    c_0_4331,
    [final] ).

cnf(c_0_5998,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),
    c_0_4332,
    [final] ).

cnf(c_0_5999,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    c_0_4333,
    [final] ).

cnf(c_0_6000,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1)) ),
    c_0_4334,
    [final] ).

cnf(c_0_6001,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
    c_0_4335,
    [final] ).

cnf(c_0_6002,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1)) ),
    c_0_4336,
    [final] ).

cnf(c_0_6003,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    c_0_4337,
    [final] ).

cnf(c_0_6004,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
    c_0_4338,
    [final] ).

cnf(c_0_6005,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    c_0_4339,
    [final] ).

cnf(c_0_6006,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    c_0_4340,
    [final] ).

cnf(c_0_6007,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
    c_0_4341,
    [final] ).

cnf(c_0_6008,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    c_0_4342,
    [final] ).

cnf(c_0_6009,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    c_0_4343,
    [final] ).

cnf(c_0_6010,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
    c_0_4344,
    [final] ).

cnf(c_0_6011,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_4345,
    [final] ).

cnf(c_0_6012,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
    c_0_4346,
    [final] ).

cnf(c_0_6013,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
    c_0_4347,
    [final] ).

cnf(c_0_6014,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_4348,
    [final] ).

cnf(c_0_6015,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4349,
    [final] ).

cnf(c_0_6016,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4350,
    [final] ).

cnf(c_0_6017,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4351,
    [final] ).

cnf(c_0_6018,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    c_0_4352,
    [final] ).

cnf(c_0_6019,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    c_0_4353,
    [final] ).

cnf(c_0_6020,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    c_0_4354,
    [final] ).

cnf(c_0_6021,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__ring(X1)
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_4355,
    [final] ).

cnf(c_0_6022,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_4356,
    [final] ).

cnf(c_0_6023,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_4357,
    [final] ).

cnf(c_0_6024,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    c_0_4358,
    [final] ).

cnf(c_0_6025,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4359,
    [final] ).

cnf(c_0_6026,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_4360,
    [final] ).

cnf(c_0_6027,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 != X3 ),
    c_0_4361,
    [final] ).

cnf(c_0_6028,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_4362,
    [final] ).

cnf(c_0_6029,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    c_0_4363,
    [final] ).

cnf(c_0_6030,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2)) ),
    c_0_4364,
    [final] ).

cnf(c_0_6031,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2)) ),
    c_0_4365,
    [final] ).

cnf(c_0_6032,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    c_0_4366,
    [final] ).

cnf(c_0_6033,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    c_0_4367,
    [final] ).

cnf(c_0_6034,plain,
    ( c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk5_1(X1))) = X1
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4368,
    [final] ).

cnf(c_0_6035,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X3 ),
    c_0_4369,
    [final] ).

cnf(c_0_6036,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    c_0_4370,
    [final] ).

cnf(c_0_6037,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    c_0_4371,
    [final] ).

cnf(c_0_6038,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    c_0_4372,
    [final] ).

cnf(c_0_6039,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4373,
    [final] ).

cnf(c_0_6040,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    c_0_4374,
    [final] ).

cnf(c_0_6041,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4375,
    [final] ).

cnf(c_0_6042,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)) ),
    c_0_4376,
    [final] ).

cnf(c_0_6043,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2) ),
    c_0_4377,
    [final] ).

cnf(c_0_6044,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2) ),
    c_0_4378,
    [final] ).

cnf(c_0_6045,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)) ),
    c_0_4379,
    [final] ).

cnf(c_0_6046,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4380,
    [final] ).

cnf(c_0_6047,plain,
    ( X1 = X2
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2) ),
    c_0_4381,
    [final] ).

cnf(c_0_6048,plain,
    ( X4 = X5
    | ~ class_Groups_Oab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | X2 != X3 ),
    c_0_4382,
    [final] ).

cnf(c_0_6049,plain,
    ( X2 = X3
    | ~ class_Groups_Oab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | X4 != X5 ),
    c_0_4383,
    [final] ).

cnf(c_0_6050,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4384,
    [final] ).

cnf(c_0_6051,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4385,
    [final] ).

cnf(c_0_6052,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4386,
    [final] ).

cnf(c_0_6053,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    c_0_4387,
    [final] ).

cnf(c_0_6054,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls) ),
    c_0_4388,
    [final] ).

cnf(c_0_6055,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2) ),
    c_0_4389,
    [final] ).

cnf(c_0_6056,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    c_0_4390,
    [final] ).

cnf(c_0_6057,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2) ),
    c_0_4391,
    [final] ).

cnf(c_0_6058,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_4392,
    [final] ).

cnf(c_0_6059,plain,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4393,
    [final] ).

cnf(c_0_6060,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4394,
    [final] ).

cnf(c_0_6061,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(X3,X1,X4) != c_Groups_Oplus__class_Oplus(X3,X2,X4)
    | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    c_0_4395,
    [final] ).

cnf(c_0_6062,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
    | ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
    c_0_4396,
    [final] ).

cnf(c_0_6063,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
    | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    c_0_4397,
    [final] ).

cnf(c_0_6064,plain,
    ( X2 = X3
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oplus__class_Oplus(X1,X3,X4) ),
    c_0_4398,
    [final] ).

cnf(c_0_6065,plain,
    ( X2 = X3
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X4,X2) != c_Groups_Oplus__class_Oplus(X1,X4,X3) ),
    c_0_4399,
    [final] ).

cnf(c_0_6066,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    c_0_4400,
    [final] ).

cnf(c_0_6067,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    c_0_4401,
    [final] ).

cnf(c_0_6068,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    c_0_4402,
    [final] ).

cnf(c_0_6069,plain,
    ( X2 = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    c_0_4403,
    [final] ).

cnf(c_0_6070,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4404,
    [final] ).

cnf(c_0_6071,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1) ),
    c_0_4405,
    [final] ).

cnf(c_0_6072,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    c_0_4406,
    [final] ).

cnf(c_0_6073,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | X2 != c_Groups_Oone__class_Oone(X1) ),
    c_0_4407,
    [final] ).

cnf(c_0_6074,plain,
    ( X1 = X2
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4408,
    [final] ).

cnf(c_0_6075,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk9_2(X2,X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    c_0_4409,
    [final] ).

cnf(c_0_6076,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
    c_0_4410,
    [final] ).

cnf(c_0_6077,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X2))
    | ~ class_Rings_Olinordered__ring(X1) ),
    c_0_4411,
    [final] ).

cnf(c_0_6078,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_4412,
    [final] ).

cnf(c_0_6079,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    c_0_4413,
    [final] ).

cnf(c_0_6080,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    c_0_4414,
    [final] ).

cnf(c_0_6081,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    c_0_4415,
    [final] ).

cnf(c_0_6082,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    c_0_4416,
    [final] ).

cnf(c_0_6083,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    c_0_4417,
    [final] ).

cnf(c_0_6084,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    c_0_4418,
    [final] ).

cnf(c_0_6085,plain,
    ( c_Divides_Odiv__class_Odiv(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4419,
    [final] ).

cnf(c_0_6086,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4420,
    [final] ).

cnf(c_0_6087,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4421,
    [final] ).

cnf(c_0_6088,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3) ),
    c_0_4422,
    [final] ).

cnf(c_0_6089,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1) ),
    c_0_4423,
    [final] ).

cnf(c_0_6090,plain,
    ( X1 = X2
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2) ),
    c_0_4424,
    [final] ).

cnf(c_0_6091,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    c_0_4425,
    [final] ).

cnf(c_0_6092,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1) ),
    c_0_4426,
    [final] ).

cnf(c_0_6093,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) ),
    c_0_4427,
    [final] ).

cnf(c_0_6094,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) ),
    c_0_4428,
    [final] ).

cnf(c_0_6095,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
    c_0_4429,
    [final] ).

cnf(c_0_6096,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
    c_0_4430,
    [final] ).

cnf(c_0_6097,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    c_0_4431,
    [final] ).

cnf(c_0_6098,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4432,
    [final] ).

cnf(c_0_6099,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    c_0_4433,
    [final] ).

cnf(c_0_6100,plain,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4434,
    [final] ).

cnf(c_0_6101,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4435,
    [final] ).

cnf(c_0_6102,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4436,
    [final] ).

cnf(c_0_6103,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    c_0_4437,
    [final] ).

cnf(c_0_6104,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    c_0_4438,
    [final] ).

cnf(c_0_6105,plain,
    ( X2 = X1
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    c_0_4439,
    [final] ).

cnf(c_0_6106,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    c_0_4440,
    [final] ).

cnf(c_0_6107,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    c_0_4441,
    [final] ).

cnf(c_0_6108,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    c_0_4442,
    [final] ).

cnf(c_0_6109,plain,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4443,
    [final] ).

cnf(c_0_6110,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    c_0_4444,
    [final] ).

cnf(c_0_6111,plain,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    c_0_4445,
    [final] ).

cnf(c_0_6112,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X2))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4446,
    [final] ).

cnf(c_0_6113,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4447,
    [final] ).

cnf(c_0_6114,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) ),
    c_0_4448,
    [final] ).

cnf(c_0_6115,plain,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) ),
    c_0_4449,
    [final] ).

cnf(c_0_6116,plain,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4450,
    [final] ).

cnf(c_0_6117,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,esk17_2(X2,X1)) = X1
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4451,
    [final] ).

cnf(c_0_6118,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_2(X2,X1)) = X1
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_4452,
    [final] ).

cnf(c_0_6119,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) = c_Int_OBit1(X1),
    c_0_4453,
    [final] ).

cnf(c_0_6120,plain,
    c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),
    c_0_4454,
    [final] ).

cnf(c_0_6121,plain,
    c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
    c_0_4455,
    [final] ).

cnf(c_0_6122,plain,
    c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X1),X2),
    c_0_4456,
    [final] ).

cnf(c_0_6123,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | X1 != X2 ),
    c_0_4457,
    [final] ).

cnf(c_0_6124,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4458,
    [final] ).

cnf(c_0_6125,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4459,
    [final] ).

cnf(c_0_6126,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4460,
    [final] ).

cnf(c_0_6127,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4461,
    [final] ).

cnf(c_0_6128,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk13_2(X1,X2)) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    c_0_4462,
    [final] ).

cnf(c_0_6129,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1)) ),
    c_0_4463,
    [final] ).

cnf(c_0_6130,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X2) = c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4464,
    [final] ).

cnf(c_0_6131,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,X2,X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_4465,
    [final] ).

cnf(c_0_6132,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Nat_OSuc(X1)),
    c_0_4466,
    [final] ).

cnf(c_0_6133,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4467,
    [final] ).

cnf(c_0_6134,plain,
    c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)),
    c_0_4468,
    [final] ).

cnf(c_0_6135,plain,
    c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)),
    c_0_4469,
    [final] ).

cnf(c_0_6136,plain,
    c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)),
    c_0_4470,
    [final] ).

cnf(c_0_6137,plain,
    c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)),
    c_0_4471,
    [final] ).

cnf(c_0_6138,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4472,
    [final] ).

cnf(c_0_6139,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
    c_0_4473,
    [final] ).

cnf(c_0_6140,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_4474,
    [final] ).

cnf(c_0_6141,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4475,
    [final] ).

cnf(c_0_6142,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
    c_0_4476,
    [final] ).

cnf(c_0_6143,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2) = X1,
    c_0_4477,
    [final] ).

cnf(c_0_6144,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4478,
    [final] ).

cnf(c_0_6145,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4479,
    [final] ).

cnf(c_0_6146,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4480,
    [final] ).

cnf(c_0_6147,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4481,
    [final] ).

cnf(c_0_6148,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4482,
    [final] ).

cnf(c_0_6149,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4483,
    [final] ).

cnf(c_0_6150,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4484,
    [final] ).

cnf(c_0_6151,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X1),
    c_0_4485,
    [final] ).

cnf(c_0_6152,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
    c_0_4486,
    [final] ).

cnf(c_0_6153,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X1)),
    c_0_4487,
    [final] ).

cnf(c_0_6154,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
    c_0_4488,
    [final] ).

cnf(c_0_6155,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
    c_0_4489,
    [final] ).

cnf(c_0_6156,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    c_0_4490,
    [final] ).

cnf(c_0_6157,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    c_0_4491,
    [final] ).

cnf(c_0_6158,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    c_0_4492,
    [final] ).

cnf(c_0_6159,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    c_0_4493,
    [final] ).

cnf(c_0_6160,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    c_0_4494,
    [final] ).

cnf(c_0_6161,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    c_0_4495,
    [final] ).

cnf(c_0_6162,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    c_0_4496,
    [final] ).

cnf(c_0_6163,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    c_0_4497,
    [final] ).

cnf(c_0_6164,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    c_0_4498,
    [final] ).

cnf(c_0_6165,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    c_0_4499,
    [final] ).

cnf(c_0_6166,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    c_0_4500,
    [final] ).

cnf(c_0_6167,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    c_0_4501,
    [final] ).

cnf(c_0_6168,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    c_0_4502,
    [final] ).

cnf(c_0_6169,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    c_0_4503,
    [final] ).

cnf(c_0_6170,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    c_0_4504,
    [final] ).

cnf(c_0_6171,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    c_0_4505,
    [final] ).

cnf(c_0_6172,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    c_0_4506,
    [final] ).

cnf(c_0_6173,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    c_0_4507,
    [final] ).

cnf(c_0_6174,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    c_0_4508,
    [final] ).

cnf(c_0_6175,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    c_0_4509,
    [final] ).

cnf(c_0_6176,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4510,
    [final] ).

cnf(c_0_6177,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4511,
    [final] ).

cnf(c_0_6178,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4512,
    [final] ).

cnf(c_0_6179,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),
    c_0_4513,
    [final] ).

cnf(c_0_6180,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),
    c_0_4514,
    [final] ).

cnf(c_0_6181,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4515,
    [final] ).

cnf(c_0_6182,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2) ),
    c_0_4516,
    [final] ).

cnf(c_0_6183,plain,
    ( X1 = c_Nat_OSuc(X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    c_0_4517,
    [final] ).

cnf(c_0_6184,plain,
    ( X1 = c_Nat_OSuc(X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    c_0_4518,
    [final] ).

cnf(c_0_6185,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | X1 != c_Nat_OSuc(X3) ),
    c_0_4519,
    [final] ).

cnf(c_0_6186,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4520,
    [final] ).

cnf(c_0_6187,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    c_0_4521,
    [final] ).

cnf(c_0_6188,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | X3 != c_Groups_Otimes__class_Otimes(X1,X2,X4)
    | ~ class_Rings_Odvd(X1) ),
    c_0_4522,
    [final] ).

cnf(c_0_6189,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4523,
    [final] ).

cnf(c_0_6190,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4524,
    [final] ).

cnf(c_0_6191,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4525,
    [final] ).

cnf(c_0_6192,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4526,
    [final] ).

cnf(c_0_6193,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4527,
    [final] ).

cnf(c_0_6194,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4528,
    [final] ).

cnf(c_0_6195,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4529,
    [final] ).

cnf(c_0_6196,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4530,
    [final] ).

cnf(c_0_6197,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4531,
    [final] ).

cnf(c_0_6198,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4532,
    [final] ).

cnf(c_0_6199,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4533,
    [final] ).

cnf(c_0_6200,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4534,
    [final] ).

cnf(c_0_6201,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4535,
    [final] ).

cnf(c_0_6202,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4536,
    [final] ).

cnf(c_0_6203,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4537,
    [final] ).

cnf(c_0_6204,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4538,
    [final] ).

cnf(c_0_6205,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4539,
    [final] ).

cnf(c_0_6206,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4540,
    [final] ).

cnf(c_0_6207,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4541,
    [final] ).

cnf(c_0_6208,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    c_0_4542,
    [final] ).

cnf(c_0_6209,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    c_0_4543,
    [final] ).

cnf(c_0_6210,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    c_0_4544,
    [final] ).

cnf(c_0_6211,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    c_0_4545,
    [final] ).

cnf(c_0_6212,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Nat_OSuc(X1) = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4546,
    [final] ).

cnf(c_0_6213,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4547,
    [final] ).

cnf(c_0_6214,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 != X1 ),
    c_0_4548,
    [final] ).

cnf(c_0_6215,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    c_0_4549,
    [final] ).

cnf(c_0_6216,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    c_0_4550,
    [final] ).

cnf(c_0_6217,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    c_0_4551,
    [final] ).

cnf(c_0_6218,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    c_0_4552,
    [final] ).

cnf(c_0_6219,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    c_0_4553,
    [final] ).

cnf(c_0_6220,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    c_0_4554,
    [final] ).

cnf(c_0_6221,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2) ),
    c_0_4555,
    [final] ).

cnf(c_0_6222,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
    c_0_4556,
    [final] ).

cnf(c_0_6223,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    c_0_4557,
    [final] ).

cnf(c_0_6224,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    c_0_4558,
    [final] ).

cnf(c_0_6225,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4559,
    [final] ).

cnf(c_0_6226,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4560,
    [final] ).

cnf(c_0_6227,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4561,
    [final] ).

cnf(c_0_6228,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4562,
    [final] ).

cnf(c_0_6229,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4563,
    [final] ).

cnf(c_0_6230,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4564,
    [final] ).

cnf(c_0_6231,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4565,
    [final] ).

cnf(c_0_6232,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4566,
    [final] ).

cnf(c_0_6233,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4567,
    [final] ).

cnf(c_0_6234,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls) ),
    c_0_4568,
    [final] ).

cnf(c_0_6235,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)) ),
    c_0_4569,
    [final] ).

cnf(c_0_6236,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls) ),
    c_0_4570,
    [final] ).

cnf(c_0_6237,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) ),
    c_0_4571,
    [final] ).

cnf(c_0_6238,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)) ),
    c_0_4572,
    [final] ).

cnf(c_0_6239,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)) ),
    c_0_4573,
    [final] ).

cnf(c_0_6240,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)) ),
    c_0_4574,
    [final] ).

cnf(c_0_6241,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin) ),
    c_0_4575,
    [final] ).

cnf(c_0_6242,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin) ),
    c_0_4576,
    [final] ).

cnf(c_0_6243,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)) ),
    c_0_4577,
    [final] ).

cnf(c_0_6244,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin) ),
    c_0_4578,
    [final] ).

cnf(c_0_6245,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)) ),
    c_0_4579,
    [final] ).

cnf(c_0_6246,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin) ),
    c_0_4580,
    [final] ).

cnf(c_0_6247,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls) ),
    c_0_4581,
    [final] ).

cnf(c_0_6248,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) ),
    c_0_4582,
    [final] ).

cnf(c_0_6249,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls) ),
    c_0_4583,
    [final] ).

cnf(c_0_6250,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4584,
    [final] ).

cnf(c_0_6251,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4585,
    [final] ).

cnf(c_0_6252,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4586,
    [final] ).

cnf(c_0_6253,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4587,
    [final] ).

cnf(c_0_6254,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    c_0_4588,
    [final] ).

cnf(c_0_6255,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4589,
    [final] ).

cnf(c_0_6256,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4590,
    [final] ).

cnf(c_0_6257,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4591,
    [final] ).

cnf(c_0_6258,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4592,
    [final] ).

cnf(c_0_6259,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    c_0_4593,
    [final] ).

cnf(c_0_6260,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4594,
    [final] ).

cnf(c_0_6261,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4595,
    [final] ).

cnf(c_0_6262,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X3 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    c_0_4596,
    [final] ).

cnf(c_0_6263,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | X1 != X3 ),
    c_0_4597,
    [final] ).

cnf(c_0_6264,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X2 != X1 ),
    c_0_4598,
    [final] ).

cnf(c_0_6265,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X2 != X1 ),
    c_0_4599,
    [final] ).

cnf(c_0_6266,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3) ),
    c_0_4600,
    [final] ).

cnf(c_0_6267,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3) ),
    c_0_4601,
    [final] ).

cnf(c_0_6268,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    c_0_4602,
    [final] ).

cnf(c_0_6269,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4603,
    [final] ).

cnf(c_0_6270,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4604,
    [final] ).

cnf(c_0_6271,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4605,
    [final] ).

cnf(c_0_6272,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4606,
    [final] ).

cnf(c_0_6273,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    c_0_4607,
    [final] ).

cnf(c_0_6274,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    c_0_4608,
    [final] ).

cnf(c_0_6275,plain,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    c_0_4609,
    [final] ).

cnf(c_0_6276,plain,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4610,
    [final] ).

cnf(c_0_6277,plain,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4611,
    [final] ).

cnf(c_0_6278,plain,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4612,
    [final] ).

cnf(c_0_6279,plain,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4613,
    [final] ).

cnf(c_0_6280,plain,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    c_0_4614,
    [final] ).

cnf(c_0_6281,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    c_0_4615,
    [final] ).

cnf(c_0_6282,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    c_0_4616,
    [final] ).

cnf(c_0_6283,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    c_0_4617,
    [final] ).

cnf(c_0_6284,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    c_0_4618,
    [final] ).

cnf(c_0_6285,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    c_0_4619,
    [final] ).

cnf(c_0_6286,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
    c_0_4620,
    [final] ).

cnf(c_0_6287,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
    c_0_4621,
    [final] ).

cnf(c_0_6288,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OMin) ),
    c_0_4622,
    [final] ).

cnf(c_0_6289,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
    c_0_4623,
    [final] ).

cnf(c_0_6290,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
    c_0_4624,
    [final] ).

cnf(c_0_6291,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
    c_0_4625,
    [final] ).

cnf(c_0_6292,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X1) ),
    c_0_4626,
    [final] ).

cnf(c_0_6293,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
    c_0_4627,
    [final] ).

cnf(c_0_6294,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    c_0_4628,
    [final] ).

cnf(c_0_6295,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
    c_0_4629,
    [final] ).

cnf(c_0_6296,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    c_0_4630,
    [final] ).

cnf(c_0_6297,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
    c_0_4631,
    [final] ).

cnf(c_0_6298,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4632,
    [final] ).

cnf(c_0_6299,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4633,
    [final] ).

cnf(c_0_6300,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))) ),
    c_0_4634,
    [final] ).

cnf(c_0_6301,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    c_0_4635,
    [final] ).

cnf(c_0_6302,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4636,
    [final] ).

cnf(c_0_6303,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4637,
    [final] ).

cnf(c_0_6304,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4638,
    [final] ).

cnf(c_0_6305,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4639,
    [final] ).

cnf(c_0_6306,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    c_0_4640,
    [final] ).

cnf(c_0_6307,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    c_0_4641,
    [final] ).

cnf(c_0_6308,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4642,
    [final] ).

cnf(c_0_6309,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    c_0_4643,
    [final] ).

cnf(c_0_6310,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4644,
    [final] ).

cnf(c_0_6311,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    c_0_4645,
    [final] ).

cnf(c_0_6312,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4646,
    [final] ).

cnf(c_0_6313,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    c_0_4647,
    [final] ).

cnf(c_0_6314,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4648,
    [final] ).

cnf(c_0_6315,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)))
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    c_0_4649,
    [final] ).

cnf(c_0_6316,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Nat_OSuc(esk9_2(X2,X1)) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    c_0_4650,
    [final] ).

cnf(c_0_6317,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk4_1(X1)) = X1
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4651,
    [final] ).

cnf(c_0_6318,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk2_1(X1)) = X1
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4652,
    [final] ).

cnf(c_0_6319,plain,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4653,
    [final] ).

cnf(c_0_6320,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4654,
    [final] ).

cnf(c_0_6321,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4655,
    [final] ).

cnf(c_0_6322,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4656,
    [final] ).

cnf(c_0_6323,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X1) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X1))),
    c_0_4657,
    [final] ).

cnf(c_0_6324,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3)
    | X2 != X3 ),
    c_0_4658,
    [final] ).

cnf(c_0_6325,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4659,
    [final] ).

cnf(c_0_6326,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    c_0_4660,
    [final] ).

cnf(c_0_6327,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4661,
    [final] ).

cnf(c_0_6328,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X4,X3)
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 != X4 ),
    c_0_4662,
    [final] ).

cnf(c_0_6329,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,X4)
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | X3 != X4 ),
    c_0_4663,
    [final] ).

cnf(c_0_6330,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    c_0_4664,
    [final] ).

cnf(c_0_6331,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    c_0_4665,
    [final] ).

cnf(c_0_6332,plain,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(X1,X3,X2)
    | X3 = X2
    | ~ class_Rings_Olinordered__idom(X1) ),
    c_0_4666,
    [final] ).

cnf(c_0_6333,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
    c_0_4667,
    [final] ).

cnf(c_0_6334,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
    c_0_4668,
    [final] ).

cnf(c_0_6335,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Ozero__class_Ozero(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    c_0_4669,
    [final] ).

cnf(c_0_6336,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != X2 ),
    c_0_4670,
    [final] ).

cnf(c_0_6337,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4671,
    [final] ).

cnf(c_0_6338,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Otimes__class_Otimes(X1,X3,X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4672,
    [final] ).

cnf(c_0_6339,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3)
    | X2 != X3 ),
    c_0_4673,
    [final] ).

cnf(c_0_6340,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)
    | X2 != X3 ),
    c_0_4674,
    [final] ).

cnf(c_0_6341,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    c_0_4675,
    [final] ).

cnf(c_0_6342,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    c_0_4676,
    [final] ).

cnf(c_0_6343,plain,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_4677,
    [final] ).

cnf(c_0_6344,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_4678,
    [final] ).

cnf(c_0_6345,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4679,
    [final] ).

cnf(c_0_6346,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4680,
    [final] ).

cnf(c_0_6347,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4681,
    [final] ).

cnf(c_0_6348,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4682,
    [final] ).

cnf(c_0_6349,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4683,
    [final] ).

cnf(c_0_6350,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    c_0_4684,
    [final] ).

cnf(c_0_6351,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk6_1(X1)) = X1
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4685,
    [final] ).

cnf(c_0_6352,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) = c_Nat_OSuc(c_Nat_OSuc(X1)),
    c_0_4686,
    [final] ).

cnf(c_0_6353,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X1)),
    c_0_4687,
    [final] ).

cnf(c_0_6354,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4688,
    [final] ).

cnf(c_0_6355,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4689,
    [final] ).

cnf(c_0_6356,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X3 = c_Groups_Ozero__class_Ozero(X2)
    | c_Groups_Otimes__class_Otimes(X2,X3,X1) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Ono__zero__divisors(X2) ),
    c_0_4690,
    [final] ).

cnf(c_0_6357,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1) ),
    c_0_4691,
    [final] ).

cnf(c_0_6358,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4692,
    [final] ).

cnf(c_0_6359,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
    | X1 != X3 ),
    c_0_4693,
    [final] ).

cnf(c_0_6360,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    c_0_4694,
    [final] ).

cnf(c_0_6361,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    c_0_4695,
    [final] ).

cnf(c_0_6362,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    c_0_4696,
    [final] ).

cnf(c_0_6363,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)
    | X1 != X3 ),
    c_0_4697,
    [final] ).

cnf(c_0_6364,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    c_0_4698,
    [final] ).

cnf(c_0_6365,plain,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4699,
    [final] ).

cnf(c_0_6366,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X2 = X1 ),
    c_0_4700,
    [final] ).

cnf(c_0_6367,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X2 = X1 ),
    c_0_4701,
    [final] ).

cnf(c_0_6368,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X2 = X1
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
    c_0_4702,
    [final] ).

cnf(c_0_6369,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ozero__class_Ozero(X2),X1)
    | ~ class_Rings_Ocomm__semiring__1(X2) ),
    c_0_4703,
    [final] ).

cnf(c_0_6370,plain,
    c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X1,
    c_0_4704,
    [final] ).

cnf(c_0_6371,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4705,
    [final] ).

cnf(c_0_6372,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    c_0_4706,
    [final] ).

cnf(c_0_6373,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4707,
    [final] ).

cnf(c_0_6374,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4708,
    [final] ).

cnf(c_0_6375,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4709,
    [final] ).

cnf(c_0_6376,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4710,
    [final] ).

cnf(c_0_6377,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    c_0_4711,
    [final] ).

cnf(c_0_6378,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
    c_0_4712,
    [final] ).

cnf(c_0_6379,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    c_0_4713,
    [final] ).

cnf(c_0_6380,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4714,
    [final] ).

cnf(c_0_6381,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4715,
    [final] ).

cnf(c_0_6382,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),
    c_0_4716,
    [final] ).

cnf(c_0_6383,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
    c_0_4717,
    [final] ).

cnf(c_0_6384,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
    c_0_4718,
    [final] ).

cnf(c_0_6385,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),
    c_0_4719,
    [final] ).

cnf(c_0_6386,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),
    c_0_4720,
    [final] ).

cnf(c_0_6387,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    c_0_4721,
    [final] ).

cnf(c_0_6388,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4722,
    [final] ).

cnf(c_0_6389,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4723,
    [final] ).

cnf(c_0_6390,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4724,
    [final] ).

cnf(c_0_6391,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4725,
    [final] ).

cnf(c_0_6392,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    c_0_4726,
    [final] ).

cnf(c_0_6393,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    c_0_4727,
    [final] ).

cnf(c_0_6394,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    c_0_4728,
    [final] ).

cnf(c_0_6395,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    c_0_4729,
    [final] ).

cnf(c_0_6396,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    c_0_4730,
    [final] ).

cnf(c_0_6397,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    c_0_4731,
    [final] ).

cnf(c_0_6398,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    c_0_4732,
    [final] ).

cnf(c_0_6399,plain,
    ( X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    c_0_4733,
    [final] ).

cnf(c_0_6400,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4734,
    [final] ).

cnf(c_0_6401,plain,
    ( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4735,
    [final] ).

cnf(c_0_6402,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4736,
    [final] ).

cnf(c_0_6403,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4737,
    [final] ).

cnf(c_0_6404,plain,
    ( X2 = X3
    | ~ class_Groups_Oab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4738,
    [final] ).

cnf(c_0_6405,plain,
    ( X2 = X3
    | ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4739,
    [final] ).

cnf(c_0_6406,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4740,
    [final] ).

cnf(c_0_6407,plain,
    ( c_Nat_OSuc(esk10_1(X1)) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4741,
    [final] ).

cnf(c_0_6408,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,X3,X2) != X3 ),
    c_0_4742,
    [final] ).

cnf(c_0_6409,plain,
    ( c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4743,
    [final] ).

cnf(c_0_6410,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk1_0) = v_na____,
    c_0_4744,
    [final] ).

cnf(c_0_6411,plain,
    ( ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2)))
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4745,
    [final] ).

cnf(c_0_6412,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    c_0_4746,
    [final] ).

cnf(c_0_6413,plain,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    c_0_4747,
    [final] ).

cnf(c_0_6414,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4748,
    [final] ).

cnf(c_0_6415,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)),X2) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4749,
    [final] ).

cnf(c_0_6416,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4750,
    [final] ).

cnf(c_0_6417,plain,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    c_0_4751,
    [final] ).

cnf(c_0_6418,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X1 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ),
    c_0_4752,
    [final] ).

cnf(c_0_6419,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1),
    c_0_4753,
    [final] ).

cnf(c_0_6420,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != X1 ),
    c_0_4754,
    [final] ).

cnf(c_0_6421,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    c_0_4755,
    [final] ).

cnf(c_0_6422,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4756,
    [final] ).

cnf(c_0_6423,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    c_0_4757,
    [final] ).

cnf(c_0_6424,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    c_0_4758,
    [final] ).

cnf(c_0_6425,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    c_0_4759,
    [final] ).

cnf(c_0_6426,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    c_0_4760,
    [final] ).

cnf(c_0_6427,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4761,
    [final] ).

cnf(c_0_6428,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4762,
    [final] ).

cnf(c_0_6429,plain,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    c_0_4763,
    [final] ).

cnf(c_0_6430,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2 ),
    c_0_4764,
    [final] ).

cnf(c_0_6431,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_4765,
    [final] ).

cnf(c_0_6432,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_4766,
    [final] ).

cnf(c_0_6433,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_4767,
    [final] ).

cnf(c_0_6434,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X1 != X2 ),
    c_0_4768,
    [final] ).

cnf(c_0_6435,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4769,
    [final] ).

cnf(c_0_6436,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    c_0_4770,
    [final] ).

cnf(c_0_6437,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    c_0_4771,
    [final] ).

cnf(c_0_6438,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    c_0_4772,
    [final] ).

cnf(c_0_6439,plain,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    c_0_4773,
    [final] ).

cnf(c_0_6440,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | X1 != X2 ),
    c_0_4774,
    [final] ).

cnf(c_0_6441,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4775,
    [final] ).

cnf(c_0_6442,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    c_0_4776,
    [final] ).

cnf(c_0_6443,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X2) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4777,
    [final] ).

cnf(c_0_6444,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4778,
    [final] ).

cnf(c_0_6445,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Nat_OSuc(X2)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    c_0_4779,
    [final] ).

cnf(c_0_6446,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4780,
    [final] ).

cnf(c_0_6447,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    c_0_4781,
    [final] ).

cnf(c_0_6448,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    c_0_4782,
    [final] ).

cnf(c_0_6449,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    c_0_4783,
    [final] ).

cnf(c_0_6450,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    c_0_4784,
    [final] ).

cnf(c_0_6451,plain,
    ( ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4785,
    [final] ).

cnf(c_0_6452,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4786,
    [final] ).

cnf(c_0_6453,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4787,
    [final] ).

cnf(c_0_6454,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4788,
    [final] ).

cnf(c_0_6455,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4789,
    [final] ).

cnf(c_0_6456,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
    c_0_4790,
    [final] ).

cnf(c_0_6457,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
    c_0_4791,
    [final] ).

cnf(c_0_6458,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
    c_0_4792,
    [final] ).

cnf(c_0_6459,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    c_0_4793,
    [final] ).

cnf(c_0_6460,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4794,
    [final] ).

cnf(c_0_6461,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    c_0_4795,
    [final] ).

cnf(c_0_6462,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4796,
    [final] ).

cnf(c_0_6463,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4797,
    [final] ).

cnf(c_0_6464,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_4798,
    [final] ).

cnf(c_0_6465,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_4799,
    [final] ).

cnf(c_0_6466,plain,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    c_0_4800,
    [final] ).

cnf(c_0_6467,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4801,
    [final] ).

cnf(c_0_6468,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4802,
    [final] ).

cnf(c_0_6469,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4803,
    [final] ).

cnf(c_0_6470,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4804,
    [final] ).

cnf(c_0_6471,plain,
    ( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    c_0_4805,
    [final] ).

cnf(c_0_6472,plain,
    c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_4806,
    [final] ).

cnf(c_0_6473,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4807,
    [final] ).

cnf(c_0_6474,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4808,
    [final] ).

cnf(c_0_6475,plain,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_4809,
    [final] ).

cnf(c_0_6476,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_4810,
    [final] ).

cnf(c_0_6477,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_4811,
    [final] ).

cnf(c_0_6478,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4812,
    [final] ).

cnf(c_0_6479,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1) ),
    c_0_4813,
    [final] ).

cnf(c_0_6480,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_4814,
    [final] ).

cnf(c_0_6481,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    c_0_4815,
    [final] ).

cnf(c_0_6482,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4816,
    [final] ).

cnf(c_0_6483,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1) ),
    c_0_4817,
    [final] ).

cnf(c_0_6484,plain,
    ( c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4818,
    [final] ).

cnf(c_0_6485,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4819,
    [final] ).

cnf(c_0_6486,plain,
    ( c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4820,
    [final] ).

cnf(c_0_6487,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4821,
    [final] ).

cnf(c_0_6488,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oab__group__add(X1)
    | X2 != X3 ),
    c_0_4822,
    [final] ).

cnf(c_0_6489,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1)
    | X2 != X3 ),
    c_0_4823,
    [final] ).

cnf(c_0_6490,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4824,
    [final] ).

cnf(c_0_6491,plain,
    ( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4825,
    [final] ).

cnf(c_0_6492,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4826,
    [final] ).

cnf(c_0_6493,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1) ),
    c_0_4827,
    [final] ).

cnf(c_0_6494,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4828,
    [final] ).

cnf(c_0_6495,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    c_0_4829,
    [final] ).

cnf(c_0_6496,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_4830,
    [final] ).

cnf(c_0_6497,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    c_0_4831,
    [final] ).

cnf(c_0_6498,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_4832,
    [final] ).

cnf(c_0_6499,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4833,
    [final] ).

cnf(c_0_6500,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4834,
    [final] ).

cnf(c_0_6501,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    c_0_4835,
    [final] ).

cnf(c_0_6502,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    c_0_4836,
    [final] ).

cnf(c_0_6503,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Omonoid__add(X1) ),
    c_0_4837,
    [final] ).

cnf(c_0_6504,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    c_0_4838,
    [final] ).

cnf(c_0_6505,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
    | ~ class_Groups_Omonoid__add(X1) ),
    c_0_4839,
    [final] ).

cnf(c_0_6506,plain,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4840,
    [final] ).

cnf(c_0_6507,plain,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4841,
    [final] ).

cnf(c_0_6508,plain,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4842,
    [final] ).

cnf(c_0_6509,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4843,
    [final] ).

cnf(c_0_6510,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4844,
    [final] ).

cnf(c_0_6511,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != c_Nat_OSuc(X2) ),
    c_0_4845,
    [final] ).

cnf(c_0_6512,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    c_0_4846,
    [final] ).

cnf(c_0_6513,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    c_0_4847,
    [final] ).

cnf(c_0_6514,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    c_0_4848,
    [final] ).

cnf(c_0_6515,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4849,
    [final] ).

cnf(c_0_6516,plain,
    ( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4850,
    [final] ).

cnf(c_0_6517,plain,
    ( c_Divides_Odiv__class_Omod(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    c_0_4851,
    [final] ).

cnf(c_0_6518,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    c_0_4852,
    [final] ).

cnf(c_0_6519,plain,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4853,
    [final] ).

cnf(c_0_6520,plain,
    ( ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4854,
    [final] ).

cnf(c_0_6521,plain,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    c_0_4855,
    [final] ).

cnf(c_0_6522,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
    c_0_4856,
    [final] ).

cnf(c_0_6523,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4857,
    [final] ).

cnf(c_0_6524,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X1 != c_Nat_OSuc(X2) ),
    c_0_4858,
    [final] ).

cnf(c_0_6525,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
    c_0_4859,
    [final] ).

cnf(c_0_6526,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != X2 ),
    c_0_4860,
    [final] ).

cnf(c_0_6527,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X1)),
    c_0_4861,
    [final] ).

cnf(c_0_6528,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    c_0_4862,
    [final] ).

cnf(c_0_6529,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4863,
    [final] ).

cnf(c_0_6530,plain,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    c_0_4864,
    [final] ).

cnf(c_0_6531,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_4865,
    [final] ).

cnf(c_0_6532,plain,
    ( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4866,
    [final] ).

cnf(c_0_6533,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4867,
    [final] ).

cnf(c_0_6534,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4868,
    [final] ).

cnf(c_0_6535,plain,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4869,
    [final] ).

cnf(c_0_6536,plain,
    ( X2 = X3
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_Int_Onumber__class_Onumber__of(X1,X2) != c_Int_Onumber__class_Onumber__of(X1,X3) ),
    c_0_4870,
    [final] ).

cnf(c_0_6537,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = c_Nat_OSuc(X1),
    c_0_4871,
    [final] ).

cnf(c_0_6538,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_OSuc(X1),
    c_0_4872,
    [final] ).

cnf(c_0_6539,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4873,
    [final] ).

cnf(c_0_6540,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4874,
    [final] ).

cnf(c_0_6541,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X2
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    c_0_4875,
    [final] ).

cnf(c_0_6542,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    c_0_4876,
    [final] ).

cnf(c_0_6543,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    c_0_4877,
    [final] ).

cnf(c_0_6544,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    c_0_4878,
    [final] ).

cnf(c_0_6545,plain,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    c_0_4879,
    [final] ).

cnf(c_0_6546,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1)),
    c_0_4880,
    [final] ).

cnf(c_0_6547,plain,
    c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),
    c_0_4881,
    [final] ).

cnf(c_0_6548,plain,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_4882,
    [final] ).

cnf(c_0_6549,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_4883,
    [final] ).

cnf(c_0_6550,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4884,
    [final] ).

cnf(c_0_6551,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4885,
    [final] ).

cnf(c_0_6552,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4886,
    [final] ).

cnf(c_0_6553,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
    c_0_4887,
    [final] ).

cnf(c_0_6554,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
    c_0_4888,
    [final] ).

cnf(c_0_6555,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = X1,
    c_0_4889,
    [final] ).

cnf(c_0_6556,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = X1,
    c_0_4890,
    [final] ).

cnf(c_0_6557,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) = X1,
    c_0_4891,
    [final] ).

cnf(c_0_6558,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
    c_0_4892,
    [final] ).

cnf(c_0_6559,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    c_0_4893,
    [final] ).

cnf(c_0_6560,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) = c_Int_OBit0(X1),
    c_0_4894,
    [final] ).

cnf(c_0_6561,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
    c_0_4895,
    [final] ).

cnf(c_0_6562,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = X1,
    c_0_4896,
    [final] ).

cnf(c_0_6563,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
    c_0_4897,
    [final] ).

cnf(c_0_6564,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    c_0_4898,
    [final] ).

cnf(c_0_6565,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    c_0_4899,
    [final] ).

cnf(c_0_6566,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    c_0_4900,
    [final] ).

cnf(c_0_6567,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    c_0_4901,
    [final] ).

cnf(c_0_6568,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | X1 != X2 ),
    c_0_4902,
    [final] ).

cnf(c_0_6569,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    c_0_4903,
    [final] ).

cnf(c_0_6570,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    c_0_4904,
    [final] ).

cnf(c_0_6571,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    c_0_4905,
    [final] ).

cnf(c_0_6572,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X2 ),
    c_0_4906,
    [final] ).

cnf(c_0_6573,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
    c_0_4907,
    [final] ).

cnf(c_0_6574,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_4908,
    [final] ).

cnf(c_0_6575,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
    c_0_4909,
    [final] ).

cnf(c_0_6576,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
    c_0_4910,
    [final] ).

cnf(c_0_6577,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_4911,
    [final] ).

cnf(c_0_6578,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4912,
    [final] ).

cnf(c_0_6579,plain,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    c_0_4913,
    [final] ).

cnf(c_0_6580,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
    c_0_4914,
    [final] ).

cnf(c_0_6581,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
    c_0_4915,
    [final] ).

cnf(c_0_6582,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
    c_0_4916,
    [final] ).

cnf(c_0_6583,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
    c_0_4917,
    [final] ).

cnf(c_0_6584,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    c_0_4918,
    [final] ).

cnf(c_0_6585,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1) = X1,
    c_0_4919,
    [final] ).

cnf(c_0_6586,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    c_0_4920,
    [final] ).

cnf(c_0_6587,plain,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,X1) = c_Int_OPls,
    c_0_4921,
    [final] ).

cnf(c_0_6588,plain,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
    c_0_4922,
    [final] ).

cnf(c_0_6589,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    c_0_4923,
    [final] ).

cnf(c_0_6590,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
    c_0_4924,
    [final] ).

cnf(c_0_6591,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
    c_0_4925,
    [final] ).

cnf(c_0_6592,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X1)) ),
    c_0_4926,
    [final] ).

cnf(c_0_6593,plain,
    ( X2 = c_Int_Onumber__class_Onumber__of(X1,X3)
    | ~ class_Int_Onumber(X1)
    | c_Int_Onumber__class_Onumber__of(X1,X3) != X2 ),
    c_0_4927,
    [final] ).

cnf(c_0_6594,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) = X3
    | ~ class_Int_Onumber(X1)
    | X3 != c_Int_Onumber__class_Onumber__of(X1,X2) ),
    c_0_4928,
    [final] ).

cnf(c_0_6595,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Int_Onumber__class_Onumber__of(X1,X3)
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != X3 ),
    c_0_4929,
    [final] ).

cnf(c_0_6596,plain,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls))
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4930,
    [final] ).

cnf(c_0_6597,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    c_0_4931,
    [final] ).

cnf(c_0_6598,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    c_0_4932,
    [final] ).

cnf(c_0_6599,plain,
    ( ~ c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    c_0_4933,
    [final] ).

cnf(c_0_6600,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__1(X1)
    | ~ c_Int_Oiszero(X1,X2) ),
    c_0_4934,
    [final] ).

cnf(c_0_6601,plain,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
    c_0_4935,
    [final] ).

cnf(c_0_6602,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    c_0_4936,
    [final] ).

cnf(c_0_6603,plain,
    ( c_Int_Oiszero(X1,X2)
    | ~ class_Rings_Osemiring__1(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4937,
    [final] ).

cnf(c_0_6604,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4938,
    [final] ).

cnf(c_0_6605,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4939,
    [final] ).

cnf(c_0_6606,plain,
    ( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    c_0_4940,
    [final] ).

cnf(c_0_6607,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    c_0_4941,
    [final] ).

cnf(c_0_6608,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    c_0_4942,
    [final] ).

cnf(c_0_6609,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4943,
    [final] ).

cnf(c_0_6610,plain,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    c_0_4944,
    [final] ).

cnf(c_0_6611,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_4945,
    [final] ).

cnf(c_0_6612,plain,
    ( X2 = c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Oone(X1)
    | c_Groups_Oone__class_Oone(X1) != X2 ),
    c_0_4946,
    [final] ).

cnf(c_0_6613,plain,
    ( c_Groups_Oone__class_Oone(X1) = X2
    | ~ class_Groups_Oone(X1)
    | X2 != c_Groups_Oone__class_Oone(X1) ),
    c_0_4947,
    [final] ).

cnf(c_0_6614,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ozero(X1)
    | c_Groups_Ozero__class_Ozero(X1) != X2 ),
    c_0_4948,
    [final] ).

cnf(c_0_6615,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = X2
    | ~ class_Groups_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    c_0_4949,
    [final] ).

cnf(c_0_6616,plain,
    ( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1) ),
    c_0_4950,
    [final] ).

cnf(c_0_6617,plain,
    ( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1) ),
    c_0_4951,
    [final] ).

cnf(c_0_6618,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    c_0_4952,
    [final] ).

cnf(c_0_6619,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    c_0_4953,
    [final] ).

cnf(c_0_6620,plain,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    c_0_4954,
    [final] ).

cnf(c_0_6621,plain,
    c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    c_0_4955,
    [final] ).

cnf(c_0_6622,plain,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    c_0_4956,
    [final] ).

cnf(c_0_6623,plain,
    ( X1 = X2
    | c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
    c_0_4957,
    [final] ).

cnf(c_0_6624,plain,
    ( X1 = X2
    | c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
    c_0_4958,
    [final] ).

cnf(c_0_6625,plain,
    ( X1 = X2
    | c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
    c_0_4959,
    [final] ).

cnf(c_0_6626,plain,
    ( X1 = X2
    | c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
    c_0_4960,
    [final] ).

cnf(c_0_6627,plain,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_4961,
    [final] ).

cnf(c_0_6628,plain,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) = X1,
    c_0_4962,
    [final] ).

cnf(c_0_6629,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4963,
    [final] ).

cnf(c_0_6630,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4964,
    [final] ).

cnf(c_0_6631,plain,
    c_Int_OBit1(X1) != c_Int_OBit0(X2),
    c_0_4965,
    [final] ).

cnf(c_0_6632,plain,
    c_Int_OBit0(X1) != c_Int_OBit1(X2),
    c_0_4966,
    [final] ).

cnf(c_0_6633,plain,
    ( c_Nat_OSuc(X1) = c_Nat_OSuc(X2)
    | X1 != X2 ),
    c_0_4967,
    [final] ).

cnf(c_0_6634,plain,
    ( c_Int_OBit0(X1) = c_Int_OBit0(X2)
    | X1 != X2 ),
    c_0_4968,
    [final] ).

cnf(c_0_6635,plain,
    ( c_Int_OBit1(X1) = c_Int_OBit1(X2)
    | X1 != X2 ),
    c_0_4969,
    [final] ).

cnf(c_0_6636,plain,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    c_0_4970,
    [final] ).

cnf(c_0_6637,plain,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4971,
    [final] ).

cnf(c_0_6638,plain,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4972,
    [final] ).

cnf(c_0_6639,plain,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4973,
    [final] ).

cnf(c_0_6640,plain,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4974,
    [final] ).

cnf(c_0_6641,plain,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4975,
    [final] ).

cnf(c_0_6642,plain,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    c_0_4976,
    [final] ).

cnf(c_0_6643,plain,
    c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    c_0_4977,
    [final] ).

cnf(c_0_6644,plain,
    ( X1 = c_Int_OMin
    | c_Int_OBit1(X1) != c_Int_OMin ),
    c_0_4978,
    [final] ).

cnf(c_0_6645,plain,
    ( c_Int_OMin = X1
    | c_Int_OBit1(X1) != c_Int_OMin ),
    c_0_4979,
    [final] ).

cnf(c_0_6646,plain,
    ( X1 = c_Int_OPls
    | c_Int_OBit0(X1) != c_Int_OPls ),
    c_0_4980,
    [final] ).

cnf(c_0_6647,plain,
    ( c_Int_OPls = X1
    | c_Int_OBit0(X1) != c_Int_OPls ),
    c_0_4981,
    [final] ).

cnf(c_0_6648,plain,
    c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    c_0_4982,
    [final] ).

cnf(c_0_6649,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    c_0_4983,
    [final] ).

cnf(c_0_6650,plain,
    c_Nat_OSuc(X1) != X1,
    c_0_4984,
    [final] ).

cnf(c_0_6651,plain,
    c_Nat_OSuc(X1) != X1,
    c_0_4985,
    [final] ).

cnf(c_0_6652,plain,
    c_Int_OBit0(X1) != c_Int_OMin,
    c_0_4986,
    [final] ).

cnf(c_0_6653,plain,
    c_Int_OBit0(X1) != c_Int_OMin,
    c_0_4987,
    [final] ).

cnf(c_0_6654,plain,
    c_Int_OBit1(X1) != c_Int_OPls,
    c_0_4988,
    [final] ).

cnf(c_0_6655,plain,
    c_Int_OBit1(X1) != c_Int_OPls,
    c_0_4989,
    [final] ).

cnf(c_0_6656,plain,
    ( c_Int_OBit1(X1) = c_Int_OMin
    | X1 != c_Int_OMin ),
    c_0_4990,
    [final] ).

cnf(c_0_6657,plain,
    ( c_Int_OBit1(X1) = c_Int_OMin
    | c_Int_OMin != X1 ),
    c_0_4991,
    [final] ).

cnf(c_0_6658,plain,
    ( c_Int_OBit0(X1) = c_Int_OPls
    | X1 != c_Int_OPls ),
    c_0_4992,
    [final] ).

cnf(c_0_6659,plain,
    ( c_Int_OBit0(X1) = c_Int_OPls
    | c_Int_OPls != X1 ),
    c_0_4993,
    [final] ).

cnf(c_0_6660,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != v_n,
    c_0_4994,
    [final] ).

cnf(c_0_6661,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != v_na____,
    c_0_4995,
    [final] ).

cnf(c_0_6662,plain,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    c_0_4996,
    [final] ).

cnf(c_0_6663,plain,
    class_Groups_Oone(tc_Complex_Ocomplex),
    c_0_4997,
    [final] ).

cnf(c_0_6664,plain,
    class_Int_Onumber(tc_Complex_Ocomplex),
    c_0_4998,
    [final] ).

cnf(c_0_6665,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    c_0_4999,
    [final] ).

cnf(c_0_6666,plain,
    class_Rings_Oring(tc_Complex_Ocomplex),
    c_0_5000,
    [final] ).

cnf(c_0_6667,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    c_0_5001,
    [final] ).

cnf(c_0_6668,plain,
    class_Power_Opower(tc_Complex_Ocomplex),
    c_0_5002,
    [final] ).

cnf(c_0_6669,plain,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    c_0_5003,
    [final] ).

cnf(c_0_6670,plain,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    c_0_5004,
    [final] ).

cnf(c_0_6671,plain,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    c_0_5005,
    [final] ).

cnf(c_0_6672,plain,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    c_0_5006,
    [final] ).

cnf(c_0_6673,plain,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    c_0_5007,
    [final] ).

cnf(c_0_6674,plain,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    c_0_5008,
    [final] ).

cnf(c_0_6675,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    c_0_5009,
    [final] ).

cnf(c_0_6676,plain,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    c_0_5010,
    [final] ).

cnf(c_0_6677,plain,
    class_Rings_Osemiring__1(tc_Complex_Ocomplex),
    c_0_5011,
    [final] ).

cnf(c_0_6678,plain,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    c_0_5012,
    [final] ).

cnf(c_0_6679,plain,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    c_0_5013,
    [final] ).

cnf(c_0_6680,plain,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    c_0_5014,
    [final] ).

cnf(c_0_6681,plain,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    c_0_5015,
    [final] ).

cnf(c_0_6682,plain,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    c_0_5016,
    [final] ).

cnf(c_0_6683,plain,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    c_0_5017,
    [final] ).

cnf(c_0_6684,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    c_0_5018,
    [final] ).

cnf(c_0_6685,plain,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    c_0_5019,
    [final] ).

cnf(c_0_6686,plain,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    c_0_5020,
    [final] ).

cnf(c_0_6687,plain,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    c_0_5021,
    [final] ).

cnf(c_0_6688,plain,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    c_0_5022,
    [final] ).

cnf(c_0_6689,plain,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    c_0_5023,
    [final] ).

cnf(c_0_6690,plain,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    c_0_5024,
    [final] ).

cnf(c_0_6691,plain,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    c_0_5025,
    [final] ).

cnf(c_0_6692,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    c_0_5026,
    [final] ).

cnf(c_0_6693,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    c_0_5027,
    [final] ).

cnf(c_0_6694,plain,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    c_0_5028,
    [final] ).

cnf(c_0_6695,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    c_0_5029,
    [final] ).

cnf(c_0_6696,plain,
    class_Rings_Odvd(tc_RealDef_Oreal),
    c_0_5030,
    [final] ).

cnf(c_0_6697,plain,
    class_Groups_Oone(tc_RealDef_Oreal),
    c_0_5031,
    [final] ).

cnf(c_0_6698,plain,
    class_Int_Onumber(tc_RealDef_Oreal),
    c_0_5032,
    [final] ).

cnf(c_0_6699,plain,
    class_Rings_Oidom(tc_RealDef_Oreal),
    c_0_5033,
    [final] ).

cnf(c_0_6700,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    c_0_5034,
    [final] ).

cnf(c_0_6701,plain,
    class_Groups_Ozero(tc_RealDef_Oreal),
    c_0_5035,
    [final] ).

cnf(c_0_6702,plain,
    class_Power_Opower(tc_RealDef_Oreal),
    c_0_5036,
    [final] ).

cnf(c_0_6703,plain,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    c_0_5037,
    [final] ).

cnf(c_0_6704,plain,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    c_0_5038,
    [final] ).

cnf(c_0_6705,plain,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    c_0_5039,
    [final] ).

cnf(c_0_6706,plain,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    c_0_5040,
    [final] ).

cnf(c_0_6707,plain,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    c_0_5041,
    [final] ).

cnf(c_0_6708,plain,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    c_0_5042,
    [final] ).

cnf(c_0_6709,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    c_0_5043,
    [final] ).

cnf(c_0_6710,plain,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    c_0_5044,
    [final] ).

cnf(c_0_6711,plain,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    c_0_5045,
    [final] ).

cnf(c_0_6712,plain,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    c_0_5046,
    [final] ).

cnf(c_0_6713,plain,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    c_0_5047,
    [final] ).

cnf(c_0_6714,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    c_0_5048,
    [final] ).

cnf(c_0_6715,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    c_0_5049,
    [final] ).

cnf(c_0_6716,plain,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    c_0_5050,
    [final] ).

cnf(c_0_6717,plain,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    c_0_5051,
    [final] ).

cnf(c_0_6718,plain,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    c_0_5052,
    [final] ).

cnf(c_0_6719,plain,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    c_0_5053,
    [final] ).

cnf(c_0_6720,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    c_0_5054,
    [final] ).

cnf(c_0_6721,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    c_0_5055,
    [final] ).

cnf(c_0_6722,plain,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    c_0_5056,
    [final] ).

cnf(c_0_6723,plain,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    c_0_5057,
    [final] ).

cnf(c_0_6724,plain,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    c_0_5058,
    [final] ).

cnf(c_0_6725,plain,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    c_0_5059,
    [final] ).

cnf(c_0_6726,plain,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    c_0_5060,
    [final] ).

cnf(c_0_6727,plain,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    c_0_5061,
    [final] ).

cnf(c_0_6728,plain,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    c_0_5062,
    [final] ).

cnf(c_0_6729,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    c_0_5063,
    [final] ).

cnf(c_0_6730,plain,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    c_0_5064,
    [final] ).

cnf(c_0_6731,plain,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    c_0_5065,
    [final] ).

cnf(c_0_6732,plain,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    c_0_5066,
    [final] ).

cnf(c_0_6733,plain,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    c_0_5067,
    [final] ).

cnf(c_0_6734,plain,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    c_0_5068,
    [final] ).

cnf(c_0_6735,plain,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    c_0_5069,
    [final] ).

cnf(c_0_6736,plain,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    c_0_5070,
    [final] ).

cnf(c_0_6737,plain,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    c_0_5071,
    [final] ).

cnf(c_0_6738,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    c_0_5072,
    [final] ).

cnf(c_0_6739,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    c_0_5073,
    [final] ).

cnf(c_0_6740,plain,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    c_0_5074,
    [final] ).

cnf(c_0_6741,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    c_0_5075,
    [final] ).

cnf(c_0_6742,plain,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    c_0_5076,
    [final] ).

cnf(c_0_6743,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    c_0_5077,
    [final] ).

cnf(c_0_6744,plain,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    c_0_5078,
    [final] ).

cnf(c_0_6745,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    c_0_5079,
    [final] ).

cnf(c_0_6746,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    c_0_5080,
    [final] ).

cnf(c_0_6747,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    c_0_5081,
    [final] ).

cnf(c_0_6748,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    c_0_5082,
    [final] ).

cnf(c_0_6749,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    c_0_5083,
    [final] ).

cnf(c_0_6750,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    c_0_5084,
    [final] ).

cnf(c_0_6751,plain,
    class_Groups_Oone(tc_Nat_Onat),
    c_0_5085,
    [final] ).

cnf(c_0_6752,plain,
    class_Int_Onumber(tc_Nat_Onat),
    c_0_5086,
    [final] ).

cnf(c_0_6753,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    c_0_5087,
    [final] ).

cnf(c_0_6754,plain,
    class_Power_Opower(tc_Nat_Onat),
    c_0_5088,
    [final] ).

cnf(c_0_6755,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    c_0_5089,
    [final] ).

cnf(c_0_6756,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    c_0_5090,
    [final] ).

cnf(c_0_6757,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    c_0_5091,
    [final] ).

cnf(c_0_6758,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    c_0_5092,
    [final] ).

cnf(c_0_6759,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    c_0_5093,
    [final] ).

cnf(c_0_6760,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    c_0_5094,
    [final] ).

cnf(c_0_6761,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    c_0_5095,
    [final] ).

cnf(c_0_6762,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    c_0_5096,
    [final] ).

cnf(c_0_6763,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    c_0_5097,
    [final] ).

cnf(c_0_6764,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    c_0_5098,
    [final] ).

cnf(c_0_6765,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    c_0_5099,
    [final] ).

cnf(c_0_6766,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    c_0_5100,
    [final] ).

cnf(c_0_6767,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    c_0_5101,
    [final] ).

cnf(c_0_6768,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    c_0_5102,
    [final] ).

cnf(c_0_6769,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    c_0_5103,
    [final] ).

cnf(c_0_6770,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    c_0_5104,
    [final] ).

cnf(c_0_6771,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    c_0_5105,
    [final] ).

cnf(c_0_6772,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    c_0_5106,
    [final] ).

cnf(c_0_6773,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    c_0_5107,
    [final] ).

cnf(c_0_6774,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    c_0_5108,
    [final] ).

cnf(c_0_6775,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    c_0_5109,
    [final] ).

cnf(c_0_6776,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    c_0_5110,
    [final] ).

cnf(c_0_6777,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    c_0_5111,
    [final] ).

cnf(c_0_6778,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    c_0_5112,
    [final] ).

cnf(c_0_6779,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    c_0_5113,
    [final] ).

cnf(c_0_6780,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    c_0_5114,
    [final] ).

cnf(c_0_6781,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    c_0_5115,
    [final] ).

cnf(c_0_6782,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    c_0_5116,
    [final] ).

cnf(c_0_6783,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    c_0_5117,
    [final] ).

cnf(c_0_6784,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    c_0_5118,
    [final] ).

cnf(c_0_6785,plain,
    class_Rings_Odvd(tc_Int_Oint),
    c_0_5119,
    [final] ).

cnf(c_0_6786,plain,
    class_Groups_Oone(tc_Int_Oint),
    c_0_5120,
    [final] ).

cnf(c_0_6787,plain,
    class_Int_Onumber(tc_Int_Oint),
    c_0_5121,
    [final] ).

cnf(c_0_6788,plain,
    class_Rings_Oidom(tc_Int_Oint),
    c_0_5122,
    [final] ).

cnf(c_0_6789,plain,
    class_Rings_Oring(tc_Int_Oint),
    c_0_5123,
    [final] ).

cnf(c_0_6790,plain,
    class_Groups_Ozero(tc_Int_Oint),
    c_0_5124,
    [final] ).

cnf(c_0_6791,plain,
    class_Power_Opower(tc_Int_Oint),
    c_0_5125,
    [final] ).

cnf(c_0_6792,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    c_0_5126,
    [final] ).

cnf(c_0_6793,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    c_0_5127,
    [final] ).

cnf(c_0_6794,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    c_0_5128,
    [final] ).

cnf(c_0_6795,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    c_0_5129,
    [final] ).

cnf(c_0_6796,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    c_0_5130,
    [final] ).

cnf(c_0_6797,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    c_0_5131,
    [final] ).

cnf(c_0_6798,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    c_0_5132,
    [final] ).

cnf(c_0_6799,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    c_0_5133,
    [final] ).

cnf(c_0_6800,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    c_0_5134,
    [final] ).

cnf(c_0_6801,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    c_0_5135,
    [final] ).

cnf(c_0_6802,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    c_0_5136,
    [final] ).

cnf(c_0_6803,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    c_0_5137,
    [final] ).

cnf(c_0_6804,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    c_0_5138,
    [final] ).

cnf(c_0_6805,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    c_0_5139,
    [final] ).

cnf(c_0_6806,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    c_0_5140,
    [final] ).

cnf(c_0_6807,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    c_0_5141,
    [final] ).

cnf(c_0_6808,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    c_0_5142,
    [final] ).

cnf(c_0_6809,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    c_0_5143,
    [final] ).

cnf(c_0_6810,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    c_0_5144,
    [final] ).

cnf(c_0_6811,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    c_0_5145,
    [final] ).

cnf(c_0_6812,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    c_0_5146,
    [final] ).

cnf(c_0_6813,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    c_0_5147,
    [final] ).

cnf(c_0_6814,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    c_0_5148,
    [final] ).

cnf(c_0_6815,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    c_0_5149,
    [final] ).

cnf(c_0_6816,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    c_0_5150,
    [final] ).

cnf(c_0_6817,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    c_0_5151,
    [final] ).

cnf(c_0_6818,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    c_0_5152,
    [final] ).

cnf(c_0_6819,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    c_0_5153,
    [final] ).

cnf(c_0_6820,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    c_0_5154,
    [final] ).

cnf(c_0_6821,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    c_0_5155,
    [final] ).

cnf(c_0_6822,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    c_0_5156,
    [final] ).

cnf(c_0_6823,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    c_0_5157,
    [final] ).

cnf(c_0_6824,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    c_0_5158,
    [final] ).

cnf(c_0_6825,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    c_0_5159,
    [final] ).

cnf(c_0_6826,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    c_0_5160,
    [final] ).

cnf(c_0_6827,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    c_0_5161,
    [final] ).

cnf(c_0_6828,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    c_0_5162,
    [final] ).

cnf(c_0_6829,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    c_0_5163,
    [final] ).

cnf(c_0_6830,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    c_0_5164,
    [final] ).

cnf(c_0_6831,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    c_0_5165,
    [final] ).

cnf(c_0_6832,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    c_0_5166,
    [final] ).

cnf(c_0_6833,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    c_0_5167,
    [final] ).

cnf(c_0_6834,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    c_0_5168,
    [final] ).

cnf(c_0_6835,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    c_0_5169,
    [final] ).

cnf(c_0_6836,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    c_0_5170,
    [final] ).

cnf(c_0_6837,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    c_0_5171,
    [final] ).

cnf(c_0_6838,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    c_0_5172,
    [final] ).

cnf(c_0_6839,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    c_0_5173,
    [final] ).

cnf(c_0_6840,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    c_0_5174,
    [final] ).

cnf(c_0_6841,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
    c_0_5175,
    [final] ).

cnf(c_0_6842,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    c_0_5176,
    [final] ).

cnf(c_0_6843,plain,
    c_Int_OMin != c_Int_OPls,
    c_0_5177,
    [final] ).

cnf(c_0_6844,plain,
    c_Int_OMin != c_Int_OPls,
    c_0_5178,
    [final] ).

% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_5179_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(X1,X3,X5)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X5)),c_Groups_Otimes__class_Otimes(X1,X4,c_Groups_Ominus__class_Ominus(X1,X3,X5))) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5179]) ).

cnf(c_0_5179_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(X1,X3,X5)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X5)),c_Groups_Otimes__class_Otimes(X1,X4,c_Groups_Ominus__class_Ominus(X1,X3,X5))) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5179]) ).

cnf(c_0_5180_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5180]) ).

cnf(c_0_5180_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5180]) ).

cnf(c_0_5180_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5180]) ).

cnf(c_0_5181_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5181]) ).

cnf(c_0_5181_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5181]) ).

cnf(c_0_5181_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5181]) ).

cnf(c_0_5182_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5182]) ).

cnf(c_0_5182_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5182]) ).

cnf(c_0_5182_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5182]) ).

cnf(c_0_5183_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5183]) ).

cnf(c_0_5183_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5183]) ).

cnf(c_0_5183_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5183]) ).

cnf(c_0_5184_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5184]) ).

cnf(c_0_5184_1,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5184]) ).

cnf(c_0_5184_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5184]) ).

cnf(c_0_5185_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5185]) ).

cnf(c_0_5185_1,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5185]) ).

cnf(c_0_5185_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4),X6)
    | ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5185]) ).

cnf(c_0_5186_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5186]) ).

cnf(c_0_5186_1,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5186]) ).

cnf(c_0_5186_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4),X6)
    | ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5186]) ).

cnf(c_0_5187_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5187]) ).

cnf(c_0_5187_1,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5187]) ).

cnf(c_0_5187_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5187]) ).

cnf(c_0_5188_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5188]) ).

cnf(c_0_5188_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5188]) ).

cnf(c_0_5188_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5188]) ).

cnf(c_0_5189_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5189]) ).

cnf(c_0_5189_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5189]) ).

cnf(c_0_5189_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5189]) ).

cnf(c_0_5190_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5190]) ).

cnf(c_0_5190_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5190]) ).

cnf(c_0_5190_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5190]) ).

cnf(c_0_5191_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5191]) ).

cnf(c_0_5191_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5191]) ).

cnf(c_0_5191_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5191]) ).

cnf(c_0_5192_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5192]) ).

cnf(c_0_5192_1,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5192]) ).

cnf(c_0_5192_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5192]) ).

cnf(c_0_5193_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5),X6)
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5193]) ).

cnf(c_0_5193_1,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5),X6)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5193]) ).

cnf(c_0_5193_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5193]) ).

cnf(c_0_5194_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5),X6)
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5194]) ).

cnf(c_0_5194_1,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5),X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5194]) ).

cnf(c_0_5194_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5194]) ).

cnf(c_0_5195_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5195]) ).

cnf(c_0_5195_1,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5195]) ).

cnf(c_0_5195_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6))
    | ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5195]) ).

cnf(c_0_5197_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5197]) ).

cnf(c_0_5197_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5197]) ).

cnf(c_0_5198_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),X3)) = c_Power_Opower__class_Opower(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5198]) ).

cnf(c_0_5198_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),X3)) = c_Power_Opower__class_Opower(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5198]) ).

cnf(c_0_5199_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),X3)) = c_Power_Opower__class_Opower(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5199]) ).

cnf(c_0_5199_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),X3)) = c_Power_Opower__class_Opower(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5199]) ).

cnf(c_0_5201_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5201]) ).

cnf(c_0_5201_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5201]) ).

cnf(c_0_5201_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5201]) ).

cnf(c_0_5202_0,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(literals_permutation,[status(thm)],[c_0_5202]) ).

cnf(c_0_5202_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(literals_permutation,[status(thm)],[c_0_5202]) ).

cnf(c_0_5202_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(literals_permutation,[status(thm)],[c_0_5202]) ).

cnf(c_0_5202_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5202]) ).

cnf(c_0_5203_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5203]) ).

cnf(c_0_5203_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5203]) ).

cnf(c_0_5203_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5203]) ).

cnf(c_0_5204_0,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5204]) ).

cnf(c_0_5204_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5204]) ).

cnf(c_0_5204_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5204]) ).

cnf(c_0_5205_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1),X2),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5205]) ).

cnf(c_0_5205_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1),X2),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5205]) ).

cnf(c_0_5206_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4),X2),X3),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5206]) ).

cnf(c_0_5206_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4),X2),X3),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5206]) ).

cnf(c_0_5207_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5207]) ).

cnf(c_0_5207_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5207]) ).

cnf(c_0_5208_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5208]) ).

cnf(c_0_5208_1,axiom,
    ( ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5208]) ).

cnf(c_0_5208_2,axiom,
    ( ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5208]) ).

cnf(c_0_5208_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5208]) ).

cnf(c_0_5208_4,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5208]) ).

cnf(c_0_5209_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5209]) ).

cnf(c_0_5209_1,axiom,
    ( ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5209]) ).

cnf(c_0_5209_2,axiom,
    ( ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5209]) ).

cnf(c_0_5209_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5209]) ).

cnf(c_0_5209_4,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X6,X3)),X5))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5209]) ).

cnf(c_0_5210_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5210]) ).

cnf(c_0_5210_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5210]) ).

cnf(c_0_5210_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5210]) ).

cnf(c_0_5210_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5210]) ).

cnf(c_0_5210_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5210]) ).

cnf(c_0_5210_5,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5210]) ).

cnf(c_0_5210_6,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X6))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5210]) ).

cnf(c_0_5211_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5211]) ).

cnf(c_0_5211_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5211]) ).

cnf(c_0_5211_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5211]) ).

cnf(c_0_5211_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5211]) ).

cnf(c_0_5211_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5211]) ).

cnf(c_0_5211_5,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5211]) ).

cnf(c_0_5211_6,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X6) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5211]) ).

cnf(c_0_5212_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X2)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5212]) ).

cnf(c_0_5212_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X2)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5212]) ).

cnf(c_0_5212_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X2)),X4))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5212]) ).

cnf(c_0_5213_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2)))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5213]) ).

cnf(c_0_5213_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5213]) ).

cnf(c_0_5214_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5214]) ).

cnf(c_0_5214_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5214]) ).

cnf(c_0_5214_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5214]) ).

cnf(c_0_5214_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5214]) ).

cnf(c_0_5214_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X1),X5),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2),X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5214]) ).

cnf(c_0_5215_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5215]) ).

cnf(c_0_5215_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5215]) ).

cnf(c_0_5215_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5215]) ).

cnf(c_0_5215_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5215]) ).

cnf(c_0_5215_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5215]) ).

cnf(c_0_5216_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5216]) ).

cnf(c_0_5216_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5216]) ).

cnf(c_0_5217_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5217]) ).

cnf(c_0_5217_1,axiom,
    ( ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6))
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5217]) ).

cnf(c_0_5217_2,axiom,
    ( ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5217]) ).

cnf(c_0_5217_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5217]) ).

cnf(c_0_5217_4,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5217]) ).

cnf(c_0_5218_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5218]) ).

cnf(c_0_5218_1,axiom,
    ( ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6))
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5218]) ).

cnf(c_0_5218_2,axiom,
    ( ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5218]) ).

cnf(c_0_5218_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5218]) ).

cnf(c_0_5218_4,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X4,X6))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X5,X3)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_5218]) ).

cnf(c_0_5219_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)),X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5219]) ).

cnf(c_0_5219_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)),X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5219]) ).

cnf(c_0_5219_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)),X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5219]) ).

cnf(c_0_5219_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5219]) ).

cnf(c_0_5220_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5220]) ).

cnf(c_0_5220_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5220]) ).

cnf(c_0_5220_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5220]) ).

cnf(c_0_5220_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5220]) ).

cnf(c_0_5221_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2)),X5))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5221]) ).

cnf(c_0_5221_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2)),X5))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5221]) ).

cnf(c_0_5221_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X5))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X2)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5221]) ).

cnf(c_0_5222_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5222]) ).

cnf(c_0_5222_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5222]) ).

cnf(c_0_5222_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5222]) ).

cnf(c_0_5223_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X3))) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5223]) ).

cnf(c_0_5223_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X3))) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5223]) ).

cnf(c_0_5224_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5224]) ).

cnf(c_0_5224_1,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5224]) ).

cnf(c_0_5224_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5224]) ).

cnf(c_0_5224_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5224]) ).

cnf(c_0_5224_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5224]) ).

cnf(c_0_5224_5,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
    | ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | ~ class_Rings_Olinordered__semiring__1__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5224]) ).

cnf(c_0_5224_6,axiom,
    ( ~ class_Rings_Olinordered__semiring__1__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X6)
    | ~ c_Orderings_Oord__class_Oless(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5224]) ).

cnf(c_0_5225_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5225]) ).

cnf(c_0_5225_1,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5225]) ).

cnf(c_0_5225_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5225]) ).

cnf(c_0_5225_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5225]) ).

cnf(c_0_5225_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
    | ~ class_Rings_Olinordered__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5225]) ).

cnf(c_0_5225_5,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6)
    | ~ class_Rings_Olinordered__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5225]) ).

cnf(c_0_5225_6,axiom,
    ( ~ class_Rings_Olinordered__semiring__1(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X5,X6)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oone__class_Oone(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5225]) ).

cnf(c_0_5226_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5226]) ).

cnf(c_0_5226_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5226]) ).

cnf(c_0_5226_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5226]) ).

cnf(c_0_5226_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5226]) ).

cnf(c_0_5227_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5227]) ).

cnf(c_0_5227_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5227]) ).

cnf(c_0_5227_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5227]) ).

cnf(c_0_5227_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5227]) ).

cnf(c_0_5228_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5228]) ).

cnf(c_0_5228_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5228]) ).

cnf(c_0_5228_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5228]) ).

cnf(c_0_5229_0,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5229]) ).

cnf(c_0_5229_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5229]) ).

cnf(c_0_5230_0,axiom,
    ( hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,sk1_esk8_3(X3,X2,X1))))
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(X2,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5230]) ).

cnf(c_0_5230_1,axiom,
    ( ~ class_Rings_Osemiring__0(X1)
    | hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,sk1_esk8_3(X3,X2,X1))))
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(X2,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5230]) ).

cnf(c_0_5230_2,axiom,
    ( ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,sk1_esk8_3(X3,X2,X1))))
    | ~ hBOOL(hAPP(X2,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5230]) ).

cnf(c_0_5230_3,axiom,
    ( ~ hBOOL(hAPP(X2,X4))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,sk1_esk8_3(X3,X2,X1))))
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5230]) ).

cnf(c_0_5230_4,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(X2,X4))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,sk1_esk8_3(X3,X2,X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_5230]) ).

cnf(c_0_5231_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5231]) ).

cnf(c_0_5231_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1))
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5231]) ).

cnf(c_0_5231_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5231]) ).

cnf(c_0_5231_3,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5231]) ).

cnf(c_0_5232_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5232]) ).

cnf(c_0_5232_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5232]) ).

cnf(c_0_5232_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(literals_permutation,[status(thm)],[c_0_5232]) ).

cnf(c_0_5233_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5233]) ).

cnf(c_0_5233_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5233]) ).

cnf(c_0_5233_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(literals_permutation,[status(thm)],[c_0_5233]) ).

cnf(c_0_5234_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5234]) ).

cnf(c_0_5234_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(literals_permutation,[status(thm)],[c_0_5234]) ).

cnf(c_0_5235_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X4 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5235]) ).

cnf(c_0_5235_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5)
    | X4 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5235]) ).

cnf(c_0_5235_2,axiom,
    ( X4 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5235]) ).

cnf(c_0_5236_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4) != X5 ),
    inference(literals_permutation,[status(thm)],[c_0_5236]) ).

cnf(c_0_5236_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4) != X5 ),
    inference(literals_permutation,[status(thm)],[c_0_5236]) ).

cnf(c_0_5236_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4) != X5
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5236]) ).

cnf(c_0_5237_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X5)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X5)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ class_Rings_Oring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5237]) ).

cnf(c_0_5237_1,axiom,
    ( ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X5)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X5)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5237]) ).

cnf(c_0_5238_0,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X3),c_Groups_Otimes__class_Otimes(X1,X2,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5238]) ).

cnf(c_0_5238_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X3),c_Groups_Otimes__class_Otimes(X1,X2,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5238]) ).

cnf(c_0_5238_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X3),c_Groups_Otimes__class_Otimes(X1,X2,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5238]) ).

cnf(c_0_5238_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X3),c_Groups_Otimes__class_Otimes(X1,X2,X2)))
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5238]) ).

cnf(c_0_5239_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5239]) ).

cnf(c_0_5239_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5239]) ).

cnf(c_0_5239_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5239]) ).

cnf(c_0_5240_0,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5240]) ).

cnf(c_0_5240_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5240]) ).

cnf(c_0_5240_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5240]) ).

cnf(c_0_5241_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5241]) ).

cnf(c_0_5241_1,axiom,
    ( ~ class_Rings_Olinordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5241]) ).

cnf(c_0_5242_0,axiom,
    ( X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5242]) ).

cnf(c_0_5242_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5242]) ).

cnf(c_0_5242_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X4),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5242]) ).

cnf(c_0_5243_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4) = X5
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5243]) ).

cnf(c_0_5243_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4) = X5
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5243]) ).

cnf(c_0_5243_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4) = X5 ),
    inference(literals_permutation,[status(thm)],[c_0_5243]) ).

cnf(c_0_5244_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5244]) ).

cnf(c_0_5244_1,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5244]) ).

cnf(c_0_5245_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)
    | ~ class_Rings_Oring(X1)
    | X4 != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5245]) ).

cnf(c_0_5245_1,axiom,
    ( ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)
    | X4 != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5245]) ).

cnf(c_0_5245_2,axiom,
    ( X4 != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6)
    | ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5245]) ).

cnf(c_0_5246_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)
    | ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4) != X6 ),
    inference(literals_permutation,[status(thm)],[c_0_5246]) ).

cnf(c_0_5246_1,axiom,
    ( ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4) != X6 ),
    inference(literals_permutation,[status(thm)],[c_0_5246]) ).

cnf(c_0_5246_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4) != X6
    | ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5246]) ).

cnf(c_0_5247_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5247]) ).

cnf(c_0_5247_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5247]) ).

cnf(c_0_5247_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1)))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5247]) ).

cnf(c_0_5248_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2
    | ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5248]) ).

cnf(c_0_5248_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2
    | epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5248]) ).

cnf(c_0_5248_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1)))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5248]) ).

cnf(c_0_5249_0,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5249]) ).

cnf(c_0_5249_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5249]) ).

cnf(c_0_5250_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)),c_Groups_Ozero__class_Ozero(X2))
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5250]) ).

cnf(c_0_5250_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)),c_Groups_Ozero__class_Ozero(X2))
    | X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Olinordered__idom(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5250]) ).

cnf(c_0_5250_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)),c_Groups_Ozero__class_Ozero(X2))
    | X1 = c_Groups_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5250]) ).

cnf(c_0_5251_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5251]) ).

cnf(c_0_5251_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5251]) ).

cnf(c_0_5252_0,axiom,
    ( X2 = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6)
    | ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5252]) ).

cnf(c_0_5252_1,axiom,
    ( ~ class_Rings_Oring(X1)
    | X2 = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5252]) ).

cnf(c_0_5252_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6)
    | ~ class_Rings_Oring(X1)
    | X2 = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5252]) ).

cnf(c_0_5253_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5) = X6
    | ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5253]) ).

cnf(c_0_5253_1,axiom,
    ( ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5) = X6
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_5253]) ).

cnf(c_0_5253_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6)
    | ~ class_Rings_Oring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5) = X6 ),
    inference(literals_permutation,[status(thm)],[c_0_5253]) ).

cnf(c_0_5254_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5254]) ).

cnf(c_0_5254_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5254]) ).

cnf(c_0_5254_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5254]) ).

cnf(c_0_5254_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5254]) ).

cnf(c_0_5255_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5255]) ).

cnf(c_0_5255_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5255]) ).

cnf(c_0_5255_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5255]) ).

cnf(c_0_5255_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5255]) ).

cnf(c_0_5256_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3),X5)
    | ~ class_Rings_Osemiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5256]) ).

cnf(c_0_5256_1,axiom,
    ( ~ class_Rings_Osemiring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5256]) ).

cnf(c_0_5257_0,axiom,
    ( X2 = X3
    | X4 = X5
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X5,X3)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X5,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5257]) ).

cnf(c_0_5257_1,axiom,
    ( X4 = X5
    | X2 = X3
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X5,X3)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X5,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5257]) ).

cnf(c_0_5257_2,axiom,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X4 = X5
    | X2 = X3
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X5,X3)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X5,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5257]) ).

cnf(c_0_5257_3,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X5,X3)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X5,X2))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X4 = X5
    | X2 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_5257]) ).

cnf(c_0_5258_0,axiom,
    ( X3 = X5
    | X2 = X4
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5258]) ).

cnf(c_0_5258_1,axiom,
    ( X2 = X4
    | X3 = X5
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5258]) ).

cnf(c_0_5258_2,axiom,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 = X4
    | X3 = X5
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5258]) ).

cnf(c_0_5258_3,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 = X4
    | X3 = X5 ),
    inference(literals_permutation,[status(thm)],[c_0_5258]) ).

cnf(c_0_5260_0,axiom,
    ( epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5260]) ).

cnf(c_0_5260_1,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1)))
    | epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5260]) ).

cnf(c_0_5260_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1)))
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5260]) ).

cnf(c_0_5261_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5261]) ).

cnf(c_0_5261_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5261]) ).

cnf(c_0_5261_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5261]) ).

cnf(c_0_5261_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5261]) ).

cnf(c_0_5262_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5262]) ).

cnf(c_0_5262_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5262]) ).

cnf(c_0_5262_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5262]) ).

cnf(c_0_5262_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5262]) ).

cnf(c_0_5263_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,sk1_esk7_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5263]) ).

cnf(c_0_5263_1,axiom,
    ( ~ class_Rings_Osemiring__0(X1)
    | c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,sk1_esk7_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5263]) ).

cnf(c_0_5263_2,axiom,
    ( ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,sk1_esk7_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5263]) ).

cnf(c_0_5263_3,axiom,
    ( ~ hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | c_Rings_Odvd__class_Odvd(X1,X3,c_Groups_Oplus__class_Oplus(X1,sk1_esk7_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5263]) ).

cnf(c_0_5264_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5264]) ).

cnf(c_0_5264_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5264]) ).

cnf(c_0_5265_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5265]) ).

cnf(c_0_5265_1,axiom,
    ( ~ class_Divides_Oring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5265]) ).

cnf(c_0_5266_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5266]) ).

cnf(c_0_5266_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5266]) ).

cnf(c_0_5268_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5268]) ).

cnf(c_0_5268_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5268]) ).

cnf(c_0_5268_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5268]) ).

cnf(c_0_5269_0,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5269]) ).

cnf(c_0_5269_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5269]) ).

cnf(c_0_5269_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5269]) ).

cnf(c_0_5270_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5270]) ).

cnf(c_0_5270_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5270]) ).

cnf(c_0_5271_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5271]) ).

cnf(c_0_5271_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5271]) ).

cnf(c_0_5272_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5272]) ).

cnf(c_0_5272_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5272]) ).

cnf(c_0_5272_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5272]) ).

cnf(c_0_5273_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5273]) ).

cnf(c_0_5273_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5273]) ).

cnf(c_0_5273_2,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5273]) ).

cnf(c_0_5274_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5274]) ).

cnf(c_0_5274_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5274]) ).

cnf(c_0_5274_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5274]) ).

cnf(c_0_5275_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5275]) ).

cnf(c_0_5275_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5275]) ).

cnf(c_0_5275_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5275]) ).

cnf(c_0_5276_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5276]) ).

cnf(c_0_5276_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5276]) ).

cnf(c_0_5276_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5276]) ).

cnf(c_0_5276_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5276]) ).

cnf(c_0_5277_0,axiom,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,sk1_esk15_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5277]) ).

cnf(c_0_5277_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ hBOOL(hAPP(X1,sk1_esk15_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5277]) ).

cnf(c_0_5277_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk15_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5277]) ).

cnf(c_0_5278_0,axiom,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,sk1_esk14_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5278]) ).

cnf(c_0_5278_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ hBOOL(hAPP(X1,sk1_esk14_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5278]) ).

cnf(c_0_5278_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk14_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5278]) ).

cnf(c_0_5279_0,axiom,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(X1,sk1_esk15_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5279]) ).

cnf(c_0_5279_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ hBOOL(hAPP(X1,sk1_esk15_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5279]) ).

cnf(c_0_5279_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk15_3(X3,X2,X1)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5279]) ).

cnf(c_0_5280_0,axiom,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(X1,sk1_esk14_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5280]) ).

cnf(c_0_5280_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ hBOOL(hAPP(X1,sk1_esk14_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5280]) ).

cnf(c_0_5280_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk14_3(X3,X2,X1)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5280]) ).

cnf(c_0_5281_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X5,X6),X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5281]) ).

cnf(c_0_5281_1,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X5,X6),X4)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5281]) ).

cnf(c_0_5281_2,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X5,X6),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5281]) ).

cnf(c_0_5281_3,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X5,X6),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5281]) ).

cnf(c_0_5282_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X5,X6),X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5282]) ).

cnf(c_0_5282_1,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X5,X6),X4)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5282]) ).

cnf(c_0_5282_2,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X5,X6),X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5282]) ).

cnf(c_0_5282_3,axiom,
    ( ~ class_Divides_Oring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X5,X6),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5282]) ).

cnf(c_0_5283_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X5,X6),X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5283]) ).

cnf(c_0_5283_1,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X5,X6),X4)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5283]) ).

cnf(c_0_5283_2,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X5,X6),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5283]) ).

cnf(c_0_5283_3,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X2,X4) != c_Divides_Odiv__class_Omod(X1,X5,X4)
    | c_Divides_Odiv__class_Omod(X1,X3,X4) != c_Divides_Odiv__class_Omod(X1,X6,X4)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X5,X6),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5283]) ).

cnf(c_0_5284_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(X1,X3,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5284]) ).

cnf(c_0_5284_1,axiom,
    ( ~ class_Rings_Ocomm__ring__1(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(X1,X3,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5284]) ).

cnf(c_0_5285_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5285]) ).

cnf(c_0_5285_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5285]) ).

cnf(c_0_5286_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5286]) ).

cnf(c_0_5286_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5286]) ).

cnf(c_0_5286_2,axiom,
    ( X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5286]) ).

cnf(c_0_5286_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5286]) ).

cnf(c_0_5286_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5286]) ).

cnf(c_0_5286_5,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5286]) ).

cnf(c_0_5286_6,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_5286]) ).

cnf(c_0_5287_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X5)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5287]) ).

cnf(c_0_5287_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_5287]) ).

cnf(c_0_5288_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,X4,c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5288]) ).

cnf(c_0_5288_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,X4,c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5288]) ).

cnf(c_0_5289_0,axiom,
    ( hBOOL(hAPP(X2,sk1_esk7_3(X3,X2,X1)))
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5289]) ).

cnf(c_0_5289_1,axiom,
    ( ~ class_Rings_Osemiring__0(X1)
    | hBOOL(hAPP(X2,sk1_esk7_3(X3,X2,X1)))
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5289]) ).

cnf(c_0_5289_2,axiom,
    ( ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | hBOOL(hAPP(X2,sk1_esk7_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_5289]) ).

cnf(c_0_5289_3,axiom,
    ( ~ hBOOL(hAPP(X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | hBOOL(hAPP(X2,sk1_esk7_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5289]) ).

cnf(c_0_5290_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5290]) ).

cnf(c_0_5290_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5290]) ).

cnf(c_0_5290_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5290]) ).

cnf(c_0_5290_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5290]) ).

cnf(c_0_5290_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5290]) ).

cnf(c_0_5290_5,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5290]) ).

cnf(c_0_5291_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5291]) ).

cnf(c_0_5291_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5291]) ).

cnf(c_0_5291_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5291]) ).

cnf(c_0_5291_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5291]) ).

cnf(c_0_5291_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5291]) ).

cnf(c_0_5291_5,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5291]) ).

cnf(c_0_5292_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5292]) ).

cnf(c_0_5292_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5292]) ).

cnf(c_0_5292_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5292]) ).

cnf(c_0_5292_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5292]) ).

cnf(c_0_5292_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5292]) ).

cnf(c_0_5292_5,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5292]) ).

cnf(c_0_5293_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5293]) ).

cnf(c_0_5293_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5293]) ).

cnf(c_0_5293_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5293]) ).

cnf(c_0_5293_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5293]) ).

cnf(c_0_5293_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5293]) ).

cnf(c_0_5293_5,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5293]) ).

cnf(c_0_5294_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5294]) ).

cnf(c_0_5294_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5294]) ).

cnf(c_0_5294_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5294]) ).

cnf(c_0_5294_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5294]) ).

cnf(c_0_5294_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5294]) ).

cnf(c_0_5294_5,axiom,
    ( ~ class_Rings_Oordered__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5294]) ).

cnf(c_0_5295_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5295]) ).

cnf(c_0_5295_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5295]) ).

cnf(c_0_5295_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5295]) ).

cnf(c_0_5295_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5295]) ).

cnf(c_0_5295_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5295]) ).

cnf(c_0_5295_5,axiom,
    ( ~ class_Rings_Oordered__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5295]) ).

cnf(c_0_5297_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5297]) ).

cnf(c_0_5297_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5297]) ).

cnf(c_0_5297_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5297]) ).

cnf(c_0_5297_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5297]) ).

cnf(c_0_5298_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5298]) ).

cnf(c_0_5298_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5298]) ).

cnf(c_0_5298_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5298]) ).

cnf(c_0_5298_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5298]) ).

cnf(c_0_5299_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5299]) ).

cnf(c_0_5299_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
    | c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X4))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5299]) ).

cnf(c_0_5299_2,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
    | c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X4)),X2) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5299]) ).

cnf(c_0_5300_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5300]) ).

cnf(c_0_5300_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)))
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5300]) ).

cnf(c_0_5301_0,axiom,
    ( hBOOL(hAPP(X1,X4))
    | ~ epred1_3(X1,X2,X3)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5301]) ).

cnf(c_0_5301_1,axiom,
    ( ~ epred1_3(X1,X2,X3)
    | hBOOL(hAPP(X1,X4))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5301]) ).

cnf(c_0_5301_2,axiom,
    ( X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ epred1_3(X1,X2,X3)
    | hBOOL(hAPP(X1,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5301]) ).

cnf(c_0_5301_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ epred1_3(X1,X2,X3)
    | hBOOL(hAPP(X1,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5301]) ).

cnf(c_0_5301_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ epred1_3(X1,X2,X3)
    | hBOOL(hAPP(X1,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5301]) ).

cnf(c_0_5301_5,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X3)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ epred1_3(X1,X2,X3)
    | hBOOL(hAPP(X1,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5301]) ).

cnf(c_0_5302_0,axiom,
    ( hBOOL(hAPP(X1,X4))
    | ~ epred1_3(X1,X2,X3)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5302]) ).

cnf(c_0_5302_1,axiom,
    ( ~ epred1_3(X1,X2,X3)
    | hBOOL(hAPP(X1,X4))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5302]) ).

cnf(c_0_5302_2,axiom,
    ( X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ epred1_3(X1,X2,X3)
    | hBOOL(hAPP(X1,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5302]) ).

cnf(c_0_5302_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ epred1_3(X1,X2,X3)
    | hBOOL(hAPP(X1,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5302]) ).

cnf(c_0_5302_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ epred1_3(X1,X2,X3)
    | hBOOL(hAPP(X1,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5302]) ).

cnf(c_0_5302_5,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X5),X4)
    | ~ epred1_3(X1,X2,X3)
    | hBOOL(hAPP(X1,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5302]) ).

cnf(c_0_5303_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5303]) ).

cnf(c_0_5303_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1))
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5303]) ).

cnf(c_0_5303_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5303]) ).

cnf(c_0_5303_3,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5303]) ).

cnf(c_0_5304_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X4)),c_Power_Opower__class_Opower(X1,X3,c_Nat_OSuc(X4)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5304]) ).

cnf(c_0_5304_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X4)),c_Power_Opower__class_Opower(X1,X3,c_Nat_OSuc(X4)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5304]) ).

cnf(c_0_5304_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X4)),c_Power_Opower__class_Opower(X1,X3,c_Nat_OSuc(X4)))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5304]) ).

cnf(c_0_5304_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X4)),c_Power_Opower__class_Opower(X1,X3,c_Nat_OSuc(X4)))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5304]) ).

cnf(c_0_5305_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X2,X4),c_Divides_Odiv__class_Odiv(X1,X3,X4)) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5305]) ).

cnf(c_0_5305_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X2,X4),c_Divides_Odiv__class_Odiv(X1,X3,X4)) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5305]) ).

cnf(c_0_5305_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X4,X2)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X2,X4),c_Divides_Odiv__class_Odiv(X1,X3,X4)) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5305]) ).

cnf(c_0_5305_3,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X2)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X2,X4),c_Divides_Odiv__class_Odiv(X1,X3,X4)) = c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5305]) ).

cnf(c_0_5306_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5306]) ).

cnf(c_0_5306_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5306]) ).

cnf(c_0_5306_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5306]) ).

cnf(c_0_5307_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5307]) ).

cnf(c_0_5307_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5307]) ).

cnf(c_0_5307_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5307]) ).

cnf(c_0_5308_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5308]) ).

cnf(c_0_5308_1,axiom,
    ( ~ class_Rings_Olinordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5308]) ).

cnf(c_0_5309_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5309]) ).

cnf(c_0_5309_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5309]) ).

cnf(c_0_5309_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1)))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5309]) ).

cnf(c_0_5310_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5310]) ).

cnf(c_0_5310_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5310]) ).

cnf(c_0_5310_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1)))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5310]) ).

cnf(c_0_5311_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5311]) ).

cnf(c_0_5311_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5311]) ).

cnf(c_0_5311_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1)))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5311]) ).

cnf(c_0_5312_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1))
    | ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5312]) ).

cnf(c_0_5312_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1))
    | epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5312]) ).

cnf(c_0_5312_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1)))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1))
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5312]) ).

cnf(c_0_5313_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5313]) ).

cnf(c_0_5313_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5313]) ).

cnf(c_0_5313_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk20_3(X3,X2,X1)),sk1_esk21_3(X3,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5313]) ).

cnf(c_0_5314_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5314]) ).

cnf(c_0_5314_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5314]) ).

cnf(c_0_5314_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,sk1_esk18_3(X3,X2,X1)),sk1_esk19_3(X3,X2,X1)) = X2
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5314]) ).

cnf(c_0_5315_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5315]) ).

cnf(c_0_5315_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5315]) ).

cnf(c_0_5315_2,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5315]) ).

cnf(c_0_5316_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5316]) ).

cnf(c_0_5316_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5316]) ).

cnf(c_0_5316_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5316]) ).

cnf(c_0_5316_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5316]) ).

cnf(c_0_5317_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5317]) ).

cnf(c_0_5317_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5317]) ).

cnf(c_0_5317_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5317]) ).

cnf(c_0_5317_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5317]) ).

cnf(c_0_5318_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5318]) ).

cnf(c_0_5318_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5318]) ).

cnf(c_0_5318_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5318]) ).

cnf(c_0_5318_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5318]) ).

cnf(c_0_5319_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5319]) ).

cnf(c_0_5319_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5319]) ).

cnf(c_0_5319_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Rings_Olinordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5319]) ).

cnf(c_0_5319_3,axiom,
    ( ~ class_Rings_Olinordered__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5319]) ).

cnf(c_0_5320_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5320]) ).

cnf(c_0_5320_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5320]) ).

cnf(c_0_5320_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5320]) ).

cnf(c_0_5320_3,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5320]) ).

cnf(c_0_5321_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5321]) ).

cnf(c_0_5321_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5321]) ).

cnf(c_0_5321_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Rings_Olinordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5321]) ).

cnf(c_0_5321_3,axiom,
    ( ~ class_Rings_Olinordered__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5321]) ).

cnf(c_0_5322_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5322]) ).

cnf(c_0_5322_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5322]) ).

cnf(c_0_5322_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5322]) ).

cnf(c_0_5322_3,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5322]) ).

cnf(c_0_5323_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5323]) ).

cnf(c_0_5323_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5323]) ).

cnf(c_0_5323_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5323]) ).

cnf(c_0_5323_3,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5323]) ).

cnf(c_0_5324_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5324]) ).

cnf(c_0_5324_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5324]) ).

cnf(c_0_5324_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5324]) ).

cnf(c_0_5324_3,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5324]) ).

cnf(c_0_5325_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5325]) ).

cnf(c_0_5325_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5325]) ).

cnf(c_0_5325_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5325]) ).

cnf(c_0_5325_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5325]) ).

cnf(c_0_5326_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5326]) ).

cnf(c_0_5326_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5326]) ).

cnf(c_0_5326_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5326]) ).

cnf(c_0_5326_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5326]) ).

cnf(c_0_5327_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5327]) ).

cnf(c_0_5327_1,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5327]) ).

cnf(c_0_5327_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5327]) ).

cnf(c_0_5327_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5327]) ).

cnf(c_0_5328_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
    | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5328]) ).

cnf(c_0_5328_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5328]) ).

cnf(c_0_5328_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
    | ~ c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5328]) ).

cnf(c_0_5328_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X3)
    | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
    | ~ c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5328]) ).

cnf(c_0_5329_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5329]) ).

cnf(c_0_5329_1,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5329]) ).

cnf(c_0_5329_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5329]) ).

cnf(c_0_5329_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5329]) ).

cnf(c_0_5330_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
    | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5330]) ).

cnf(c_0_5330_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5330]) ).

cnf(c_0_5330_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5330]) ).

cnf(c_0_5330_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X3)
    | ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5330]) ).

cnf(c_0_5331_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4))
    | ~ class_Rings_Oring(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5331]) ).

cnf(c_0_5331_1,axiom,
    ( ~ class_Rings_Oring(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4))
    | ~ class_Int_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5331]) ).

cnf(c_0_5331_2,axiom,
    ( ~ class_Int_Onumber(X1)
    | ~ class_Rings_Oring(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5331]) ).

cnf(c_0_5332_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,X3,X4))
    | ~ class_Rings_Oring(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5332]) ).

cnf(c_0_5332_1,axiom,
    ( ~ class_Rings_Oring(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,X3,X4))
    | ~ class_Int_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5332]) ).

cnf(c_0_5332_2,axiom,
    ( ~ class_Int_Onumber(X1)
    | ~ class_Rings_Oring(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5332]) ).

cnf(c_0_5333_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4))
    | ~ class_Rings_Osemiring(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5333]) ).

cnf(c_0_5333_1,axiom,
    ( ~ class_Rings_Osemiring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4))
    | ~ class_Int_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5333]) ).

cnf(c_0_5333_2,axiom,
    ( ~ class_Int_Onumber(X1)
    | ~ class_Rings_Osemiring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5333]) ).

cnf(c_0_5334_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Rings_Osemiring(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5334]) ).

cnf(c_0_5334_1,axiom,
    ( ~ class_Rings_Osemiring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Int_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5334]) ).

cnf(c_0_5334_2,axiom,
    ( ~ class_Int_Onumber(X1)
    | ~ class_Rings_Osemiring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5334]) ).

cnf(c_0_5335_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5335]) ).

cnf(c_0_5335_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5335]) ).

cnf(c_0_5336_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5336]) ).

cnf(c_0_5336_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5336]) ).

cnf(c_0_5336_2,axiom,
    ( X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5336]) ).

cnf(c_0_5336_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5336]) ).

cnf(c_0_5336_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5336]) ).

cnf(c_0_5336_5,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_5336]) ).

cnf(c_0_5337_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_5337]) ).

cnf(c_0_5337_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5337]) ).

cnf(c_0_5338_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5338]) ).

cnf(c_0_5338_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5338]) ).

cnf(c_0_5338_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5338]) ).

cnf(c_0_5339_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5339]) ).

cnf(c_0_5339_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5339]) ).

cnf(c_0_5339_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5339]) ).

cnf(c_0_5340_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5340]) ).

cnf(c_0_5340_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5340]) ).

cnf(c_0_5340_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5340]) ).

cnf(c_0_5341_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5341]) ).

cnf(c_0_5341_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5341]) ).

cnf(c_0_5341_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5341]) ).

cnf(c_0_5342_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5342]) ).

cnf(c_0_5342_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5342]) ).

cnf(c_0_5342_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5342]) ).

cnf(c_0_5343_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5343]) ).

cnf(c_0_5343_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5343]) ).

cnf(c_0_5343_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5343]) ).

cnf(c_0_5344_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5344]) ).

cnf(c_0_5344_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5344]) ).

cnf(c_0_5344_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5344]) ).

cnf(c_0_5345_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5345]) ).

cnf(c_0_5345_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5345]) ).

cnf(c_0_5345_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5345]) ).

cnf(c_0_5346_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5346]) ).

cnf(c_0_5346_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5346]) ).

cnf(c_0_5346_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5346]) ).

cnf(c_0_5347_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5347]) ).

cnf(c_0_5347_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5347]) ).

cnf(c_0_5347_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5347]) ).

cnf(c_0_5348_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5348]) ).

cnf(c_0_5348_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5348]) ).

cnf(c_0_5348_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5348]) ).

cnf(c_0_5349_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5349]) ).

cnf(c_0_5349_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5349]) ).

cnf(c_0_5349_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5349]) ).

cnf(c_0_5349_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5349]) ).

cnf(c_0_5349_4,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5349]) ).

cnf(c_0_5350_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5350]) ).

cnf(c_0_5350_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5350]) ).

cnf(c_0_5350_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5350]) ).

cnf(c_0_5350_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5350]) ).

cnf(c_0_5350_4,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5350]) ).

cnf(c_0_5351_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5351]) ).

cnf(c_0_5351_1,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5351]) ).

cnf(c_0_5351_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5351]) ).

cnf(c_0_5351_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5351]) ).

cnf(c_0_5352_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5352]) ).

cnf(c_0_5352_1,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5352]) ).

cnf(c_0_5352_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5352]) ).

cnf(c_0_5352_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5352]) ).

cnf(c_0_5353_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 != X4 ),
    inference(literals_permutation,[status(thm)],[c_0_5353]) ).

cnf(c_0_5353_1,axiom,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | X2 != X4 ),
    inference(literals_permutation,[status(thm)],[c_0_5353]) ).

cnf(c_0_5353_2,axiom,
    ( X2 != X4
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5353]) ).

cnf(c_0_5354_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != X5 ),
    inference(literals_permutation,[status(thm)],[c_0_5354]) ).

cnf(c_0_5354_1,axiom,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | X3 != X5 ),
    inference(literals_permutation,[status(thm)],[c_0_5354]) ).

cnf(c_0_5354_2,axiom,
    ( X3 != X5
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5354]) ).

cnf(c_0_5355_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 != X4 ),
    inference(literals_permutation,[status(thm)],[c_0_5355]) ).

cnf(c_0_5355_1,axiom,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | X2 != X4 ),
    inference(literals_permutation,[status(thm)],[c_0_5355]) ).

cnf(c_0_5355_2,axiom,
    ( X2 != X4
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5355]) ).

cnf(c_0_5356_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != X5 ),
    inference(literals_permutation,[status(thm)],[c_0_5356]) ).

cnf(c_0_5356_1,axiom,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | X3 != X5 ),
    inference(literals_permutation,[status(thm)],[c_0_5356]) ).

cnf(c_0_5356_2,axiom,
    ( X3 != X5
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5356]) ).

cnf(c_0_5357_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5357]) ).

cnf(c_0_5357_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5357]) ).

cnf(c_0_5357_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5357]) ).

cnf(c_0_5357_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5357]) ).

cnf(c_0_5357_4,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5357]) ).

cnf(c_0_5358_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5358]) ).

cnf(c_0_5358_1,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X4,X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5358]) ).

cnf(c_0_5358_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X4,X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5358]) ).

cnf(c_0_5358_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X4,X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5358]) ).

cnf(c_0_5359_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5359]) ).

cnf(c_0_5359_1,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5359]) ).

cnf(c_0_5359_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5359]) ).

cnf(c_0_5359_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5359]) ).

cnf(c_0_5360_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5360]) ).

cnf(c_0_5360_1,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X4,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5360]) ).

cnf(c_0_5360_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X4,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5360]) ).

cnf(c_0_5360_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X4,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5360]) ).

cnf(c_0_5361_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5361]) ).

cnf(c_0_5361_1,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5361]) ).

cnf(c_0_5361_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5361]) ).

cnf(c_0_5361_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5361]) ).

cnf(c_0_5362_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5362]) ).

cnf(c_0_5362_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5362]) ).

cnf(c_0_5363_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5363]) ).

cnf(c_0_5363_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5363]) ).

cnf(c_0_5364_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5364]) ).

cnf(c_0_5364_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5364]) ).

cnf(c_0_5365_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5365]) ).

cnf(c_0_5365_1,axiom,
    ( ~ class_Divides_Oring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5365]) ).

cnf(c_0_5366_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ class_Divides_Oring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5366]) ).

cnf(c_0_5366_1,axiom,
    ( ~ class_Divides_Oring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5366]) ).

cnf(c_0_5367_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5367]) ).

cnf(c_0_5367_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5367]) ).

cnf(c_0_5368_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5368]) ).

cnf(c_0_5368_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5368]) ).

cnf(c_0_5369_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5369]) ).

cnf(c_0_5369_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5369]) ).

cnf(c_0_5370_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5370]) ).

cnf(c_0_5370_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5370]) ).

cnf(c_0_5371_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5371]) ).

cnf(c_0_5371_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5371]) ).

cnf(c_0_5372_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5372]) ).

cnf(c_0_5372_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5372]) ).

cnf(c_0_5373_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5373]) ).

cnf(c_0_5373_1,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X4,X2)
    | c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5373]) ).

cnf(c_0_5373_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X4,X2)
    | c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5373]) ).

cnf(c_0_5373_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X4,X2)
    | c_Orderings_Oord__class_Oless(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5373]) ).

cnf(c_0_5374_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X3,X4)
    | c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5374]) ).

cnf(c_0_5374_1,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X4,X3)
    | c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5374]) ).

cnf(c_0_5374_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X4,X3)
    | c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5374]) ).

cnf(c_0_5374_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,X4,X3)
    | c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5374]) ).

cnf(c_0_5375_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5375]) ).

cnf(c_0_5375_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5375]) ).

cnf(c_0_5375_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5375]) ).

cnf(c_0_5375_3,axiom,
    ( X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5375]) ).

cnf(c_0_5375_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5375]) ).

cnf(c_0_5375_5,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_5375]) ).

cnf(c_0_5376_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5376]) ).

cnf(c_0_5376_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5376]) ).

cnf(c_0_5377_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5377]) ).

cnf(c_0_5377_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5377]) ).

cnf(c_0_5378_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),X4)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5378]) ).

cnf(c_0_5378_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5378]) ).

cnf(c_0_5379_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2) = c_Power_Opower__class_Opower(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5379]) ).

cnf(c_0_5379_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2) = c_Power_Opower__class_Opower(X1,X2,X3)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5379]) ).

cnf(c_0_5379_2,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2) = c_Power_Opower__class_Opower(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5379]) ).

cnf(c_0_5380_0,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5380]) ).

cnf(c_0_5380_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5380]) ).

cnf(c_0_5381_0,axiom,
    ( X4 = X6
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) != c_Groups_Oplus__class_Oplus(X1,X5,c_Groups_Otimes__class_Otimes(X1,X3,X6))
    | X2 != X5
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5381]) ).

cnf(c_0_5381_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | X4 = X6
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) != c_Groups_Oplus__class_Oplus(X1,X5,c_Groups_Otimes__class_Otimes(X1,X3,X6))
    | X2 != X5
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5381]) ).

cnf(c_0_5381_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) != c_Groups_Oplus__class_Oplus(X1,X5,c_Groups_Otimes__class_Otimes(X1,X3,X6))
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | X4 = X6
    | X2 != X5
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5381]) ).

cnf(c_0_5381_3,axiom,
    ( X2 != X5
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) != c_Groups_Oplus__class_Oplus(X1,X5,c_Groups_Otimes__class_Otimes(X1,X3,X6))
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | X4 = X6
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5381]) ).

cnf(c_0_5381_4,axiom,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 != X5
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) != c_Groups_Oplus__class_Oplus(X1,X5,c_Groups_Otimes__class_Otimes(X1,X3,X6))
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | X4 = X6 ),
    inference(literals_permutation,[status(thm)],[c_0_5381]) ).

cnf(c_0_5382_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4)) = c_Power_Opower__class_Opower(X1,c_Divides_Odiv__class_Odiv(X1,X2,X3),X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5382]) ).

cnf(c_0_5382_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
    | c_Divides_Odiv__class_Odiv(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4)) = c_Power_Opower__class_Opower(X1,c_Divides_Odiv__class_Odiv(X1,X2,X3),X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5382]) ).

cnf(c_0_5382_2,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
    | c_Divides_Odiv__class_Odiv(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4)) = c_Power_Opower__class_Opower(X1,c_Divides_Odiv__class_Odiv(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5382]) ).

cnf(c_0_5383_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5383]) ).

cnf(c_0_5383_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5383]) ).

cnf(c_0_5383_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5383]) ).

cnf(c_0_5383_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5383]) ).

cnf(c_0_5384_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5384]) ).

cnf(c_0_5384_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5384]) ).

cnf(c_0_5384_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5384]) ).

cnf(c_0_5384_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5384]) ).

cnf(c_0_5385_0,axiom,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | c_Power_Opower__class_Opower(X3,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5385]) ).

cnf(c_0_5385_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | c_Power_Opower__class_Opower(X3,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5385]) ).

cnf(c_0_5385_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | X1 = X2
    | c_Power_Opower__class_Opower(X3,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5385]) ).

cnf(c_0_5385_3,axiom,
    ( c_Power_Opower__class_Opower(X3,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | X1 = X2
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5385]) ).

cnf(c_0_5385_4,axiom,
    ( ~ class_Rings_Olinordered__semidom(X3)
    | c_Power_Opower__class_Opower(X3,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5385]) ).

cnf(c_0_5391_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5391]) ).

cnf(c_0_5391_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5391]) ).

cnf(c_0_5392_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5392]) ).

cnf(c_0_5392_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5392]) ).

cnf(c_0_5393_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5393]) ).

cnf(c_0_5393_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5393]) ).

cnf(c_0_5393_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5393]) ).

cnf(c_0_5393_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5393]) ).

cnf(c_0_5394_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5394]) ).

cnf(c_0_5394_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5394]) ).

cnf(c_0_5394_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5394]) ).

cnf(c_0_5394_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5394]) ).

cnf(c_0_5395_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X5),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5395]) ).

cnf(c_0_5395_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
    | c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X5),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5395]) ).

cnf(c_0_5395_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X5),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
    | c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5395]) ).

cnf(c_0_5395_3,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X5),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
    | c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5395]) ).

cnf(c_0_5396_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5396]) ).

cnf(c_0_5396_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5396]) ).

cnf(c_0_5397_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5397]) ).

cnf(c_0_5397_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5397]) ).

cnf(c_0_5398_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2))) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5398]) ).

cnf(c_0_5398_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2))) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_5398]) ).

cnf(c_0_5399_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5399]) ).

cnf(c_0_5399_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5399]) ).

cnf(c_0_5399_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk21_3(X3,X2,X1)))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5399]) ).

cnf(c_0_5400_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5400]) ).

cnf(c_0_5400_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5400]) ).

cnf(c_0_5400_2,axiom,
    ( ~ hBOOL(hAPP(X1,sk1_esk19_3(X3,X2,X1)))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5400]) ).

cnf(c_0_5401_0,axiom,
    ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5401]) ).

cnf(c_0_5401_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5401]) ).

cnf(c_0_5401_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(literals_permutation,[status(thm)],[c_0_5401]) ).

cnf(c_0_5402_0,axiom,
    ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5402]) ).

cnf(c_0_5402_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5402]) ).

cnf(c_0_5402_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(literals_permutation,[status(thm)],[c_0_5402]) ).

cnf(c_0_5403_0,axiom,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5403]) ).

cnf(c_0_5403_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | hBOOL(hAPP(X1,X4))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5403]) ).

cnf(c_0_5403_2,axiom,
    ( X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | hBOOL(hAPP(X1,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5403]) ).

cnf(c_0_5404_0,axiom,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5404]) ).

cnf(c_0_5404_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | hBOOL(hAPP(X1,X4))
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5404]) ).

cnf(c_0_5404_2,axiom,
    ( X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)
    | ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | hBOOL(hAPP(X1,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5404]) ).

cnf(c_0_5405_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | X4 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5405]) ).

cnf(c_0_5405_1,axiom,
    ( X4 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5405]) ).

cnf(c_0_5405_2,axiom,
    ( ~ class_Rings_Oidom(X1)
    | X4 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5405]) ).

cnf(c_0_5405_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Oidom(X1)
    | X4 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5405]) ).

cnf(c_0_5406_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | X4 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5406]) ).

cnf(c_0_5406_1,axiom,
    ( X4 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5406]) ).

cnf(c_0_5406_2,axiom,
    ( ~ class_Rings_Oidom(X1)
    | X4 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5406]) ).

cnf(c_0_5406_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Oidom(X1)
    | X4 = c_Groups_Ozero__class_Ozero(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5406]) ).

cnf(c_0_5407_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5407]) ).

cnf(c_0_5407_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5407]) ).

cnf(c_0_5407_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5407]) ).

cnf(c_0_5408_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5408]) ).

cnf(c_0_5408_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5408]) ).

cnf(c_0_5408_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5408]) ).

cnf(c_0_5409_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5409]) ).

cnf(c_0_5409_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5409]) ).

cnf(c_0_5409_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5409]) ).

cnf(c_0_5409_3,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5409]) ).

cnf(c_0_5410_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5410]) ).

cnf(c_0_5410_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5410]) ).

cnf(c_0_5410_2,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5410]) ).

cnf(c_0_5411_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5411]) ).

cnf(c_0_5411_1,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5411]) ).

cnf(c_0_5411_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5411]) ).

cnf(c_0_5412_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5412]) ).

cnf(c_0_5412_1,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5412]) ).

cnf(c_0_5412_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5412]) ).

cnf(c_0_5413_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5413]) ).

cnf(c_0_5413_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5413]) ).

cnf(c_0_5413_2,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5413]) ).

cnf(c_0_5414_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5414]) ).

cnf(c_0_5414_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5414]) ).

cnf(c_0_5414_2,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5414]) ).

cnf(c_0_5415_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5415]) ).

cnf(c_0_5415_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5415]) ).

cnf(c_0_5415_2,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5415]) ).

cnf(c_0_5416_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5416]) ).

cnf(c_0_5416_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5416]) ).

cnf(c_0_5416_2,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5416]) ).

cnf(c_0_5417_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5417]) ).

cnf(c_0_5417_1,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5417]) ).

cnf(c_0_5417_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5417]) ).

cnf(c_0_5418_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5418]) ).

cnf(c_0_5418_1,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5418]) ).

cnf(c_0_5418_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5418]) ).

cnf(c_0_5419_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1)) != X3
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5419]) ).

cnf(c_0_5419_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1)) != X3
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5419]) ).

cnf(c_0_5419_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1)) != X3
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5419]) ).

cnf(c_0_5419_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1)) != X3
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5419]) ).

cnf(c_0_5420_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5420]) ).

cnf(c_0_5420_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5420]) ).

cnf(c_0_5420_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5420]) ).

cnf(c_0_5421_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1)) != X3
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5421]) ).

cnf(c_0_5421_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1)) != X3
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5421]) ).

cnf(c_0_5421_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1)) != X3
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5421]) ).

cnf(c_0_5421_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1)) != X3
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5421]) ).

cnf(c_0_5422_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5422]) ).

cnf(c_0_5422_1,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5422]) ).

cnf(c_0_5422_2,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5422]) ).

cnf(c_0_5422_3,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5422]) ).

cnf(c_0_5423_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5423]) ).

cnf(c_0_5423_1,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5423]) ).

cnf(c_0_5424_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5424]) ).

cnf(c_0_5424_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5424]) ).

cnf(c_0_5425_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5425]) ).

cnf(c_0_5425_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5425]) ).

cnf(c_0_5425_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5425]) ).

cnf(c_0_5425_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5425]) ).

cnf(c_0_5426_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5426]) ).

cnf(c_0_5426_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5426]) ).

cnf(c_0_5426_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5426]) ).

cnf(c_0_5426_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5426]) ).

cnf(c_0_5427_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5427]) ).

cnf(c_0_5427_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5427]) ).

cnf(c_0_5427_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1))
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5427]) ).

cnf(c_0_5428_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X3),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5428]) ).

cnf(c_0_5428_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X3),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5428]) ).

cnf(c_0_5428_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X3),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X3))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5428]) ).

cnf(c_0_5429_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3),c_Power_Opower__class_Opower(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5429]) ).

cnf(c_0_5429_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3),c_Power_Opower__class_Opower(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5429]) ).

cnf(c_0_5429_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3),c_Power_Opower__class_Opower(tc_Int_Oint,X2,X3))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5429]) ).

cnf(c_0_5430_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X1),c_Power_Opower__class_Opower(tc_Int_Oint,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5430]) ).

cnf(c_0_5430_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X1),c_Power_Opower__class_Opower(tc_Int_Oint,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5430]) ).

cnf(c_0_5430_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X1),c_Power_Opower__class_Opower(tc_Int_Oint,X3,X1))
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5430]) ).

cnf(c_0_5431_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1))) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Oring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5431]) ).

cnf(c_0_5431_1,axiom,
    ( ~ class_Rings_Oring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1))) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5431]) ).

cnf(c_0_5432_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5432]) ).

cnf(c_0_5432_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5432]) ).

cnf(c_0_5432_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5432]) ).

cnf(c_0_5433_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5433]) ).

cnf(c_0_5433_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5433]) ).

cnf(c_0_5433_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5433]) ).

cnf(c_0_5434_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5434]) ).

cnf(c_0_5434_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5434]) ).

cnf(c_0_5434_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5434]) ).

cnf(c_0_5435_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5435]) ).

cnf(c_0_5435_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5435]) ).

cnf(c_0_5436_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5436]) ).

cnf(c_0_5436_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5436]) ).

cnf(c_0_5437_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5437]) ).

cnf(c_0_5437_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5437]) ).

cnf(c_0_5437_2,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5437]) ).

cnf(c_0_5438_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5438]) ).

cnf(c_0_5438_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5438]) ).

cnf(c_0_5439_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5439]) ).

cnf(c_0_5439_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5439]) ).

cnf(c_0_5440_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5440]) ).

cnf(c_0_5440_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5440]) ).

cnf(c_0_5441_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5441]) ).

cnf(c_0_5441_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5441]) ).

cnf(c_0_5442_0,axiom,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Rings_Olinordered__semidom(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5442]) ).

cnf(c_0_5442_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Rings_Olinordered__semidom(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5442]) ).

cnf(c_0_5442_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Rings_Olinordered__semidom(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5442]) ).

cnf(c_0_5442_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | X1 = X2
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ class_Rings_Olinordered__semidom(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5442]) ).

cnf(c_0_5442_4,axiom,
    ( c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | X1 = X2
    | ~ class_Rings_Olinordered__semidom(X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5442]) ).

cnf(c_0_5442_5,axiom,
    ( ~ class_Rings_Olinordered__semidom(X4)
    | c_Power_Opower__class_Opower(X4,X1,X3) != c_Power_Opower__class_Opower(X4,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5442]) ).

cnf(c_0_5443_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5443]) ).

cnf(c_0_5443_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5443]) ).

cnf(c_0_5443_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5443]) ).

cnf(c_0_5443_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5443]) ).

cnf(c_0_5444_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5444]) ).

cnf(c_0_5444_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5444]) ).

cnf(c_0_5444_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5444]) ).

cnf(c_0_5444_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5444]) ).

cnf(c_0_5445_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5445]) ).

cnf(c_0_5445_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5445]) ).

cnf(c_0_5445_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5445]) ).

cnf(c_0_5445_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5445]) ).

cnf(c_0_5446_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5446]) ).

cnf(c_0_5446_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5446]) ).

cnf(c_0_5446_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5446]) ).

cnf(c_0_5446_3,axiom,
    ( ~ class_Rings_Oordered__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5446]) ).

cnf(c_0_5447_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5447]) ).

cnf(c_0_5447_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5447]) ).

cnf(c_0_5447_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Oordered__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5447]) ).

cnf(c_0_5447_3,axiom,
    ( ~ class_Rings_Oordered__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5447]) ).

cnf(c_0_5448_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Oordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5448]) ).

cnf(c_0_5448_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Rings_Oordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5448]) ).

cnf(c_0_5448_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Oordered__comm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5448]) ).

cnf(c_0_5448_3,axiom,
    ( ~ class_Rings_Oordered__comm__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5448]) ).

cnf(c_0_5449_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5449]) ).

cnf(c_0_5449_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5449]) ).

cnf(c_0_5449_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5449]) ).

cnf(c_0_5449_3,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5449]) ).

cnf(c_0_5450_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5450]) ).

cnf(c_0_5450_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5450]) ).

cnf(c_0_5450_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5450]) ).

cnf(c_0_5450_3,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5450]) ).

cnf(c_0_5451_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5451]) ).

cnf(c_0_5451_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5451]) ).

cnf(c_0_5451_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5451]) ).

cnf(c_0_5451_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5451]) ).

cnf(c_0_5452_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5452]) ).

cnf(c_0_5452_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5452]) ).

cnf(c_0_5452_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5452]) ).

cnf(c_0_5452_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5452]) ).

cnf(c_0_5453_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5453]) ).

cnf(c_0_5453_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5453]) ).

cnf(c_0_5453_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5453]) ).

cnf(c_0_5453_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5453]) ).

cnf(c_0_5454_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5454]) ).

cnf(c_0_5454_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5454]) ).

cnf(c_0_5454_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5454]) ).

cnf(c_0_5454_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5454]) ).

cnf(c_0_5455_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5455]) ).

cnf(c_0_5455_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5455]) ).

cnf(c_0_5455_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5455]) ).

cnf(c_0_5455_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5455]) ).

cnf(c_0_5456_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5456]) ).

cnf(c_0_5456_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5456]) ).

cnf(c_0_5456_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5456]) ).

cnf(c_0_5456_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5456]) ).

cnf(c_0_5457_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5457]) ).

cnf(c_0_5457_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5457]) ).

cnf(c_0_5457_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5457]) ).

cnf(c_0_5457_3,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5457]) ).

cnf(c_0_5458_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5458]) ).

cnf(c_0_5458_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5458]) ).

cnf(c_0_5458_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5458]) ).

cnf(c_0_5458_3,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5458]) ).

cnf(c_0_5459_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5459]) ).

cnf(c_0_5459_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5459]) ).

cnf(c_0_5459_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5459]) ).

cnf(c_0_5459_3,axiom,
    ( ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5459]) ).

cnf(c_0_5460_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5460]) ).

cnf(c_0_5460_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5460]) ).

cnf(c_0_5460_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5460]) ).

cnf(c_0_5460_3,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5460]) ).

cnf(c_0_5461_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5461]) ).

cnf(c_0_5461_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5461]) ).

cnf(c_0_5461_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5461]) ).

cnf(c_0_5461_3,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5461]) ).

cnf(c_0_5462_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5462]) ).

cnf(c_0_5462_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5462]) ).

cnf(c_0_5462_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5462]) ).

cnf(c_0_5462_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5462]) ).

cnf(c_0_5462_4,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5462]) ).

cnf(c_0_5463_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5463]) ).

cnf(c_0_5463_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5463]) ).

cnf(c_0_5463_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5463]) ).

cnf(c_0_5463_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5463]) ).

cnf(c_0_5463_4,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5463]) ).

cnf(c_0_5464_0,axiom,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk15_3(X3,X2,X1)) = X2
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(literals_permutation,[status(thm)],[c_0_5464]) ).

cnf(c_0_5464_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk15_3(X3,X2,X1)) = X2
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(literals_permutation,[status(thm)],[c_0_5464]) ).

cnf(c_0_5464_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk15_3(X3,X2,X1)) = X2
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5464]) ).

cnf(c_0_5465_0,axiom,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk14_3(X3,X2,X1)) = X2
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(literals_permutation,[status(thm)],[c_0_5465]) ).

cnf(c_0_5465_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk14_3(X3,X2,X1)) = X2
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(literals_permutation,[status(thm)],[c_0_5465]) ).

cnf(c_0_5465_2,axiom,
    ( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk14_3(X3,X2,X1)) = X2
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5465]) ).

cnf(c_0_5466_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5466]) ).

cnf(c_0_5466_1,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5466]) ).

cnf(c_0_5466_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5466]) ).

cnf(c_0_5466_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5466]) ).

cnf(c_0_5467_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5467]) ).

cnf(c_0_5467_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5467]) ).

cnf(c_0_5467_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5467]) ).

cnf(c_0_5467_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5467]) ).

cnf(c_0_5468_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5468]) ).

cnf(c_0_5468_1,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5468]) ).

cnf(c_0_5468_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5468]) ).

cnf(c_0_5468_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5468]) ).

cnf(c_0_5469_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5469]) ).

cnf(c_0_5469_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5469]) ).

cnf(c_0_5469_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5469]) ).

cnf(c_0_5469_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5469]) ).

cnf(c_0_5470_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5470]) ).

cnf(c_0_5470_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5470]) ).

cnf(c_0_5470_2,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5470]) ).

cnf(c_0_5470_3,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5470]) ).

cnf(c_0_5470_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5470]) ).

cnf(c_0_5471_0,axiom,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk15_3(X3,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5471]) ).

cnf(c_0_5471_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk15_3(X3,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5471]) ).

cnf(c_0_5471_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk15_3(X3,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5471]) ).

cnf(c_0_5472_0,axiom,
    ( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk14_3(X3,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5472]) ).

cnf(c_0_5472_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk14_3(X3,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5472]) ).

cnf(c_0_5472_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,sk1_esk14_3(X3,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5472]) ).

cnf(c_0_5473_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5473]) ).

cnf(c_0_5473_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5473]) ).

cnf(c_0_5473_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5473]) ).

cnf(c_0_5473_3,axiom,
    ( X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5473]) ).

cnf(c_0_5473_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_5473]) ).

cnf(c_0_5474_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5474]) ).

cnf(c_0_5474_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5474]) ).

cnf(c_0_5474_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5474]) ).

cnf(c_0_5474_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5474]) ).

cnf(c_0_5474_4,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5474]) ).

cnf(c_0_5475_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5475]) ).

cnf(c_0_5475_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5475]) ).

cnf(c_0_5476_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5476]) ).

cnf(c_0_5476_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5476]) ).

cnf(c_0_5477_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5477]) ).

cnf(c_0_5477_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5477]) ).

cnf(c_0_5477_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5477]) ).

cnf(c_0_5477_3,axiom,
    ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5477]) ).

cnf(c_0_5478_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5478]) ).

cnf(c_0_5478_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5478]) ).

cnf(c_0_5478_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5478]) ).

cnf(c_0_5478_3,axiom,
    ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5478]) ).

cnf(c_0_5479_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5479]) ).

cnf(c_0_5479_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5479]) ).

cnf(c_0_5479_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5479]) ).

cnf(c_0_5479_3,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5479]) ).

cnf(c_0_5480_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5480]) ).

cnf(c_0_5480_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5480]) ).

cnf(c_0_5480_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5480]) ).

cnf(c_0_5480_3,axiom,
    ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X5)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5480]) ).

cnf(c_0_5481_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5481]) ).

cnf(c_0_5481_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
    | c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5481]) ).

cnf(c_0_5481_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
    | c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5481]) ).

cnf(c_0_5481_3,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X5)
    | c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5481]) ).

cnf(c_0_5482_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(X1,X2,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Power_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5482]) ).

cnf(c_0_5482_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(X1,X2,X3)
    | ~ class_Power_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5482]) ).

cnf(c_0_5482_2,axiom,
    ( ~ class_Power_Opower(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5482]) ).

cnf(c_0_5483_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5483]) ).

cnf(c_0_5483_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5483]) ).

cnf(c_0_5483_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5483]) ).

cnf(c_0_5484_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X5))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5484]) ).

cnf(c_0_5484_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
    | c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X5))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5484]) ).

cnf(c_0_5484_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
    | c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X5))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5484]) ).

cnf(c_0_5484_3,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X5)
    | c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_5484]) ).

cnf(c_0_5485_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5485]) ).

cnf(c_0_5485_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5485]) ).

cnf(c_0_5485_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5485]) ).

cnf(c_0_5486_0,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5486]) ).

cnf(c_0_5486_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5486]) ).

cnf(c_0_5486_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5486]) ).

cnf(c_0_5487_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5487]) ).

cnf(c_0_5487_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5487]) ).

cnf(c_0_5487_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5487]) ).

cnf(c_0_5487_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5487]) ).

cnf(c_0_5488_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5488]) ).

cnf(c_0_5488_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5488]) ).

cnf(c_0_5488_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5488]) ).

cnf(c_0_5488_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5488]) ).

cnf(c_0_5489_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5489]) ).

cnf(c_0_5489_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5489]) ).

cnf(c_0_5490_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5490]) ).

cnf(c_0_5490_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5490]) ).

cnf(c_0_5491_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5491]) ).

cnf(c_0_5491_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5491]) ).

cnf(c_0_5492_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5492]) ).

cnf(c_0_5492_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5492]) ).

cnf(c_0_5493_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5493]) ).

cnf(c_0_5493_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5493]) ).

cnf(c_0_5494_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5494]) ).

cnf(c_0_5494_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5494]) ).

cnf(c_0_5495_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5495]) ).

cnf(c_0_5495_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5495]) ).

cnf(c_0_5496_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5496]) ).

cnf(c_0_5496_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5496]) ).

cnf(c_0_5497_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4)) = c_Power_Opower__class_Opower(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5497]) ).

cnf(c_0_5497_1,axiom,
    ( ~ class_Groups_Ocomm__monoid__mult(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4)) = c_Power_Opower__class_Opower(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5497]) ).

cnf(c_0_5498_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5498]) ).

cnf(c_0_5498_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5498]) ).

cnf(c_0_5499_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5499]) ).

cnf(c_0_5499_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5499]) ).

cnf(c_0_5500_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5500]) ).

cnf(c_0_5500_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5500]) ).

cnf(c_0_5501_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5501]) ).

cnf(c_0_5501_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5501]) ).

cnf(c_0_5502_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
    | ~ class_Rings_Ocomm__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5502]) ).

cnf(c_0_5502_1,axiom,
    ( ~ class_Rings_Ocomm__semiring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5502]) ).

cnf(c_0_5503_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5503]) ).

cnf(c_0_5503_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5503]) ).

cnf(c_0_5504_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5504]) ).

cnf(c_0_5504_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5504]) ).

cnf(c_0_5505_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5505]) ).

cnf(c_0_5505_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5505]) ).

cnf(c_0_5506_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4)) = c_Power_Opower__class_Opower(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5506]) ).

cnf(c_0_5506_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4)) = c_Power_Opower__class_Opower(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5506]) ).

cnf(c_0_5507_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5507]) ).

cnf(c_0_5507_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5507]) ).

cnf(c_0_5507_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5507]) ).

cnf(c_0_5507_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5507]) ).

cnf(c_0_5508_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5508]) ).

cnf(c_0_5508_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5508]) ).

cnf(c_0_5508_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5508]) ).

cnf(c_0_5508_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5508]) ).

cnf(c_0_5509_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5509]) ).

cnf(c_0_5509_1,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5509]) ).

cnf(c_0_5510_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5510]) ).

cnf(c_0_5510_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5510]) ).

cnf(c_0_5511_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5511]) ).

cnf(c_0_5511_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5511]) ).

cnf(c_0_5511_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5511]) ).

cnf(c_0_5512_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5512]) ).

cnf(c_0_5512_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5512]) ).

cnf(c_0_5512_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5512]) ).

cnf(c_0_5513_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5513]) ).

cnf(c_0_5513_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5513]) ).

cnf(c_0_5513_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5513]) ).

cnf(c_0_5514_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5514]) ).

cnf(c_0_5514_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5514]) ).

cnf(c_0_5514_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5514]) ).

cnf(c_0_5515_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5515]) ).

cnf(c_0_5515_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5515]) ).

cnf(c_0_5515_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5515]) ).

cnf(c_0_5516_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5516]) ).

cnf(c_0_5516_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5516]) ).

cnf(c_0_5516_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5516]) ).

cnf(c_0_5517_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5517]) ).

cnf(c_0_5517_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5517]) ).

cnf(c_0_5517_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5517]) ).

cnf(c_0_5518_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5518]) ).

cnf(c_0_5518_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5518]) ).

cnf(c_0_5518_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5518]) ).

cnf(c_0_5519_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5519]) ).

cnf(c_0_5519_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5519]) ).

cnf(c_0_5519_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5519]) ).

cnf(c_0_5520_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5520]) ).

cnf(c_0_5520_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5520]) ).

cnf(c_0_5520_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5520]) ).

cnf(c_0_5521_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5521]) ).

cnf(c_0_5521_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5521]) ).

cnf(c_0_5521_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5521]) ).

cnf(c_0_5522_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5522]) ).

cnf(c_0_5522_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5522]) ).

cnf(c_0_5522_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5522]) ).

cnf(c_0_5523_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5523]) ).

cnf(c_0_5523_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5523]) ).

cnf(c_0_5523_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5523]) ).

cnf(c_0_5524_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5524]) ).

cnf(c_0_5524_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5524]) ).

cnf(c_0_5524_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5524]) ).

cnf(c_0_5525_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5525]) ).

cnf(c_0_5525_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5525]) ).

cnf(c_0_5526_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5526]) ).

cnf(c_0_5526_1,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5526]) ).

cnf(c_0_5527_0,axiom,
    ( epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5527]) ).

cnf(c_0_5527_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5527]) ).

cnf(c_0_5528_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5528]) ).

cnf(c_0_5528_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5528]) ).

cnf(c_0_5528_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5528]) ).

cnf(c_0_5529_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5529]) ).

cnf(c_0_5529_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5529]) ).

cnf(c_0_5529_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5529]) ).

cnf(c_0_5530_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5530]) ).

cnf(c_0_5530_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5530]) ).

cnf(c_0_5530_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5530]) ).

cnf(c_0_5531_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5531]) ).

cnf(c_0_5531_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5531]) ).

cnf(c_0_5531_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5531]) ).

cnf(c_0_5532_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5532]) ).

cnf(c_0_5532_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5532]) ).

cnf(c_0_5532_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5532]) ).

cnf(c_0_5533_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5533]) ).

cnf(c_0_5533_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5533]) ).

cnf(c_0_5533_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5533]) ).

cnf(c_0_5534_0,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(literals_permutation,[status(thm)],[c_0_5534]) ).

cnf(c_0_5534_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(literals_permutation,[status(thm)],[c_0_5534]) ).

cnf(c_0_5534_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5534]) ).

cnf(c_0_5535_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X3,X2))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5535]) ).

cnf(c_0_5535_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X3,X2))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5535]) ).

cnf(c_0_5535_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5535]) ).

cnf(c_0_5535_3,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5535]) ).

cnf(c_0_5536_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5536]) ).

cnf(c_0_5536_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5536]) ).

cnf(c_0_5536_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5536]) ).

cnf(c_0_5536_3,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5536]) ).

cnf(c_0_5537_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5537]) ).

cnf(c_0_5537_1,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5537]) ).

cnf(c_0_5537_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5537]) ).

cnf(c_0_5537_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5537]) ).

cnf(c_0_5537_4,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5537]) ).

cnf(c_0_5538_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5538]) ).

cnf(c_0_5538_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5538]) ).

cnf(c_0_5538_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5538]) ).

cnf(c_0_5538_3,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5538]) ).

cnf(c_0_5538_4,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5538]) ).

cnf(c_0_5539_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5539]) ).

cnf(c_0_5539_1,axiom,
    ( X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5539]) ).

cnf(c_0_5540_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5540]) ).

cnf(c_0_5540_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5540]) ).

cnf(c_0_5540_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5540]) ).

cnf(c_0_5540_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5540]) ).

cnf(c_0_5541_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5541]) ).

cnf(c_0_5541_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5541]) ).

cnf(c_0_5543_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5543]) ).

cnf(c_0_5543_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5543]) ).

cnf(c_0_5544_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5544]) ).

cnf(c_0_5544_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5544]) ).

cnf(c_0_5558_0,axiom,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | X3 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5558]) ).

cnf(c_0_5558_1,axiom,
    ( ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | hBOOL(hAPP(X1,X2))
    | X3 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5558]) ).

cnf(c_0_5558_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5558]) ).

cnf(c_0_5559_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5559]) ).

cnf(c_0_5559_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5559]) ).

cnf(c_0_5559_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5559]) ).

cnf(c_0_5559_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5559]) ).

cnf(c_0_5560_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5560]) ).

cnf(c_0_5560_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5560]) ).

cnf(c_0_5560_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5560]) ).

cnf(c_0_5560_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5560]) ).

cnf(c_0_5561_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5561]) ).

cnf(c_0_5561_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5561]) ).

cnf(c_0_5562_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5562]) ).

cnf(c_0_5562_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5562]) ).

cnf(c_0_5563_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5563]) ).

cnf(c_0_5563_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5563]) ).

cnf(c_0_5564_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5564]) ).

cnf(c_0_5564_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5564]) ).

cnf(c_0_5565_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5565]) ).

cnf(c_0_5565_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5565]) ).

cnf(c_0_5565_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5565]) ).

cnf(c_0_5566_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5566]) ).

cnf(c_0_5566_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5566]) ).

cnf(c_0_5566_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5566]) ).

cnf(c_0_5566_3,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5566]) ).

cnf(c_0_5567_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5567]) ).

cnf(c_0_5567_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5567]) ).

cnf(c_0_5567_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5567]) ).

cnf(c_0_5567_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X4,X3))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5567]) ).

cnf(c_0_5568_0,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X3) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5568]) ).

cnf(c_0_5568_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X3) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5568]) ).

cnf(c_0_5569_0,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5569]) ).

cnf(c_0_5569_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5569]) ).

cnf(c_0_5569_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5569]) ).

cnf(c_0_5570_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5570]) ).

cnf(c_0_5570_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5570]) ).

cnf(c_0_5571_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5571]) ).

cnf(c_0_5571_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5571]) ).

cnf(c_0_5572_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5572]) ).

cnf(c_0_5572_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5572]) ).

cnf(c_0_5573_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5573]) ).

cnf(c_0_5573_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5573]) ).

cnf(c_0_5574_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5574]) ).

cnf(c_0_5574_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5574]) ).

cnf(c_0_5575_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5575]) ).

cnf(c_0_5575_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5575]) ).

cnf(c_0_5575_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5575]) ).

cnf(c_0_5576_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5576]) ).

cnf(c_0_5576_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5576]) ).

cnf(c_0_5576_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5576]) ).

cnf(c_0_5577_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5577]) ).

cnf(c_0_5577_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5577]) ).

cnf(c_0_5577_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5577]) ).

cnf(c_0_5578_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5578]) ).

cnf(c_0_5578_1,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5578]) ).

cnf(c_0_5578_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5578]) ).

cnf(c_0_5579_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5579]) ).

cnf(c_0_5579_1,axiom,
    ( hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5579]) ).

cnf(c_0_5579_2,axiom,
    ( ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5579]) ).

cnf(c_0_5579_3,axiom,
    ( ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5579]) ).

cnf(c_0_5580_0,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5580]) ).

cnf(c_0_5580_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5580]) ).

cnf(c_0_5580_2,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5580]) ).

cnf(c_0_5580_3,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5580]) ).

cnf(c_0_5581_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5581]) ).

cnf(c_0_5581_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5581]) ).

cnf(c_0_5581_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5581]) ).

cnf(c_0_5582_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5582]) ).

cnf(c_0_5582_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5582]) ).

cnf(c_0_5582_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5582]) ).

cnf(c_0_5583_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5583]) ).

cnf(c_0_5583_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5583]) ).

cnf(c_0_5583_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5583]) ).

cnf(c_0_5583_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5583]) ).

cnf(c_0_5584_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5584]) ).

cnf(c_0_5584_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5584]) ).

cnf(c_0_5584_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5584]) ).

cnf(c_0_5584_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5584]) ).

cnf(c_0_5585_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5585]) ).

cnf(c_0_5585_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5585]) ).

cnf(c_0_5585_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5585]) ).

cnf(c_0_5585_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5585]) ).

cnf(c_0_5586_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5586]) ).

cnf(c_0_5586_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5586]) ).

cnf(c_0_5586_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5586]) ).

cnf(c_0_5586_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5586]) ).

cnf(c_0_5587_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5587]) ).

cnf(c_0_5587_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5587]) ).

cnf(c_0_5587_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5587]) ).

cnf(c_0_5587_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5587]) ).

cnf(c_0_5588_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5588]) ).

cnf(c_0_5588_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5588]) ).

cnf(c_0_5588_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5588]) ).

cnf(c_0_5588_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5588]) ).

cnf(c_0_5589_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5589]) ).

cnf(c_0_5589_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5589]) ).

cnf(c_0_5589_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5589]) ).

cnf(c_0_5589_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5589]) ).

cnf(c_0_5590_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5590]) ).

cnf(c_0_5590_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5590]) ).

cnf(c_0_5590_2,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5590]) ).

cnf(c_0_5590_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5590]) ).

cnf(c_0_5591_0,axiom,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | c_Power_Opower__class_Opower(X3,X1,c_Nat_OSuc(X4)) != c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X4))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5591]) ).

cnf(c_0_5591_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | c_Power_Opower__class_Opower(X3,X1,c_Nat_OSuc(X4)) != c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X4))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5591]) ).

cnf(c_0_5591_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | X1 = X2
    | c_Power_Opower__class_Opower(X3,X1,c_Nat_OSuc(X4)) != c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X4))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5591]) ).

cnf(c_0_5591_3,axiom,
    ( c_Power_Opower__class_Opower(X3,X1,c_Nat_OSuc(X4)) != c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | X1 = X2
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5591]) ).

cnf(c_0_5591_4,axiom,
    ( ~ class_Rings_Olinordered__semidom(X3)
    | c_Power_Opower__class_Opower(X3,X1,c_Nat_OSuc(X4)) != c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5591]) ).

cnf(c_0_5592_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5592]) ).

cnf(c_0_5592_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5592]) ).

cnf(c_0_5593_0,axiom,
    ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5593]) ).

cnf(c_0_5593_1,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5593]) ).

cnf(c_0_5594_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5594]) ).

cnf(c_0_5594_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5594]) ).

cnf(c_0_5594_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5594]) ).

cnf(c_0_5595_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5595]) ).

cnf(c_0_5595_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5595]) ).

cnf(c_0_5595_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5595]) ).

cnf(c_0_5596_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5596]) ).

cnf(c_0_5596_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5596]) ).

cnf(c_0_5596_2,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5596]) ).

cnf(c_0_5597_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5597]) ).

cnf(c_0_5597_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5597]) ).

cnf(c_0_5597_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5597]) ).

cnf(c_0_5597_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5597]) ).

cnf(c_0_5598_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5598]) ).

cnf(c_0_5598_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5598]) ).

cnf(c_0_5598_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5598]) ).

cnf(c_0_5599_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5599]) ).

cnf(c_0_5599_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5599]) ).

cnf(c_0_5599_2,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5599]) ).

cnf(c_0_5600_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5600]) ).

cnf(c_0_5600_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5600]) ).

cnf(c_0_5600_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5600]) ).

cnf(c_0_5601_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5601]) ).

cnf(c_0_5601_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5601]) ).

cnf(c_0_5601_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5601]) ).

cnf(c_0_5602_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5602]) ).

cnf(c_0_5602_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5602]) ).

cnf(c_0_5602_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5602]) ).

cnf(c_0_5603_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5603]) ).

cnf(c_0_5603_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5603]) ).

cnf(c_0_5603_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5603]) ).

cnf(c_0_5603_3,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5603]) ).

cnf(c_0_5604_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5604]) ).

cnf(c_0_5604_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5604]) ).

cnf(c_0_5604_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5604]) ).

cnf(c_0_5604_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5604]) ).

cnf(c_0_5605_0,axiom,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | ~ epred1_3(X1,X2,X3)
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5605]) ).

cnf(c_0_5605_1,axiom,
    ( ~ epred1_3(X1,X2,X3)
    | hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5605]) ).

cnf(c_0_5605_2,axiom,
    ( ~ hBOOL(hAPP(X1,X2))
    | ~ epred1_3(X1,X2,X3)
    | hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5605]) ).

cnf(c_0_5606_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5606]) ).

cnf(c_0_5606_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5606]) ).

cnf(c_0_5607_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5607]) ).

cnf(c_0_5607_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5607]) ).

cnf(c_0_5608_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5608]) ).

cnf(c_0_5608_1,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5608]) ).

cnf(c_0_5608_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5608]) ).

cnf(c_0_5608_3,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5608]) ).

cnf(c_0_5608_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5608]) ).

cnf(c_0_5609_0,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5609]) ).

cnf(c_0_5609_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5609]) ).

cnf(c_0_5609_2,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5609]) ).

cnf(c_0_5610_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5610]) ).

cnf(c_0_5610_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5610]) ).

cnf(c_0_5610_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5610]) ).

cnf(c_0_5610_3,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5610]) ).

cnf(c_0_5611_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5611]) ).

cnf(c_0_5611_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5611]) ).

cnf(c_0_5611_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5611]) ).

cnf(c_0_5611_3,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5611]) ).

cnf(c_0_5612_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5612]) ).

cnf(c_0_5612_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5612]) ).

cnf(c_0_5612_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5612]) ).

cnf(c_0_5612_3,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5612]) ).

cnf(c_0_5613_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5613]) ).

cnf(c_0_5613_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5613]) ).

cnf(c_0_5613_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5613]) ).

cnf(c_0_5613_3,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5613]) ).

cnf(c_0_5614_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5614]) ).

cnf(c_0_5614_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5614]) ).

cnf(c_0_5614_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5614]) ).

cnf(c_0_5614_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5614]) ).

cnf(c_0_5615_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5615]) ).

cnf(c_0_5615_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5615]) ).

cnf(c_0_5615_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5615]) ).

cnf(c_0_5615_3,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5615]) ).

cnf(c_0_5616_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5616]) ).

cnf(c_0_5616_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5616]) ).

cnf(c_0_5616_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5616]) ).

cnf(c_0_5616_3,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5616]) ).

cnf(c_0_5617_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5617]) ).

cnf(c_0_5617_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5617]) ).

cnf(c_0_5617_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5617]) ).

cnf(c_0_5617_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5617]) ).

cnf(c_0_5618_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5618]) ).

cnf(c_0_5618_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5618]) ).

cnf(c_0_5618_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5618]) ).

cnf(c_0_5618_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5618]) ).

cnf(c_0_5619_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5619]) ).

cnf(c_0_5619_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5619]) ).

cnf(c_0_5619_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5619]) ).

cnf(c_0_5619_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5619]) ).

cnf(c_0_5620_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5620]) ).

cnf(c_0_5620_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5620]) ).

cnf(c_0_5620_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5620]) ).

cnf(c_0_5620_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5620]) ).

cnf(c_0_5621_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5621]) ).

cnf(c_0_5621_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5621]) ).

cnf(c_0_5621_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5621]) ).

cnf(c_0_5621_3,axiom,
    ( ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5621]) ).

cnf(c_0_5622_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5622]) ).

cnf(c_0_5622_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5622]) ).

cnf(c_0_5622_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5622]) ).

cnf(c_0_5622_3,axiom,
    ( ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5622]) ).

cnf(c_0_5623_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5623]) ).

cnf(c_0_5623_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5623]) ).

cnf(c_0_5623_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5623]) ).

cnf(c_0_5623_3,axiom,
    ( ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5623]) ).

cnf(c_0_5624_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5624]) ).

cnf(c_0_5624_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5624]) ).

cnf(c_0_5624_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5624]) ).

cnf(c_0_5624_3,axiom,
    ( ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5624]) ).

cnf(c_0_5625_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5625]) ).

cnf(c_0_5625_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5625]) ).

cnf(c_0_5625_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5625]) ).

cnf(c_0_5625_3,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5625]) ).

cnf(c_0_5626_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5626]) ).

cnf(c_0_5626_1,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5626]) ).

cnf(c_0_5626_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5626]) ).

cnf(c_0_5626_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5626]) ).

cnf(c_0_5627_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Oordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5627]) ).

cnf(c_0_5627_1,axiom,
    ( ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5627]) ).

cnf(c_0_5627_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5627]) ).

cnf(c_0_5627_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5627]) ).

cnf(c_0_5628_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5628]) ).

cnf(c_0_5628_1,axiom,
    ( ~ class_Rings_Oordered__cancel__semiring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5628]) ).

cnf(c_0_5628_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5628]) ).

cnf(c_0_5628_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5628]) ).

cnf(c_0_5629_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5629]) ).

cnf(c_0_5629_1,axiom,
    ( ~ class_Rings_Oordered__cancel__semiring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5629]) ).

cnf(c_0_5629_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5629]) ).

cnf(c_0_5629_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5629]) ).

cnf(c_0_5630_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5630]) ).

cnf(c_0_5630_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5630]) ).

cnf(c_0_5630_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5630]) ).

cnf(c_0_5630_3,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5630]) ).

cnf(c_0_5631_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5631]) ).

cnf(c_0_5631_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5631]) ).

cnf(c_0_5631_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5631]) ).

cnf(c_0_5631_3,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5631]) ).

cnf(c_0_5632_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5632]) ).

cnf(c_0_5632_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5632]) ).

cnf(c_0_5632_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5632]) ).

cnf(c_0_5632_3,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5632]) ).

cnf(c_0_5633_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5633]) ).

cnf(c_0_5633_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5633]) ).

cnf(c_0_5633_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5633]) ).

cnf(c_0_5633_3,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5633]) ).

cnf(c_0_5634_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5634]) ).

cnf(c_0_5634_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5634]) ).

cnf(c_0_5634_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5634]) ).

cnf(c_0_5634_3,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5634]) ).

cnf(c_0_5635_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5635]) ).

cnf(c_0_5635_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5635]) ).

cnf(c_0_5635_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semiring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5635]) ).

cnf(c_0_5635_3,axiom,
    ( ~ class_Rings_Olinordered__semiring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5635]) ).

cnf(c_0_5636_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5636]) ).

cnf(c_0_5636_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5636]) ).

cnf(c_0_5636_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5636]) ).

cnf(c_0_5636_3,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5636]) ).

cnf(c_0_5638_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5638]) ).

cnf(c_0_5638_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5638]) ).

cnf(c_0_5638_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5638]) ).

cnf(c_0_5639_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5639]) ).

cnf(c_0_5639_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5639]) ).

cnf(c_0_5639_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5639]) ).

cnf(c_0_5640_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5640]) ).

cnf(c_0_5640_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5640]) ).

cnf(c_0_5640_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5640]) ).

cnf(c_0_5641_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5641]) ).

cnf(c_0_5641_1,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5641]) ).

cnf(c_0_5641_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5641]) ).

cnf(c_0_5642_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5642]) ).

cnf(c_0_5642_1,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5642]) ).

cnf(c_0_5642_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5642]) ).

cnf(c_0_5643_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5643]) ).

cnf(c_0_5643_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5643]) ).

cnf(c_0_5643_2,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5643]) ).

cnf(c_0_5644_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5644]) ).

cnf(c_0_5644_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5644]) ).

cnf(c_0_5644_2,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5644]) ).

cnf(c_0_5645_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5645]) ).

cnf(c_0_5645_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5645]) ).

cnf(c_0_5645_2,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5645]) ).

cnf(c_0_5646_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5646]) ).

cnf(c_0_5646_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5646]) ).

cnf(c_0_5646_2,axiom,
    ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5646]) ).

cnf(c_0_5647_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5647]) ).

cnf(c_0_5647_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5647]) ).

cnf(c_0_5647_2,axiom,
    ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5647]) ).

cnf(c_0_5648_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5648]) ).

cnf(c_0_5648_1,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5648]) ).

cnf(c_0_5648_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5648]) ).

cnf(c_0_5649_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5649]) ).

cnf(c_0_5649_1,axiom,
    ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5649]) ).

cnf(c_0_5649_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5649]) ).

cnf(c_0_5650_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5650]) ).

cnf(c_0_5650_1,axiom,
    ( ~ class_Rings_Oidom(X1)
    | c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5650]) ).

cnf(c_0_5650_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Oidom(X1)
    | c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5650]) ).

cnf(c_0_5651_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Oidom(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5651]) ).

cnf(c_0_5651_1,axiom,
    ( ~ class_Rings_Oidom(X1)
    | c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5651]) ).

cnf(c_0_5651_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
    | ~ class_Rings_Oidom(X1)
    | c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5651]) ).

cnf(c_0_5652_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5652]) ).

cnf(c_0_5652_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5652]) ).

cnf(c_0_5652_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5652]) ).

cnf(c_0_5652_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5652]) ).

cnf(c_0_5653_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5653]) ).

cnf(c_0_5653_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5653]) ).

cnf(c_0_5653_2,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
    | c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5653]) ).

cnf(c_0_5654_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5654]) ).

cnf(c_0_5654_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5654]) ).

cnf(c_0_5654_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5654]) ).

cnf(c_0_5654_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5654]) ).

cnf(c_0_5654_4,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5654]) ).

cnf(c_0_5655_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5655]) ).

cnf(c_0_5655_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5655]) ).

cnf(c_0_5656_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5656]) ).

cnf(c_0_5656_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5656]) ).

cnf(c_0_5656_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5656]) ).

cnf(c_0_5656_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5656]) ).

cnf(c_0_5657_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5657]) ).

cnf(c_0_5657_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5657]) ).

cnf(c_0_5657_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5657]) ).

cnf(c_0_5657_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5657]) ).

cnf(c_0_5658_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5658]) ).

cnf(c_0_5658_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5658]) ).

cnf(c_0_5658_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5658]) ).

cnf(c_0_5658_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5658]) ).

cnf(c_0_5659_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5659]) ).

cnf(c_0_5659_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5659]) ).

cnf(c_0_5659_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5659]) ).

cnf(c_0_5659_3,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5659]) ).

cnf(c_0_5660_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5660]) ).

cnf(c_0_5660_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5660]) ).

cnf(c_0_5660_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5660]) ).

cnf(c_0_5660_3,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5660]) ).

cnf(c_0_5661_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5661]) ).

cnf(c_0_5661_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5661]) ).

cnf(c_0_5661_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5661]) ).

cnf(c_0_5661_3,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5661]) ).

cnf(c_0_5662_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5662]) ).

cnf(c_0_5662_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5662]) ).

cnf(c_0_5662_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oordered__comm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5662]) ).

cnf(c_0_5662_3,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5662]) ).

cnf(c_0_5663_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5663]) ).

cnf(c_0_5663_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5663]) ).

cnf(c_0_5663_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5663]) ).

cnf(c_0_5663_3,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5663]) ).

cnf(c_0_5664_0,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ class_Int_Onumber(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5664]) ).

cnf(c_0_5664_1,axiom,
    ( ~ class_Int_Onumber(X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5664]) ).

cnf(c_0_5664_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber(X1)
    | ~ class_Orderings_Olinorder(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5664]) ).

cnf(c_0_5664_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber(X1)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5664]) ).

cnf(c_0_5665_0,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5665]) ).

cnf(c_0_5665_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5665]) ).

cnf(c_0_5665_2,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5665]) ).

cnf(c_0_5665_3,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5665]) ).

cnf(c_0_5665_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5665]) ).

cnf(c_0_5666_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5666]) ).

cnf(c_0_5666_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5666]) ).

cnf(c_0_5666_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5666]) ).

cnf(c_0_5667_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X1),c_Power_Opower__class_Opower(tc_Int_Oint,X3,X1))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5667]) ).

cnf(c_0_5667_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X1),c_Power_Opower__class_Opower(tc_Int_Oint,X3,X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5667]) ).

cnf(c_0_5667_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X1),c_Power_Opower__class_Opower(tc_Int_Oint,X3,X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5667]) ).

cnf(c_0_5668_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5668]) ).

cnf(c_0_5668_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5668]) ).

cnf(c_0_5668_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5668]) ).

cnf(c_0_5669_0,axiom,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5669]) ).

cnf(c_0_5669_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5669]) ).

cnf(c_0_5669_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5669]) ).

cnf(c_0_5669_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5669]) ).

cnf(c_0_5669_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5669]) ).

cnf(c_0_5670_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5670]) ).

cnf(c_0_5670_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5670]) ).

cnf(c_0_5670_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5670]) ).

cnf(c_0_5670_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5670]) ).

cnf(c_0_5671_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5671]) ).

cnf(c_0_5671_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5671]) ).

cnf(c_0_5671_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5671]) ).

cnf(c_0_5671_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5671]) ).

cnf(c_0_5672_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5672]) ).

cnf(c_0_5672_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5672]) ).

cnf(c_0_5672_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5672]) ).

cnf(c_0_5672_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5672]) ).

cnf(c_0_5673_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5673]) ).

cnf(c_0_5673_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5673]) ).

cnf(c_0_5673_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5673]) ).

cnf(c_0_5673_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5673]) ).

cnf(c_0_5674_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5674]) ).

cnf(c_0_5674_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5674]) ).

cnf(c_0_5675_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5675]) ).

cnf(c_0_5675_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5675]) ).

cnf(c_0_5676_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5676]) ).

cnf(c_0_5676_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5676]) ).

cnf(c_0_5677_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5677]) ).

cnf(c_0_5677_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5677]) ).

cnf(c_0_5678_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5678]) ).

cnf(c_0_5678_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5678]) ).

cnf(c_0_5679_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5679]) ).

cnf(c_0_5679_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5679]) ).

cnf(c_0_5680_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5680]) ).

cnf(c_0_5680_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5680]) ).

cnf(c_0_5681_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5681]) ).

cnf(c_0_5681_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5681]) ).

cnf(c_0_5682_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5682]) ).

cnf(c_0_5682_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5682]) ).

cnf(c_0_5683_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5683]) ).

cnf(c_0_5683_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5683]) ).

cnf(c_0_5684_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5684]) ).

cnf(c_0_5684_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5684]) ).

cnf(c_0_5685_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5685]) ).

cnf(c_0_5685_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5685]) ).

cnf(c_0_5686_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5686]) ).

cnf(c_0_5686_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5686]) ).

cnf(c_0_5687_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5687]) ).

cnf(c_0_5687_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5687]) ).

cnf(c_0_5688_0,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5688]) ).

cnf(c_0_5688_1,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5688]) ).

cnf(c_0_5688_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5688]) ).

cnf(c_0_5688_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5688]) ).

cnf(c_0_5688_4,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5688]) ).

cnf(c_0_5689_0,axiom,
    ( X3 = X2
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5689]) ).

cnf(c_0_5689_1,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X3 = X2
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5689]) ).

cnf(c_0_5689_2,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | X3 = X2
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5689]) ).

cnf(c_0_5689_3,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | X3 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5689]) ).

cnf(c_0_5690_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5690]) ).

cnf(c_0_5690_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5690]) ).

cnf(c_0_5691_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X2)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1)),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5691]) ).

cnf(c_0_5691_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X2)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5691]) ).

cnf(c_0_5692_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5692]) ).

cnf(c_0_5692_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5692]) ).

cnf(c_0_5692_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5692]) ).

cnf(c_0_5692_3,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5692]) ).

cnf(c_0_5693_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X4,X3))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5693]) ).

cnf(c_0_5693_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X4,X3))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5693]) ).

cnf(c_0_5693_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X4,X3))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5693]) ).

cnf(c_0_5693_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5693]) ).

cnf(c_0_5694_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5694]) ).

cnf(c_0_5694_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5694]) ).

cnf(c_0_5694_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5694]) ).

cnf(c_0_5694_3,axiom,
    ( ~ class_Rings_Ocomm__ring__1(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5694]) ).

cnf(c_0_5695_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5695]) ).

cnf(c_0_5695_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5695]) ).

cnf(c_0_5695_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5695]) ).

cnf(c_0_5695_3,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5695]) ).

cnf(c_0_5696_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5696]) ).

cnf(c_0_5696_1,axiom,
    ( X1 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5696]) ).

cnf(c_0_5697_0,axiom,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5697]) ).

cnf(c_0_5697_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5697]) ).

cnf(c_0_5697_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5697]) ).

cnf(c_0_5698_0,axiom,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5698]) ).

cnf(c_0_5698_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5698]) ).

cnf(c_0_5698_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5698]) ).

cnf(c_0_5699_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5699]) ).

cnf(c_0_5699_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5699]) ).

cnf(c_0_5699_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5699]) ).

cnf(c_0_5700_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5700]) ).

cnf(c_0_5700_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5700]) ).

cnf(c_0_5700_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5700]) ).

cnf(c_0_5701_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5701]) ).

cnf(c_0_5701_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5701]) ).

cnf(c_0_5701_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5701]) ).

cnf(c_0_5702_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5702]) ).

cnf(c_0_5702_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5702]) ).

cnf(c_0_5702_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5702]) ).

cnf(c_0_5703_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5703]) ).

cnf(c_0_5703_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5703]) ).

cnf(c_0_5703_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5703]) ).

cnf(c_0_5704_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5704]) ).

cnf(c_0_5704_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5704]) ).

cnf(c_0_5704_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5704]) ).

cnf(c_0_5705_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5705]) ).

cnf(c_0_5705_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5705]) ).

cnf(c_0_5705_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5705]) ).

cnf(c_0_5706_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5706]) ).

cnf(c_0_5706_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5706]) ).

cnf(c_0_5706_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5706]) ).

cnf(c_0_5707_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5707]) ).

cnf(c_0_5707_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5707]) ).

cnf(c_0_5707_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5707]) ).

cnf(c_0_5708_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5708]) ).

cnf(c_0_5708_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5708]) ).

cnf(c_0_5708_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5708]) ).

cnf(c_0_5708_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5708]) ).

cnf(c_0_5709_0,axiom,
    ( X2 = X3
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5709]) ).

cnf(c_0_5709_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 = X3
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5709]) ).

cnf(c_0_5709_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 = X3
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5709]) ).

cnf(c_0_5709_3,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_5709]) ).

cnf(c_0_5710_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5710]) ).

cnf(c_0_5710_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5710]) ).

cnf(c_0_5710_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5710]) ).

cnf(c_0_5711_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5711]) ).

cnf(c_0_5711_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5711]) ).

cnf(c_0_5711_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5711]) ).

cnf(c_0_5712_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5712]) ).

cnf(c_0_5712_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5712]) ).

cnf(c_0_5712_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5712]) ).

cnf(c_0_5713_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5713]) ).

cnf(c_0_5713_1,axiom,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5713]) ).

cnf(c_0_5713_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5713]) ).

cnf(c_0_5714_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5714]) ).

cnf(c_0_5714_1,axiom,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5714]) ).

cnf(c_0_5714_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5714]) ).

cnf(c_0_5715_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5715]) ).

cnf(c_0_5715_1,axiom,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5715]) ).

cnf(c_0_5715_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5715]) ).

cnf(c_0_5716_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5716]) ).

cnf(c_0_5716_1,axiom,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5716]) ).

cnf(c_0_5716_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5716]) ).

cnf(c_0_5717_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5717]) ).

cnf(c_0_5717_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5717]) ).

cnf(c_0_5717_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5717]) ).

cnf(c_0_5718_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5718]) ).

cnf(c_0_5718_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5718]) ).

cnf(c_0_5718_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5718]) ).

cnf(c_0_5720_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5720]) ).

cnf(c_0_5720_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5720]) ).

cnf(c_0_5721_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5721]) ).

cnf(c_0_5721_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5721]) ).

cnf(c_0_5722_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5722]) ).

cnf(c_0_5722_1,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5722]) ).

cnf(c_0_5723_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Groups_Oab__semigroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5723]) ).

cnf(c_0_5723_1,axiom,
    ( ~ class_Groups_Oab__semigroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5723]) ).

cnf(c_0_5724_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Groups_Oab__semigroup__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5724]) ).

cnf(c_0_5724_1,axiom,
    ( ~ class_Groups_Oab__semigroup__mult(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5724]) ).

cnf(c_0_5725_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5725]) ).

cnf(c_0_5725_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5725]) ).

cnf(c_0_5726_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5726]) ).

cnf(c_0_5726_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5726]) ).

cnf(c_0_5727_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5727]) ).

cnf(c_0_5727_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5727]) ).

cnf(c_0_5728_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5728]) ).

cnf(c_0_5728_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5728]) ).

cnf(c_0_5729_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5729]) ).

cnf(c_0_5729_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5729]) ).

cnf(c_0_5730_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5730]) ).

cnf(c_0_5730_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5730]) ).

cnf(c_0_5731_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5731]) ).

cnf(c_0_5731_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5731]) ).

cnf(c_0_5732_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5732]) ).

cnf(c_0_5732_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5732]) ).

cnf(c_0_5733_0,axiom,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5733]) ).

cnf(c_0_5733_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
    | ~ epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5733]) ).

cnf(c_0_5733_2,axiom,
    ( ~ epred1_3(X1,X2,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5733]) ).

cnf(c_0_5734_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5734]) ).

cnf(c_0_5734_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5734]) ).

cnf(c_0_5734_2,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5734]) ).

cnf(c_0_5734_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5734]) ).

cnf(c_0_5734_4,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5734]) ).

cnf(c_0_5735_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5735]) ).

cnf(c_0_5735_1,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5735]) ).

cnf(c_0_5736_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5736]) ).

cnf(c_0_5736_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5736]) ).

cnf(c_0_5737_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5737]) ).

cnf(c_0_5737_1,axiom,
    ( ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5737]) ).

cnf(c_0_5737_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5737]) ).

cnf(c_0_5738_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5738]) ).

cnf(c_0_5738_1,axiom,
    ( ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5738]) ).

cnf(c_0_5738_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5738]) ).

cnf(c_0_5741_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5741]) ).

cnf(c_0_5741_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5741]) ).

cnf(c_0_5741_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5741]) ).

cnf(c_0_5742_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5742]) ).

cnf(c_0_5742_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5742]) ).

cnf(c_0_5742_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5742]) ).

cnf(c_0_5743_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5743]) ).

cnf(c_0_5743_1,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5743]) ).

cnf(c_0_5744_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5744]) ).

cnf(c_0_5744_1,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5744]) ).

cnf(c_0_5745_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5745]) ).

cnf(c_0_5745_1,axiom,
    ( ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,X4,X5)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5745]) ).

cnf(c_0_5745_2,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5745]) ).

cnf(c_0_5745_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5745]) ).

cnf(c_0_5746_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5746]) ).

cnf(c_0_5746_1,axiom,
    ( ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5746]) ).

cnf(c_0_5746_2,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5746]) ).

cnf(c_0_5746_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X4,X5)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5746]) ).

cnf(c_0_5747_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5747]) ).

cnf(c_0_5747_1,axiom,
    ( ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5747]) ).

cnf(c_0_5747_2,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5747]) ).

cnf(c_0_5747_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5747]) ).

cnf(c_0_5748_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5748]) ).

cnf(c_0_5748_1,axiom,
    ( ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5748]) ).

cnf(c_0_5748_2,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_5748]) ).

cnf(c_0_5748_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5748]) ).

cnf(c_0_5749_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_5749]) ).

cnf(c_0_5749_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_5749]) ).

cnf(c_0_5749_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_5749]) ).

cnf(c_0_5750_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5750]) ).

cnf(c_0_5750_1,axiom,
    ( hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5750]) ).

cnf(c_0_5750_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5750]) ).

cnf(c_0_5750_3,axiom,
    ( ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5750]) ).

cnf(c_0_5751_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5751]) ).

cnf(c_0_5751_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5751]) ).

cnf(c_0_5752_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5752]) ).

cnf(c_0_5752_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5752]) ).

cnf(c_0_5753_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5753]) ).

cnf(c_0_5753_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),X3)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5753]) ).

cnf(c_0_5753_2,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),X3)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5753]) ).

cnf(c_0_5754_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5754]) ).

cnf(c_0_5754_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5754]) ).

cnf(c_0_5754_2,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5754]) ).

cnf(c_0_5767_0,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(literals_permutation,[status(thm)],[c_0_5767]) ).

cnf(c_0_5767_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(literals_permutation,[status(thm)],[c_0_5767]) ).

cnf(c_0_5767_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5767]) ).

cnf(c_0_5768_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5768]) ).

cnf(c_0_5768_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5768]) ).

cnf(c_0_5768_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5768]) ).

cnf(c_0_5769_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5769]) ).

cnf(c_0_5769_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5769]) ).

cnf(c_0_5769_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5769]) ).

cnf(c_0_5770_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(literals_permutation,[status(thm)],[c_0_5770]) ).

cnf(c_0_5770_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5770]) ).

cnf(c_0_5771_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5771]) ).

cnf(c_0_5771_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5771]) ).

cnf(c_0_5772_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(literals_permutation,[status(thm)],[c_0_5772]) ).

cnf(c_0_5772_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5772]) ).

cnf(c_0_5773_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_5773]) ).

cnf(c_0_5773_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5773]) ).

cnf(c_0_5774_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5774]) ).

cnf(c_0_5774_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5774]) ).

cnf(c_0_5774_2,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5774]) ).

cnf(c_0_5775_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5775]) ).

cnf(c_0_5775_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5775]) ).

cnf(c_0_5776_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5776]) ).

cnf(c_0_5776_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5776]) ).

cnf(c_0_5777_0,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5777]) ).

cnf(c_0_5777_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5777]) ).

cnf(c_0_5777_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5777]) ).

cnf(c_0_5777_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5777]) ).

cnf(c_0_5777_4,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5777]) ).

cnf(c_0_5778_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5778]) ).

cnf(c_0_5778_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5778]) ).

cnf(c_0_5779_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5779]) ).

cnf(c_0_5779_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5779]) ).

cnf(c_0_5780_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(literals_permutation,[status(thm)],[c_0_5780]) ).

cnf(c_0_5780_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5780]) ).

cnf(c_0_5781_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5781]) ).

cnf(c_0_5781_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5781]) ).

cnf(c_0_5781_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5781]) ).

cnf(c_0_5781_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5781]) ).

cnf(c_0_5782_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5782]) ).

cnf(c_0_5782_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5782]) ).

cnf(c_0_5782_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5782]) ).

cnf(c_0_5782_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5782]) ).

cnf(c_0_5783_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5783]) ).

cnf(c_0_5783_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5783]) ).

cnf(c_0_5783_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5783]) ).

cnf(c_0_5783_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5783]) ).

cnf(c_0_5784_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5784]) ).

cnf(c_0_5784_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5784]) ).

cnf(c_0_5784_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5784]) ).

cnf(c_0_5784_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5784]) ).

cnf(c_0_5785_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5785]) ).

cnf(c_0_5785_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5785]) ).

cnf(c_0_5785_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5785]) ).

cnf(c_0_5786_0,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5786]) ).

cnf(c_0_5786_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5786]) ).

cnf(c_0_5786_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5786]) ).

cnf(c_0_5786_3,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5786]) ).

cnf(c_0_5786_4,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5786]) ).

cnf(c_0_5787_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5787]) ).

cnf(c_0_5787_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5787]) ).

cnf(c_0_5787_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5787]) ).

cnf(c_0_5788_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5788]) ).

cnf(c_0_5788_1,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5788]) ).

cnf(c_0_5788_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5788]) ).

cnf(c_0_5788_3,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5788]) ).

cnf(c_0_5788_4,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5788]) ).

cnf(c_0_5789_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5789]) ).

cnf(c_0_5789_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5789]) ).

cnf(c_0_5790_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5790]) ).

cnf(c_0_5790_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5790]) ).

cnf(c_0_5791_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5791]) ).

cnf(c_0_5791_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5791]) ).

cnf(c_0_5792_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5792]) ).

cnf(c_0_5792_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5792]) ).

cnf(c_0_5793_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5793]) ).

cnf(c_0_5793_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5793]) ).

cnf(c_0_5794_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5794]) ).

cnf(c_0_5794_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5794]) ).

cnf(c_0_5795_0,axiom,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5795]) ).

cnf(c_0_5795_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
    | c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5795]) ).

cnf(c_0_5796_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5796]) ).

cnf(c_0_5796_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5796]) ).

cnf(c_0_5796_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5796]) ).

cnf(c_0_5796_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5796]) ).

cnf(c_0_5797_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5797]) ).

cnf(c_0_5797_1,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5797]) ).

cnf(c_0_5797_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5797]) ).

cnf(c_0_5797_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5797]) ).

cnf(c_0_5797_4,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5797]) ).

cnf(c_0_5798_0,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5798]) ).

cnf(c_0_5798_1,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5798]) ).

cnf(c_0_5798_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5798]) ).

cnf(c_0_5798_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5798]) ).

cnf(c_0_5798_4,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5798]) ).

cnf(c_0_5799_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5799]) ).

cnf(c_0_5799_1,axiom,
    ( ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5799]) ).

cnf(c_0_5799_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5799]) ).

cnf(c_0_5799_3,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5799]) ).

cnf(c_0_5800_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5800]) ).

cnf(c_0_5800_1,axiom,
    ( ~ class_Int_Onumber(X1)
    | c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5800]) ).

cnf(c_0_5800_2,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | ~ class_Int_Onumber(X1)
    | c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5800]) ).

cnf(c_0_5800_3,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ class_Int_Onumber(X1)
    | c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5800]) ).

cnf(c_0_5801_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5801]) ).

cnf(c_0_5801_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5801]) ).

cnf(c_0_5802_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5802]) ).

cnf(c_0_5802_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5802]) ).

cnf(c_0_5803_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Int_Onumber(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5803]) ).

cnf(c_0_5803_1,axiom,
    ( ~ class_Int_Onumber(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5803]) ).

cnf(c_0_5803_2,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | ~ class_Int_Onumber(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5803]) ).

cnf(c_0_5803_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ class_Int_Onumber(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5803]) ).

cnf(c_0_5804_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5804]) ).

cnf(c_0_5804_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5804]) ).

cnf(c_0_5804_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5804]) ).

cnf(c_0_5805_0,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5805]) ).

cnf(c_0_5805_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5805]) ).

cnf(c_0_5805_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5805]) ).

cnf(c_0_5806_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5806]) ).

cnf(c_0_5806_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5806]) ).

cnf(c_0_5806_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5806]) ).

cnf(c_0_5806_3,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5806]) ).

cnf(c_0_5806_4,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5806]) ).

cnf(c_0_5807_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5807]) ).

cnf(c_0_5807_1,axiom,
    ( X1 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5807]) ).

cnf(c_0_5808_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5808]) ).

cnf(c_0_5808_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5808]) ).

cnf(c_0_5809_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | ~ class_Rings_Oidom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5809]) ).

cnf(c_0_5809_1,axiom,
    ( ~ class_Rings_Oidom(X1)
    | c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5809]) ).

cnf(c_0_5809_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oidom(X1)
    | c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5809]) ).

cnf(c_0_5810_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | ~ class_Rings_Oidom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5810]) ).

cnf(c_0_5810_1,axiom,
    ( ~ class_Rings_Oidom(X1)
    | c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5810]) ).

cnf(c_0_5810_2,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oidom(X1)
    | c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5810]) ).

cnf(c_0_5811_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5811]) ).

cnf(c_0_5811_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5811]) ).

cnf(c_0_5811_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5811]) ).

cnf(c_0_5811_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5811]) ).

cnf(c_0_5812_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5812]) ).

cnf(c_0_5812_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5812]) ).

cnf(c_0_5812_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5812]) ).

cnf(c_0_5812_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5812]) ).

cnf(c_0_5813_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5813]) ).

cnf(c_0_5813_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5813]) ).

cnf(c_0_5813_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5813]) ).

cnf(c_0_5813_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5813]) ).

cnf(c_0_5814_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5814]) ).

cnf(c_0_5814_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5814]) ).

cnf(c_0_5814_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5814]) ).

cnf(c_0_5814_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5814]) ).

cnf(c_0_5815_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5815]) ).

cnf(c_0_5815_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5815]) ).

cnf(c_0_5815_2,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5815]) ).

cnf(c_0_5816_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5816]) ).

cnf(c_0_5816_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5816]) ).

cnf(c_0_5816_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5816]) ).

cnf(c_0_5816_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5816]) ).

cnf(c_0_5817_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sk1_esk12_1(X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5817]) ).

cnf(c_0_5817_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sk1_esk12_1(X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5817]) ).

cnf(c_0_5818_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5818]) ).

cnf(c_0_5818_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5818]) ).

cnf(c_0_5819_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5819]) ).

cnf(c_0_5819_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5819]) ).

cnf(c_0_5820_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_5820]) ).

cnf(c_0_5820_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_5820]) ).

cnf(c_0_5820_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_5820]) ).

cnf(c_0_5820_3,axiom,
    ( X2 != X3
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5820]) ).

cnf(c_0_5821_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5821]) ).

cnf(c_0_5821_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5821]) ).

cnf(c_0_5821_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5821]) ).

cnf(c_0_5822_0,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5822]) ).

cnf(c_0_5822_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5822]) ).

cnf(c_0_5822_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5822]) ).

cnf(c_0_5823_0,axiom,
    ( X3 = X4
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Power_Opower__class_Opower(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5823]) ).

cnf(c_0_5823_1,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | X3 = X4
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Power_Opower__class_Opower(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5823]) ).

cnf(c_0_5823_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1)
    | X3 = X4
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Power_Opower__class_Opower(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5823]) ).

cnf(c_0_5823_3,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,X3) != c_Power_Opower__class_Opower(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1)
    | X3 = X4 ),
    inference(literals_permutation,[status(thm)],[c_0_5823]) ).

cnf(c_0_5824_0,axiom,
    ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5824]) ).

cnf(c_0_5824_1,axiom,
    ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = X2
    | c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5824]) ).

cnf(c_0_5825_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5825]) ).

cnf(c_0_5825_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5825]) ).

cnf(c_0_5825_2,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5825]) ).

cnf(c_0_5826_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5826]) ).

cnf(c_0_5826_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5826]) ).

cnf(c_0_5826_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(literals_permutation,[status(thm)],[c_0_5826]) ).

cnf(c_0_5827_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5827]) ).

cnf(c_0_5827_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5827]) ).

cnf(c_0_5827_2,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sk1_esk21_3(X3,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5827]) ).

cnf(c_0_5828_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5828]) ).

cnf(c_0_5828_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5828]) ).

cnf(c_0_5828_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sk1_esk19_3(X3,X2,X1))
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5828]) ).

cnf(c_0_5829_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5829]) ).

cnf(c_0_5829_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5829]) ).

cnf(c_0_5829_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5829]) ).

cnf(c_0_5829_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5829]) ).

cnf(c_0_5830_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5830]) ).

cnf(c_0_5830_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5830]) ).

cnf(c_0_5830_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5830]) ).

cnf(c_0_5830_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5830]) ).

cnf(c_0_5831_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5831]) ).

cnf(c_0_5831_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5831]) ).

cnf(c_0_5831_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5831]) ).

cnf(c_0_5831_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5831]) ).

cnf(c_0_5832_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5832]) ).

cnf(c_0_5832_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5832]) ).

cnf(c_0_5832_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5832]) ).

cnf(c_0_5832_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5832]) ).

cnf(c_0_5833_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5833]) ).

cnf(c_0_5833_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5833]) ).

cnf(c_0_5833_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5833]) ).

cnf(c_0_5833_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5833]) ).

cnf(c_0_5834_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5834]) ).

cnf(c_0_5834_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5834]) ).

cnf(c_0_5834_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5834]) ).

cnf(c_0_5834_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5834]) ).

cnf(c_0_5835_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5835]) ).

cnf(c_0_5835_1,axiom,
    ( ~ class_Groups_Oordered__comm__monoid__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5835]) ).

cnf(c_0_5835_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5835]) ).

cnf(c_0_5835_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5835]) ).

cnf(c_0_5835_4,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5835]) ).

cnf(c_0_5835_5,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5835]) ).

cnf(c_0_5836_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5836]) ).

cnf(c_0_5836_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5836]) ).

cnf(c_0_5837_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5837]) ).

cnf(c_0_5837_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5837]) ).

cnf(c_0_5837_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,sk1_esk21_3(X3,X2,X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5837]) ).

cnf(c_0_5838_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5838]) ).

cnf(c_0_5838_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5838]) ).

cnf(c_0_5838_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,sk1_esk19_3(X3,X2,X1),X3)
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5838]) ).

cnf(c_0_5839_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5839]) ).

cnf(c_0_5839_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5839]) ).

cnf(c_0_5839_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5839]) ).

cnf(c_0_5840_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5840]) ).

cnf(c_0_5840_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5840]) ).

cnf(c_0_5840_2,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5840]) ).

cnf(c_0_5841_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5841]) ).

cnf(c_0_5841_1,axiom,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5841]) ).

cnf(c_0_5841_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5841]) ).

cnf(c_0_5842_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5842]) ).

cnf(c_0_5842_1,axiom,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5842]) ).

cnf(c_0_5842_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5842]) ).

cnf(c_0_5843_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5843]) ).

cnf(c_0_5843_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5843]) ).

cnf(c_0_5843_2,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5843]) ).

cnf(c_0_5844_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5844]) ).

cnf(c_0_5844_1,axiom,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5844]) ).

cnf(c_0_5844_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5844]) ).

cnf(c_0_5845_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5845]) ).

cnf(c_0_5845_1,axiom,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5845]) ).

cnf(c_0_5845_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5845]) ).

cnf(c_0_5846_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5846]) ).

cnf(c_0_5846_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5846]) ).

cnf(c_0_5846_2,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5846]) ).

cnf(c_0_5847_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5847]) ).

cnf(c_0_5847_1,axiom,
    ( ~ class_Rings_Olinordered__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5847]) ).

cnf(c_0_5848_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5848]) ).

cnf(c_0_5848_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5848]) ).

cnf(c_0_5848_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5848]) ).

cnf(c_0_5849_0,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5849]) ).

cnf(c_0_5849_1,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5849]) ).

cnf(c_0_5850_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5850]) ).

cnf(c_0_5850_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5850]) ).

cnf(c_0_5850_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5850]) ).

cnf(c_0_5850_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5850]) ).

cnf(c_0_5851_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5851]) ).

cnf(c_0_5851_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5851]) ).

cnf(c_0_5851_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5851]) ).

cnf(c_0_5851_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5851]) ).

cnf(c_0_5852_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5852]) ).

cnf(c_0_5852_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5852]) ).

cnf(c_0_5852_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5852]) ).

cnf(c_0_5852_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5852]) ).

cnf(c_0_5853_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5853]) ).

cnf(c_0_5853_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5853]) ).

cnf(c_0_5853_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5853]) ).

cnf(c_0_5853_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5853]) ).

cnf(c_0_5854_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5854]) ).

cnf(c_0_5854_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(literals_permutation,[status(thm)],[c_0_5854]) ).

cnf(c_0_5855_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5855]) ).

cnf(c_0_5855_1,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5855]) ).

cnf(c_0_5855_2,axiom,
    ( hBOOL(hAPP(hAPP(X3,X2),X1))
    | X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ hBOOL(hAPP(hAPP(X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5855]) ).

cnf(c_0_5855_3,axiom,
    ( ~ hBOOL(hAPP(hAPP(X3,X2),X1))
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5855]) ).

cnf(c_0_5856_0,axiom,
    ( X3 = X2
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5856]) ).

cnf(c_0_5856_1,axiom,
    ( hBOOL(hAPP(hAPP(X1,X2),X3))
    | X3 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5856]) ).

cnf(c_0_5856_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | X3 = X2
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5856]) ).

cnf(c_0_5856_3,axiom,
    ( ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
    | hBOOL(hAPP(hAPP(X1,X2),X3))
    | X3 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5856]) ).

cnf(c_0_5859_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_5859]) ).

cnf(c_0_5859_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5859]) ).

cnf(c_0_5860_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5860]) ).

cnf(c_0_5860_1,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5860]) ).

cnf(c_0_5861_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5861]) ).

cnf(c_0_5861_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5861]) ).

cnf(c_0_5861_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5861]) ).

cnf(c_0_5862_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5862]) ).

cnf(c_0_5862_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5862]) ).

cnf(c_0_5863_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5863]) ).

cnf(c_0_5863_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5863]) ).

cnf(c_0_5864_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5864]) ).

cnf(c_0_5864_1,axiom,
    ( ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5864]) ).

cnf(c_0_5864_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5864]) ).

cnf(c_0_5865_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5865]) ).

cnf(c_0_5865_1,axiom,
    ( ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5865]) ).

cnf(c_0_5865_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5865]) ).

cnf(c_0_5866_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5866]) ).

cnf(c_0_5866_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5866]) ).

cnf(c_0_5866_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_5866]) ).

cnf(c_0_5868_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5868]) ).

cnf(c_0_5868_1,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5868]) ).

cnf(c_0_5869_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5869]) ).

cnf(c_0_5869_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5869]) ).

cnf(c_0_5870_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1))
    | X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_5870]) ).

cnf(c_0_5870_1,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5870]) ).

cnf(c_0_5871_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5871]) ).

cnf(c_0_5871_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5871]) ).

cnf(c_0_5871_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5871]) ).

cnf(c_0_5872_0,axiom,
    ( X2 = X3
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5872]) ).

cnf(c_0_5872_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5872]) ).

cnf(c_0_5872_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_5872]) ).

cnf(c_0_5873_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5873]) ).

cnf(c_0_5873_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5873]) ).

cnf(c_0_5874_0,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5874]) ).

cnf(c_0_5874_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5874]) ).

cnf(c_0_5874_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5874]) ).

cnf(c_0_5875_0,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5875]) ).

cnf(c_0_5875_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5875]) ).

cnf(c_0_5875_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5875]) ).

cnf(c_0_5876_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Odiv(X1,X3,X2)) = X3
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5876]) ).

cnf(c_0_5876_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Odiv(X1,X3,X2)) = X3
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5876]) ).

cnf(c_0_5876_2,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Odiv(X1,X3,X2)) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_5876]) ).

cnf(c_0_5877_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5877]) ).

cnf(c_0_5877_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5877]) ).

cnf(c_0_5877_2,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5877]) ).

cnf(c_0_5878_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5878]) ).

cnf(c_0_5878_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5878]) ).

cnf(c_0_5878_2,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_5878]) ).

cnf(c_0_5879_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5879]) ).

cnf(c_0_5879_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5879]) ).

cnf(c_0_5881_0,axiom,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5881]) ).

cnf(c_0_5881_1,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5881]) ).

cnf(c_0_5881_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5881]) ).

cnf(c_0_5881_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5881]) ).

cnf(c_0_5882_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5882]) ).

cnf(c_0_5882_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),X1)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5882]) ).

cnf(c_0_5882_2,axiom,
    ( X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5882]) ).

cnf(c_0_5883_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5883]) ).

cnf(c_0_5883_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X1)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5883]) ).

cnf(c_0_5883_2,axiom,
    ( X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5883]) ).

cnf(c_0_5884_0,axiom,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5884]) ).

cnf(c_0_5884_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5884]) ).

cnf(c_0_5885_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5885]) ).

cnf(c_0_5885_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5885]) ).

cnf(c_0_5886_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5886]) ).

cnf(c_0_5886_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5886]) ).

cnf(c_0_5887_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5887]) ).

cnf(c_0_5887_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5887]) ).

cnf(c_0_5888_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5888]) ).

cnf(c_0_5888_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5888]) ).

cnf(c_0_5889_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5889]) ).

cnf(c_0_5889_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5889]) ).

cnf(c_0_5890_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5890]) ).

cnf(c_0_5890_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5890]) ).

cnf(c_0_5891_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5891]) ).

cnf(c_0_5891_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5891]) ).

cnf(c_0_5892_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5892]) ).

cnf(c_0_5892_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5892]) ).

cnf(c_0_5893_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5893]) ).

cnf(c_0_5893_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5893]) ).

cnf(c_0_5894_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber(X1)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5894]) ).

cnf(c_0_5894_1,axiom,
    ( ~ class_Int_Onumber(X1)
    | c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5894]) ).

cnf(c_0_5894_2,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | ~ class_Int_Onumber(X1)
    | c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5894]) ).

cnf(c_0_5895_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5895]) ).

cnf(c_0_5895_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5895]) ).

cnf(c_0_5896_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5896]) ).

cnf(c_0_5896_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(literals_permutation,[status(thm)],[c_0_5896]) ).

cnf(c_0_5897_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5897]) ).

cnf(c_0_5897_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(literals_permutation,[status(thm)],[c_0_5897]) ).

cnf(c_0_5898_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5898]) ).

cnf(c_0_5898_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5898]) ).

cnf(c_0_5899_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5899]) ).

cnf(c_0_5899_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5899]) ).

cnf(c_0_5900_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5900]) ).

cnf(c_0_5900_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(literals_permutation,[status(thm)],[c_0_5900]) ).

cnf(c_0_5903_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5903]) ).

cnf(c_0_5903_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5903]) ).

cnf(c_0_5904_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5904]) ).

cnf(c_0_5904_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5904]) ).

cnf(c_0_5905_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5905]) ).

cnf(c_0_5905_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5905]) ).

cnf(c_0_5906_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5906]) ).

cnf(c_0_5906_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5906]) ).

cnf(c_0_5907_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5907]) ).

cnf(c_0_5907_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5907]) ).

cnf(c_0_5908_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5908]) ).

cnf(c_0_5908_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5908]) ).

cnf(c_0_5909_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5909]) ).

cnf(c_0_5909_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5909]) ).

cnf(c_0_5910_0,axiom,
    ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sk1_esk11_2(X1,X2))) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5910]) ).

cnf(c_0_5910_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sk1_esk11_2(X1,X2))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5910]) ).

cnf(c_0_5911_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_5911]) ).

cnf(c_0_5911_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_5911]) ).

cnf(c_0_5911_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_5911]) ).

cnf(c_0_5912_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5912]) ).

cnf(c_0_5912_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5912]) ).

cnf(c_0_5912_2,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_5912]) ).

cnf(c_0_5913_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5913]) ).

cnf(c_0_5913_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5913]) ).

cnf(c_0_5914_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5914]) ).

cnf(c_0_5914_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5914]) ).

cnf(c_0_5915_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5915]) ).

cnf(c_0_5915_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(literals_permutation,[status(thm)],[c_0_5915]) ).

cnf(c_0_5916_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5916]) ).

cnf(c_0_5916_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5916]) ).

cnf(c_0_5917_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5917]) ).

cnf(c_0_5917_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5917]) ).

cnf(c_0_5918_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5918]) ).

cnf(c_0_5918_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5918]) ).

cnf(c_0_5919_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5919]) ).

cnf(c_0_5919_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5919]) ).

cnf(c_0_5920_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5920]) ).

cnf(c_0_5920_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5920]) ).

cnf(c_0_5921_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5921]) ).

cnf(c_0_5921_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5921]) ).

cnf(c_0_5922_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5922]) ).

cnf(c_0_5922_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5922]) ).

cnf(c_0_5923_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5923]) ).

cnf(c_0_5923_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5923]) ).

cnf(c_0_5924_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5924]) ).

cnf(c_0_5924_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5924]) ).

cnf(c_0_5925_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5925]) ).

cnf(c_0_5925_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5925]) ).

cnf(c_0_5926_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5926]) ).

cnf(c_0_5926_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5926]) ).

cnf(c_0_5927_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5927]) ).

cnf(c_0_5927_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5927]) ).

cnf(c_0_5927_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5927]) ).

cnf(c_0_5928_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5928]) ).

cnf(c_0_5928_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5928]) ).

cnf(c_0_5928_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5928]) ).

cnf(c_0_5928_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5928]) ).

cnf(c_0_5929_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5929]) ).

cnf(c_0_5929_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5929]) ).

cnf(c_0_5929_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5929]) ).

cnf(c_0_5929_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5929]) ).

cnf(c_0_5930_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5930]) ).

cnf(c_0_5930_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5930]) ).

cnf(c_0_5930_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5930]) ).

cnf(c_0_5930_3,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
    | ~ c_Rings_Odvd__class_Odvd(X1,X4,X3)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5930]) ).

cnf(c_0_5931_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5931]) ).

cnf(c_0_5931_1,axiom,
    ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) != X2
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5931]) ).

cnf(c_0_5932_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5932]) ).

cnf(c_0_5932_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5932]) ).

cnf(c_0_5933_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5933]) ).

cnf(c_0_5933_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5933]) ).

cnf(c_0_5934_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5934]) ).

cnf(c_0_5934_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5934]) ).

cnf(c_0_5935_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5935]) ).

cnf(c_0_5935_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5935]) ).

cnf(c_0_5936_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5936]) ).

cnf(c_0_5936_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5936]) ).

cnf(c_0_5937_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)))
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_5937]) ).

cnf(c_0_5937_1,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_5937]) ).

cnf(c_0_5938_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5938]) ).

cnf(c_0_5938_1,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5938]) ).

cnf(c_0_5939_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
    | ~ class_Power_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5939]) ).

cnf(c_0_5939_1,axiom,
    ( ~ class_Power_Opower(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5939]) ).

cnf(c_0_5940_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5940]) ).

cnf(c_0_5940_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5940]) ).

cnf(c_0_5941_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5941]) ).

cnf(c_0_5941_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5941]) ).

cnf(c_0_5942_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5942]) ).

cnf(c_0_5942_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5942]) ).

cnf(c_0_5943_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5943]) ).

cnf(c_0_5943_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5943]) ).

cnf(c_0_5943_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5943]) ).

cnf(c_0_5944_0,axiom,
    ( c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sk1_esk3_1(X1))) = X1
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5944]) ).

cnf(c_0_5944_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sk1_esk3_1(X1))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5944]) ).

cnf(c_0_5945_0,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5945]) ).

cnf(c_0_5945_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5945]) ).

cnf(c_0_5945_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5945]) ).

cnf(c_0_5946_0,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5946]) ).

cnf(c_0_5946_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5946]) ).

cnf(c_0_5946_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5946]) ).

cnf(c_0_5947_0,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5947]) ).

cnf(c_0_5947_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5947]) ).

cnf(c_0_5947_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5947]) ).

cnf(c_0_5948_0,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5948]) ).

cnf(c_0_5948_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5948]) ).

cnf(c_0_5948_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_5948]) ).

cnf(c_0_5949_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Orderings_Olinorder(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5949]) ).

cnf(c_0_5949_1,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5949]) ).

cnf(c_0_5949_2,axiom,
    ( ~ class_Orderings_Olinorder(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5949]) ).

cnf(c_0_5949_3,axiom,
    ( ~ class_Int_Onumber(X1)
    | ~ class_Orderings_Olinorder(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
    | c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5949]) ).

cnf(c_0_5950_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5950]) ).

cnf(c_0_5950_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5950]) ).

cnf(c_0_5950_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5950]) ).

cnf(c_0_5951_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5951]) ).

cnf(c_0_5951_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5951]) ).

cnf(c_0_5951_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5951]) ).

cnf(c_0_5952_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5952]) ).

cnf(c_0_5952_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5952]) ).

cnf(c_0_5952_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5952]) ).

cnf(c_0_5953_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5953]) ).

cnf(c_0_5953_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5953]) ).

cnf(c_0_5953_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5953]) ).

cnf(c_0_5954_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5954]) ).

cnf(c_0_5954_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5954]) ).

cnf(c_0_5954_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5954]) ).

cnf(c_0_5955_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5955]) ).

cnf(c_0_5955_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5955]) ).

cnf(c_0_5955_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5955]) ).

cnf(c_0_5956_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_5956]) ).

cnf(c_0_5956_1,axiom,
    ( X2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5956]) ).

cnf(c_0_5957_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X3
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5957]) ).

cnf(c_0_5957_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X3
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5957]) ).

cnf(c_0_5957_2,axiom,
    ( X1 != X3
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5957]) ).

cnf(c_0_5957_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | X1 != X3
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5957]) ).

cnf(c_0_5958_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5958]) ).

cnf(c_0_5958_1,axiom,
    ( X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5958]) ).

cnf(c_0_5958_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5958]) ).

cnf(c_0_5958_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5958]) ).

cnf(c_0_5959_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5959]) ).

cnf(c_0_5959_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5959]) ).

cnf(c_0_5959_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5959]) ).

cnf(c_0_5960_0,axiom,
    ( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_5960]) ).

cnf(c_0_5960_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_5960]) ).

cnf(c_0_5960_2,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != X3
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5960]) ).

cnf(c_0_5961_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5961]) ).

cnf(c_0_5961_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5961]) ).

cnf(c_0_5961_2,axiom,
    ( X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_5961]) ).

cnf(c_0_5962_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5962]) ).

cnf(c_0_5962_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5962]) ).

cnf(c_0_5963_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X2) = c_Divides_Odiv__class_Omod(X1,X3,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5963]) ).

cnf(c_0_5963_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X2) = c_Divides_Odiv__class_Omod(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5963]) ).

cnf(c_0_5964_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5964]) ).

cnf(c_0_5964_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5964]) ).

cnf(c_0_5965_0,axiom,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5965]) ).

cnf(c_0_5965_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_5965]) ).

cnf(c_0_5967_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5967]) ).

cnf(c_0_5967_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5967]) ).

cnf(c_0_5967_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5967]) ).

cnf(c_0_5968_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5968]) ).

cnf(c_0_5968_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5968]) ).

cnf(c_0_5968_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5968]) ).

cnf(c_0_5969_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5969]) ).

cnf(c_0_5969_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5969]) ).

cnf(c_0_5969_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5969]) ).

cnf(c_0_5970_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5970]) ).

cnf(c_0_5970_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_5970]) ).

cnf(c_0_5970_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5970]) ).

cnf(c_0_5971_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5971]) ).

cnf(c_0_5971_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))) ),
    inference(literals_permutation,[status(thm)],[c_0_5971]) ).

cnf(c_0_5972_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5972]) ).

cnf(c_0_5972_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_5972]) ).

cnf(c_0_5973_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5973]) ).

cnf(c_0_5973_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_5973]) ).

cnf(c_0_5974_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5974]) ).

cnf(c_0_5974_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5974]) ).

cnf(c_0_5974_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5974]) ).

cnf(c_0_5975_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5975]) ).

cnf(c_0_5975_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5975]) ).

cnf(c_0_5975_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5975]) ).

cnf(c_0_5976_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5976]) ).

cnf(c_0_5976_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5976]) ).

cnf(c_0_5976_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5976]) ).

cnf(c_0_5977_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5977]) ).

cnf(c_0_5977_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5977]) ).

cnf(c_0_5977_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5977]) ).

cnf(c_0_5978_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5978]) ).

cnf(c_0_5978_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5978]) ).

cnf(c_0_5978_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5978]) ).

cnf(c_0_5979_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5979]) ).

cnf(c_0_5979_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5979]) ).

cnf(c_0_5979_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5979]) ).

cnf(c_0_5980_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5980]) ).

cnf(c_0_5980_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5980]) ).

cnf(c_0_5980_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5980]) ).

cnf(c_0_5981_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5981]) ).

cnf(c_0_5981_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5981]) ).

cnf(c_0_5981_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5981]) ).

cnf(c_0_5982_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5982]) ).

cnf(c_0_5982_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5982]) ).

cnf(c_0_5982_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5982]) ).

cnf(c_0_5983_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5983]) ).

cnf(c_0_5983_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5983]) ).

cnf(c_0_5983_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5983]) ).

cnf(c_0_5984_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5984]) ).

cnf(c_0_5984_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5984]) ).

cnf(c_0_5984_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5984]) ).

cnf(c_0_5985_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5985]) ).

cnf(c_0_5985_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5985]) ).

cnf(c_0_5985_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5985]) ).

cnf(c_0_5986_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5986]) ).

cnf(c_0_5986_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5986]) ).

cnf(c_0_5986_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5986]) ).

cnf(c_0_5987_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5987]) ).

cnf(c_0_5987_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5987]) ).

cnf(c_0_5987_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5987]) ).

cnf(c_0_5988_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5988]) ).

cnf(c_0_5988_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5988]) ).

cnf(c_0_5988_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5988]) ).

cnf(c_0_5989_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5989]) ).

cnf(c_0_5989_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5989]) ).

cnf(c_0_5989_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5989]) ).

cnf(c_0_5990_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5990]) ).

cnf(c_0_5990_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5990]) ).

cnf(c_0_5990_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5990]) ).

cnf(c_0_5991_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5991]) ).

cnf(c_0_5991_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5991]) ).

cnf(c_0_5991_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_5991]) ).

cnf(c_0_5992_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5992]) ).

cnf(c_0_5992_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5992]) ).

cnf(c_0_5993_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_5993]) ).

cnf(c_0_5993_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_5993]) ).

cnf(c_0_5996_0,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,X3) = c_Power_Opower__class_Opower(X1,X2,X4)
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | X3 != X4 ),
    inference(literals_permutation,[status(thm)],[c_0_5996]) ).

cnf(c_0_5996_1,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) = c_Power_Opower__class_Opower(X1,X2,X4)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | X3 != X4 ),
    inference(literals_permutation,[status(thm)],[c_0_5996]) ).

cnf(c_0_5996_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) = c_Power_Opower__class_Opower(X1,X2,X4)
    | X3 != X4 ),
    inference(literals_permutation,[status(thm)],[c_0_5996]) ).

cnf(c_0_5996_3,axiom,
    ( X3 != X4
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Olinordered__semidom(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) = c_Power_Opower__class_Opower(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_5996]) ).

cnf(c_0_5999_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_5999]) ).

cnf(c_0_5999_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_5999]) ).

cnf(c_0_6000_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6000]) ).

cnf(c_0_6000_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6000]) ).

cnf(c_0_6000_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6000]) ).

cnf(c_0_6001_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6001]) ).

cnf(c_0_6001_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6001]) ).

cnf(c_0_6001_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6001]) ).

cnf(c_0_6002_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6002]) ).

cnf(c_0_6002_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6002]) ).

cnf(c_0_6002_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6002]) ).

cnf(c_0_6003_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6003]) ).

cnf(c_0_6003_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6003]) ).

cnf(c_0_6004_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6004]) ).

cnf(c_0_6004_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6004]) ).

cnf(c_0_6005_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6005]) ).

cnf(c_0_6005_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6005]) ).

cnf(c_0_6006_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6006]) ).

cnf(c_0_6006_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6006]) ).

cnf(c_0_6006_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6006]) ).

cnf(c_0_6006_3,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6006]) ).

cnf(c_0_6006_4,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6006]) ).

cnf(c_0_6007_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6007]) ).

cnf(c_0_6007_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6007]) ).

cnf(c_0_6007_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6007]) ).

cnf(c_0_6007_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)) ),
    inference(literals_permutation,[status(thm)],[c_0_6007]) ).

cnf(c_0_6008_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6008]) ).

cnf(c_0_6008_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6008]) ).

cnf(c_0_6008_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6008]) ).

cnf(c_0_6008_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6008]) ).

cnf(c_0_6009_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6009]) ).

cnf(c_0_6009_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6009]) ).

cnf(c_0_6009_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6009]) ).

cnf(c_0_6009_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6009]) ).

cnf(c_0_6010_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6010]) ).

cnf(c_0_6010_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6010]) ).

cnf(c_0_6010_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6010]) ).

cnf(c_0_6010_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)) ),
    inference(literals_permutation,[status(thm)],[c_0_6010]) ).

cnf(c_0_6011_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6011]) ).

cnf(c_0_6011_1,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6011]) ).

cnf(c_0_6012_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6012]) ).

cnf(c_0_6012_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6012]) ).

cnf(c_0_6012_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6012]) ).

cnf(c_0_6012_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_6012]) ).

cnf(c_0_6013_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6013]) ).

cnf(c_0_6013_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6013]) ).

cnf(c_0_6013_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6013]) ).

cnf(c_0_6013_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_6013]) ).

cnf(c_0_6014_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6014]) ).

cnf(c_0_6014_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6014]) ).

cnf(c_0_6014_2,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6014]) ).

cnf(c_0_6014_3,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6014]) ).

cnf(c_0_6015_0,axiom,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6015]) ).

cnf(c_0_6015_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6015]) ).

cnf(c_0_6016_0,axiom,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6016]) ).

cnf(c_0_6016_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6016]) ).

cnf(c_0_6017_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6017]) ).

cnf(c_0_6017_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6017]) ).

cnf(c_0_6017_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6017]) ).

cnf(c_0_6017_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6017]) ).

cnf(c_0_6018_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6018]) ).

cnf(c_0_6018_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6018]) ).

cnf(c_0_6018_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6018]) ).

cnf(c_0_6018_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6018]) ).

cnf(c_0_6019_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6019]) ).

cnf(c_0_6019_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6019]) ).

cnf(c_0_6019_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6019]) ).

cnf(c_0_6019_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6019]) ).

cnf(c_0_6020_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6020]) ).

cnf(c_0_6020_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6020]) ).

cnf(c_0_6020_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6020]) ).

cnf(c_0_6020_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6020]) ).

cnf(c_0_6021_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__ring(X1)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6021]) ).

cnf(c_0_6021_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__ring(X1)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6021]) ).

cnf(c_0_6021_2,axiom,
    ( ~ class_Rings_Olinordered__ring(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6021]) ).

cnf(c_0_6021_3,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | ~ class_Rings_Olinordered__ring(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_6021]) ).

cnf(c_0_6022_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6022]) ).

cnf(c_0_6022_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6022]) ).

cnf(c_0_6022_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6022]) ).

cnf(c_0_6022_3,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6022]) ).

cnf(c_0_6023_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6023]) ).

cnf(c_0_6023_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6023]) ).

cnf(c_0_6023_2,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6023]) ).

cnf(c_0_6023_3,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6023]) ).

cnf(c_0_6024_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6024]) ).

cnf(c_0_6024_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6024]) ).

cnf(c_0_6024_2,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6024]) ).

cnf(c_0_6024_3,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_6024]) ).

cnf(c_0_6025_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6025]) ).

cnf(c_0_6025_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6025]) ).

cnf(c_0_6026_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6026]) ).

cnf(c_0_6026_1,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_6026]) ).

cnf(c_0_6027_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6027]) ).

cnf(c_0_6027_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6027]) ).

cnf(c_0_6027_2,axiom,
    ( X2 != X3
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6027]) ).

cnf(c_0_6028_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6028]) ).

cnf(c_0_6028_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6028]) ).

cnf(c_0_6028_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6028]) ).

cnf(c_0_6028_3,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6028]) ).

cnf(c_0_6029_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6029]) ).

cnf(c_0_6029_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6029]) ).

cnf(c_0_6030_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6030]) ).

cnf(c_0_6030_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6030]) ).

cnf(c_0_6031_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6031]) ).

cnf(c_0_6031_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6031]) ).

cnf(c_0_6032_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6032]) ).

cnf(c_0_6032_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6032]) ).

cnf(c_0_6032_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_6032]) ).

cnf(c_0_6033_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6033]) ).

cnf(c_0_6033_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6033]) ).

cnf(c_0_6033_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_6033]) ).

cnf(c_0_6034_0,axiom,
    ( c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),sk1_esk5_1(X1))) = X1
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6034]) ).

cnf(c_0_6034_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),sk1_esk5_1(X1))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6034]) ).

cnf(c_0_6035_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6035]) ).

cnf(c_0_6035_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6035]) ).

cnf(c_0_6035_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6035]) ).

cnf(c_0_6035_3,axiom,
    ( X1 != X3
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6035]) ).

cnf(c_0_6036_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6036]) ).

cnf(c_0_6036_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6036]) ).

cnf(c_0_6036_2,axiom,
    ( X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6036]) ).

cnf(c_0_6036_3,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
    | X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6036]) ).

cnf(c_0_6037_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6037]) ).

cnf(c_0_6037_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6037]) ).

cnf(c_0_6038_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6038]) ).

cnf(c_0_6038_1,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6038]) ).

cnf(c_0_6038_2,axiom,
    ( hBOOL(hAPP(hAPP(X3,X2),X1))
    | X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6038]) ).

cnf(c_0_6038_3,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | hBOOL(hAPP(hAPP(X3,X2),X1))
    | X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6038]) ).

cnf(c_0_6039_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6039]) ).

cnf(c_0_6039_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6039]) ).

cnf(c_0_6039_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6039]) ).

cnf(c_0_6040_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6040]) ).

cnf(c_0_6040_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6040]) ).

cnf(c_0_6040_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6040]) ).

cnf(c_0_6041_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6041]) ).

cnf(c_0_6041_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6041]) ).

cnf(c_0_6041_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6041]) ).

cnf(c_0_6042_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)) ),
    inference(literals_permutation,[status(thm)],[c_0_6042]) ).

cnf(c_0_6042_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)) ),
    inference(literals_permutation,[status(thm)],[c_0_6042]) ).

cnf(c_0_6042_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)) ),
    inference(literals_permutation,[status(thm)],[c_0_6042]) ).

cnf(c_0_6042_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6042]) ).

cnf(c_0_6043_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6043]) ).

cnf(c_0_6043_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6043]) ).

cnf(c_0_6043_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6043]) ).

cnf(c_0_6043_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6043]) ).

cnf(c_0_6044_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6044]) ).

cnf(c_0_6044_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6044]) ).

cnf(c_0_6044_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6044]) ).

cnf(c_0_6044_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6044]) ).

cnf(c_0_6045_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)) ),
    inference(literals_permutation,[status(thm)],[c_0_6045]) ).

cnf(c_0_6045_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)) ),
    inference(literals_permutation,[status(thm)],[c_0_6045]) ).

cnf(c_0_6045_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)) ),
    inference(literals_permutation,[status(thm)],[c_0_6045]) ).

cnf(c_0_6045_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6045]) ).

cnf(c_0_6046_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6046]) ).

cnf(c_0_6046_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6046]) ).

cnf(c_0_6047_0,axiom,
    ( X1 = X2
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6047]) ).

cnf(c_0_6047_1,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6047]) ).

cnf(c_0_6048_0,axiom,
    ( X4 = X5
    | ~ class_Groups_Oab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6048]) ).

cnf(c_0_6048_1,axiom,
    ( ~ class_Groups_Oab__group__add(X1)
    | X4 = X5
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6048]) ).

cnf(c_0_6048_2,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oab__group__add(X1)
    | X4 = X5
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6048]) ).

cnf(c_0_6048_3,axiom,
    ( X2 != X3
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oab__group__add(X1)
    | X4 = X5 ),
    inference(literals_permutation,[status(thm)],[c_0_6048]) ).

cnf(c_0_6049_0,axiom,
    ( X2 = X3
    | ~ class_Groups_Oab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | X4 != X5 ),
    inference(literals_permutation,[status(thm)],[c_0_6049]) ).

cnf(c_0_6049_1,axiom,
    ( ~ class_Groups_Oab__group__add(X1)
    | X2 = X3
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | X4 != X5 ),
    inference(literals_permutation,[status(thm)],[c_0_6049]) ).

cnf(c_0_6049_2,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oab__group__add(X1)
    | X2 = X3
    | X4 != X5 ),
    inference(literals_permutation,[status(thm)],[c_0_6049]) ).

cnf(c_0_6049_3,axiom,
    ( X4 != X5
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
    | ~ class_Groups_Oab__group__add(X1)
    | X2 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6049]) ).

cnf(c_0_6050_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6050]) ).

cnf(c_0_6050_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6050]) ).

cnf(c_0_6051_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6051]) ).

cnf(c_0_6051_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6051]) ).

cnf(c_0_6052_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6052]) ).

cnf(c_0_6052_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6052]) ).

cnf(c_0_6053_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6053]) ).

cnf(c_0_6053_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6053]) ).

cnf(c_0_6054_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6054]) ).

cnf(c_0_6054_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6054]) ).

cnf(c_0_6054_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6054]) ).

cnf(c_0_6054_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6054]) ).

cnf(c_0_6055_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6055]) ).

cnf(c_0_6055_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6055]) ).

cnf(c_0_6055_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6055]) ).

cnf(c_0_6055_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6055]) ).

cnf(c_0_6056_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6056]) ).

cnf(c_0_6056_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6056]) ).

cnf(c_0_6056_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6056]) ).

cnf(c_0_6056_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6056]) ).

cnf(c_0_6057_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Rings_Olinordered__idom(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6057]) ).

cnf(c_0_6057_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6057]) ).

cnf(c_0_6057_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6057]) ).

cnf(c_0_6057_3,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6057]) ).

cnf(c_0_6058_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6058]) ).

cnf(c_0_6058_1,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_6058]) ).

cnf(c_0_6059_0,axiom,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6059]) ).

cnf(c_0_6059_1,axiom,
    ( ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6059]) ).

cnf(c_0_6059_2,axiom,
    ( ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6059]) ).

cnf(c_0_6059_3,axiom,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6059]) ).

cnf(c_0_6059_4,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6059]) ).

cnf(c_0_6059_5,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6059]) ).

cnf(c_0_6060_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6060]) ).

cnf(c_0_6060_1,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6060]) ).

cnf(c_0_6060_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Olinordered__idom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_6060]) ).

cnf(c_0_6061_0,axiom,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(X3,X1,X4) != c_Groups_Oplus__class_Oplus(X3,X2,X4)
    | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6061]) ).

cnf(c_0_6061_1,axiom,
    ( c_Groups_Oplus__class_Oplus(X3,X1,X4) != c_Groups_Oplus__class_Oplus(X3,X2,X4)
    | X1 = X2
    | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6061]) ).

cnf(c_0_6061_2,axiom,
    ( ~ class_Groups_Ocancel__semigroup__add(X3)
    | c_Groups_Oplus__class_Oplus(X3,X1,X4) != c_Groups_Oplus__class_Oplus(X3,X2,X4)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6061]) ).

cnf(c_0_6062_0,axiom,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
    | ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6062]) ).

cnf(c_0_6062_1,axiom,
    ( c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
    | X1 = X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6062]) ).

cnf(c_0_6062_2,axiom,
    ( ~ class_Groups_Ocancel__ab__semigroup__add(X3)
    | c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6062]) ).

cnf(c_0_6063_0,axiom,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
    | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6063]) ).

cnf(c_0_6063_1,axiom,
    ( c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
    | X1 = X2
    | ~ class_Groups_Ocancel__semigroup__add(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6063]) ).

cnf(c_0_6063_2,axiom,
    ( ~ class_Groups_Ocancel__semigroup__add(X3)
    | c_Groups_Oplus__class_Oplus(X3,X4,X1) != c_Groups_Oplus__class_Oplus(X3,X4,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6063]) ).

cnf(c_0_6064_0,axiom,
    ( X2 = X3
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oplus__class_Oplus(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_6064]) ).

cnf(c_0_6064_1,axiom,
    ( ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 = X3
    | c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oplus__class_Oplus(X1,X3,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_6064]) ).

cnf(c_0_6064_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X4) != c_Groups_Oplus__class_Oplus(X1,X3,X4)
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6064]) ).

cnf(c_0_6065_0,axiom,
    ( X2 = X3
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X4,X2) != c_Groups_Oplus__class_Oplus(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6065]) ).

cnf(c_0_6065_1,axiom,
    ( ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 = X3
    | c_Groups_Oplus__class_Oplus(X1,X4,X2) != c_Groups_Oplus__class_Oplus(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6065]) ).

cnf(c_0_6065_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X4,X2) != c_Groups_Oplus__class_Oplus(X1,X4,X3)
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6065]) ).

cnf(c_0_6066_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6066]) ).

cnf(c_0_6066_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6066]) ).

cnf(c_0_6067_0,axiom,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6067]) ).

cnf(c_0_6067_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6067]) ).

cnf(c_0_6067_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6067]) ).

cnf(c_0_6068_0,axiom,
    ( X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6068]) ).

cnf(c_0_6068_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6068]) ).

cnf(c_0_6068_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6068]) ).

cnf(c_0_6069_0,axiom,
    ( X2 = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6069]) ).

cnf(c_0_6069_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6069]) ).

cnf(c_0_6069_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6069]) ).

cnf(c_0_6070_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6070]) ).

cnf(c_0_6070_1,axiom,
    ( ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6070]) ).

cnf(c_0_6070_2,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6070]) ).

cnf(c_0_6071_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6071]) ).

cnf(c_0_6071_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6071]) ).

cnf(c_0_6072_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6072]) ).

cnf(c_0_6072_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6072]) ).

cnf(c_0_6073_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | X2 != c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6073]) ).

cnf(c_0_6073_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
    | X2 != c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6073]) ).

cnf(c_0_6073_2,axiom,
    ( X2 != c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_6073]) ).

cnf(c_0_6074_0,axiom,
    ( X1 = X2
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6074]) ).

cnf(c_0_6074_1,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = X2
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6074]) ).

cnf(c_0_6074_2,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6074]) ).

cnf(c_0_6075_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk9_2(X2,X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6075]) ).

cnf(c_0_6075_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk9_2(X2,X1),X2)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6075]) ).

cnf(c_0_6075_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,sk1_esk9_2(X2,X1),X2)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6075]) ).

cnf(c_0_6076_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6076]) ).

cnf(c_0_6076_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6076]) ).

cnf(c_0_6077_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X2))
    | ~ class_Rings_Olinordered__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6077]) ).

cnf(c_0_6077_1,axiom,
    ( ~ class_Rings_Olinordered__ring(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6077]) ).

cnf(c_0_6078_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6078]) ).

cnf(c_0_6078_1,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6078]) ).

cnf(c_0_6085_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6085]) ).

cnf(c_0_6085_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Odiv(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6085]) ).

cnf(c_0_6086_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6086]) ).

cnf(c_0_6086_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6086]) ).

cnf(c_0_6087_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6087]) ).

cnf(c_0_6087_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6087]) ).

cnf(c_0_6088_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6088]) ).

cnf(c_0_6088_1,axiom,
    ( X2 = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6088]) ).

cnf(c_0_6088_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3)
    | X2 = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_6088]) ).

cnf(c_0_6089_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6089]) ).

cnf(c_0_6089_1,axiom,
    ( X2 = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6089]) ).

cnf(c_0_6089_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)
    | X2 = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_6089]) ).

cnf(c_0_6090_0,axiom,
    ( X1 = X2
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6090]) ).

cnf(c_0_6090_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = X2
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6090]) ).

cnf(c_0_6090_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6090]) ).

cnf(c_0_6091_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6091]) ).

cnf(c_0_6091_1,axiom,
    ( X2 = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6091]) ).

cnf(c_0_6091_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X2 = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6091]) ).

cnf(c_0_6092_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = X3
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6092]) ).

cnf(c_0_6092_1,axiom,
    ( X2 = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6092]) ).

cnf(c_0_6092_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1)
    | X2 = X3
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6092]) ).

cnf(c_0_6093_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6093]) ).

cnf(c_0_6093_1,axiom,
    ( X1 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6093]) ).

cnf(c_0_6094_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6094]) ).

cnf(c_0_6094_1,axiom,
    ( X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6094]) ).

cnf(c_0_6095_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6095]) ).

cnf(c_0_6095_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6095]) ).

cnf(c_0_6096_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6096]) ).

cnf(c_0_6096_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6096]) ).

cnf(c_0_6097_0,axiom,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(literals_permutation,[status(thm)],[c_0_6097]) ).

cnf(c_0_6097_1,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(literals_permutation,[status(thm)],[c_0_6097]) ).

cnf(c_0_6097_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6097]) ).

cnf(c_0_6098_0,axiom,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6098]) ).

cnf(c_0_6098_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6098]) ).

cnf(c_0_6098_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6098]) ).

cnf(c_0_6099_0,axiom,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6099]) ).

cnf(c_0_6099_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6099]) ).

cnf(c_0_6099_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6099]) ).

cnf(c_0_6100_0,axiom,
    ( X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6100]) ).

cnf(c_0_6100_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6100]) ).

cnf(c_0_6100_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6100]) ).

cnf(c_0_6101_0,axiom,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6101]) ).

cnf(c_0_6101_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6101]) ).

cnf(c_0_6101_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6101]) ).

cnf(c_0_6102_0,axiom,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6102]) ).

cnf(c_0_6102_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6102]) ).

cnf(c_0_6102_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6102]) ).

cnf(c_0_6103_0,axiom,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6103]) ).

cnf(c_0_6103_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6103]) ).

cnf(c_0_6103_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6103]) ).

cnf(c_0_6104_0,axiom,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6104]) ).

cnf(c_0_6104_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6104]) ).

cnf(c_0_6104_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6104]) ).

cnf(c_0_6105_0,axiom,
    ( X2 = X1
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6105]) ).

cnf(c_0_6105_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X2 = X1
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6105]) ).

cnf(c_0_6105_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6105]) ).

cnf(c_0_6106_0,axiom,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6106]) ).

cnf(c_0_6106_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6106]) ).

cnf(c_0_6106_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6106]) ).

cnf(c_0_6107_0,axiom,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6107]) ).

cnf(c_0_6107_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6107]) ).

cnf(c_0_6107_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6107]) ).

cnf(c_0_6108_0,axiom,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6108]) ).

cnf(c_0_6108_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6108]) ).

cnf(c_0_6108_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6108]) ).

cnf(c_0_6109_0,axiom,
    ( X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6109]) ).

cnf(c_0_6109_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6109]) ).

cnf(c_0_6109_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6109]) ).

cnf(c_0_6110_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6110]) ).

cnf(c_0_6110_1,axiom,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6110]) ).

cnf(c_0_6111_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6111]) ).

cnf(c_0_6111_1,axiom,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6111]) ).

cnf(c_0_6112_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X2))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6112]) ).

cnf(c_0_6112_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6112]) ).

cnf(c_0_6113_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X2,X3))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6113]) ).

cnf(c_0_6113_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_6113]) ).

cnf(c_0_6114_0,axiom,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6114]) ).

cnf(c_0_6114_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6114]) ).

cnf(c_0_6115_0,axiom,
    ( X1 = X2
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6115]) ).

cnf(c_0_6115_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6115]) ).

cnf(c_0_6116_0,axiom,
    ( epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_6116]) ).

cnf(c_0_6116_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | epred1_3(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_6116]) ).

cnf(c_0_6116_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
    | epred1_3(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6116]) ).

cnf(c_0_6117_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,sk1_esk17_2(X2,X1)) = X1
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6117]) ).

cnf(c_0_6117_1,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,sk1_esk17_2(X2,X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6117]) ).

cnf(c_0_6118_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,sk1_esk16_2(X2,X1)) = X1
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6118]) ).

cnf(c_0_6118_1,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,sk1_esk16_2(X2,X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6118]) ).

cnf(c_0_6123_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6123]) ).

cnf(c_0_6123_1,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(literals_permutation,[status(thm)],[c_0_6123]) ).

cnf(c_0_6124_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6124]) ).

cnf(c_0_6124_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) = c_Groups_Oplus__class_Oplus(X1,X2,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6124]) ).

cnf(c_0_6125_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6125]) ).

cnf(c_0_6125_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6125]) ).

cnf(c_0_6126_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6126]) ).

cnf(c_0_6126_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6126]) ).

cnf(c_0_6127_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6127]) ).

cnf(c_0_6127_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6127]) ).

cnf(c_0_6128_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sk1_esk13_2(X1,X2)) = X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6128]) ).

cnf(c_0_6128_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sk1_esk13_2(X1,X2)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6128]) ).

cnf(c_0_6129_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6129]) ).

cnf(c_0_6129_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1))
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_6129]) ).

cnf(c_0_6130_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X2) = c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6130]) ).

cnf(c_0_6130_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X2) = c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    inference(literals_permutation,[status(thm)],[c_0_6130]) ).

cnf(c_0_6131_0,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,X2,X2)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6131]) ).

cnf(c_0_6131_1,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,X2,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6131]) ).

cnf(c_0_6133_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6133]) ).

cnf(c_0_6133_1,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6133]) ).

cnf(c_0_6138_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6138]) ).

cnf(c_0_6138_1,axiom,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6138]) ).

cnf(c_0_6138_2,axiom,
    ( ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6138]) ).

cnf(c_0_6138_3,axiom,
    ( ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6138]) ).

cnf(c_0_6138_4,axiom,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6138]) ).

cnf(c_0_6138_5,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6138]) ).

cnf(c_0_6139_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6139]) ).

cnf(c_0_6139_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6139]) ).

cnf(c_0_6144_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6144]) ).

cnf(c_0_6144_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6144]) ).

cnf(c_0_6144_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6144]) ).

cnf(c_0_6145_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6145]) ).

cnf(c_0_6145_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6145]) ).

cnf(c_0_6145_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6145]) ).

cnf(c_0_6146_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6146]) ).

cnf(c_0_6146_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6146]) ).

cnf(c_0_6146_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6146]) ).

cnf(c_0_6147_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6147]) ).

cnf(c_0_6147_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6147]) ).

cnf(c_0_6147_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6147]) ).

cnf(c_0_6148_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6148]) ).

cnf(c_0_6148_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6148]) ).

cnf(c_0_6148_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6148]) ).

cnf(c_0_6149_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6149]) ).

cnf(c_0_6149_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6149]) ).

cnf(c_0_6149_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6149]) ).

cnf(c_0_6150_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6150]) ).

cnf(c_0_6150_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6150]) ).

cnf(c_0_6150_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6150]) ).

cnf(c_0_6156_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6156]) ).

cnf(c_0_6156_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6156]) ).

cnf(c_0_6157_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6157]) ).

cnf(c_0_6157_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6157]) ).

cnf(c_0_6158_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6158]) ).

cnf(c_0_6158_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6158]) ).

cnf(c_0_6159_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6159]) ).

cnf(c_0_6159_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6159]) ).

cnf(c_0_6160_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6160]) ).

cnf(c_0_6160_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6160]) ).

cnf(c_0_6161_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6161]) ).

cnf(c_0_6161_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6161]) ).

cnf(c_0_6162_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6162]) ).

cnf(c_0_6162_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6162]) ).

cnf(c_0_6163_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6163]) ).

cnf(c_0_6163_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6163]) ).

cnf(c_0_6164_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6164]) ).

cnf(c_0_6164_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6164]) ).

cnf(c_0_6165_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6165]) ).

cnf(c_0_6165_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6165]) ).

cnf(c_0_6166_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6166]) ).

cnf(c_0_6166_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6166]) ).

cnf(c_0_6167_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6167]) ).

cnf(c_0_6167_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6167]) ).

cnf(c_0_6168_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6168]) ).

cnf(c_0_6168_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6168]) ).

cnf(c_0_6169_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6169]) ).

cnf(c_0_6169_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6169]) ).

cnf(c_0_6170_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6170]) ).

cnf(c_0_6170_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6170]) ).

cnf(c_0_6171_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6171]) ).

cnf(c_0_6171_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6171]) ).

cnf(c_0_6172_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6172]) ).

cnf(c_0_6172_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6172]) ).

cnf(c_0_6173_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6173]) ).

cnf(c_0_6173_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6173]) ).

cnf(c_0_6174_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6174]) ).

cnf(c_0_6174_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6174]) ).

cnf(c_0_6175_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6175]) ).

cnf(c_0_6175_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6175]) ).

cnf(c_0_6175_2,axiom,
    ( X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6175]) ).

cnf(c_0_6175_3,axiom,
    ( X1 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6175]) ).

cnf(c_0_6176_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_6176]) ).

cnf(c_0_6176_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_6176]) ).

cnf(c_0_6177_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_6177]) ).

cnf(c_0_6177_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_6177]) ).

cnf(c_0_6178_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6178]) ).

cnf(c_0_6178_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | c_Divides_Odiv__class_Omod(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6178]) ).

cnf(c_0_6178_2,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6178]) ).

cnf(c_0_6181_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6181]) ).

cnf(c_0_6181_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
    | c_Divides_Odiv__class_Omod(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6181]) ).

cnf(c_0_6181_2,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
    | c_Divides_Odiv__class_Omod(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6181]) ).

cnf(c_0_6182_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6182]) ).

cnf(c_0_6182_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Rings_Odvd__class_Odvd(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6182]) ).

cnf(c_0_6182_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X1,X3,X2)
    | ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6182]) ).

cnf(c_0_6183_0,axiom,
    ( X1 = c_Nat_OSuc(X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6183]) ).

cnf(c_0_6183_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 = c_Nat_OSuc(X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6183]) ).

cnf(c_0_6183_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 = c_Nat_OSuc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6183]) ).

cnf(c_0_6184_0,axiom,
    ( X1 = c_Nat_OSuc(X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6184]) ).

cnf(c_0_6184_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 = c_Nat_OSuc(X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6184]) ).

cnf(c_0_6184_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 = c_Nat_OSuc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6184]) ).

cnf(c_0_6185_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | X1 != c_Nat_OSuc(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6185]) ).

cnf(c_0_6185_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != c_Nat_OSuc(X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6185]) ).

cnf(c_0_6185_2,axiom,
    ( X1 != c_Nat_OSuc(X3)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6185]) ).

cnf(c_0_6186_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_6186]) ).

cnf(c_0_6186_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_6186]) ).

cnf(c_0_6187_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_6187]) ).

cnf(c_0_6187_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(literals_permutation,[status(thm)],[c_0_6187]) ).

cnf(c_0_6188_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | X3 != c_Groups_Otimes__class_Otimes(X1,X2,X4)
    | ~ class_Rings_Odvd(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6188]) ).

cnf(c_0_6188_1,axiom,
    ( X3 != c_Groups_Otimes__class_Otimes(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3)
    | ~ class_Rings_Odvd(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6188]) ).

cnf(c_0_6188_2,axiom,
    ( ~ class_Rings_Odvd(X1)
    | X3 != c_Groups_Otimes__class_Otimes(X1,X2,X4)
    | c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6188]) ).

cnf(c_0_6189_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6189]) ).

cnf(c_0_6189_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6189]) ).

cnf(c_0_6190_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6190]) ).

cnf(c_0_6190_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6190]) ).

cnf(c_0_6191_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6191]) ).

cnf(c_0_6191_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6191]) ).

cnf(c_0_6192_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6192]) ).

cnf(c_0_6192_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6192]) ).

cnf(c_0_6193_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6193]) ).

cnf(c_0_6193_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6193]) ).

cnf(c_0_6194_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6194]) ).

cnf(c_0_6194_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6194]) ).

cnf(c_0_6195_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6195]) ).

cnf(c_0_6195_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6195]) ).

cnf(c_0_6196_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6196]) ).

cnf(c_0_6196_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6196]) ).

cnf(c_0_6197_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6197]) ).

cnf(c_0_6197_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6197]) ).

cnf(c_0_6198_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6198]) ).

cnf(c_0_6198_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6198]) ).

cnf(c_0_6199_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6199]) ).

cnf(c_0_6199_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6199]) ).

cnf(c_0_6200_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6200]) ).

cnf(c_0_6200_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6200]) ).

cnf(c_0_6201_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6201]) ).

cnf(c_0_6201_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6201]) ).

cnf(c_0_6202_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6202]) ).

cnf(c_0_6202_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6202]) ).

cnf(c_0_6203_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6203]) ).

cnf(c_0_6203_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6203]) ).

cnf(c_0_6204_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6204]) ).

cnf(c_0_6204_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6204]) ).

cnf(c_0_6205_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6205]) ).

cnf(c_0_6205_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6205]) ).

cnf(c_0_6206_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6206]) ).

cnf(c_0_6206_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6206]) ).

cnf(c_0_6207_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6207]) ).

cnf(c_0_6207_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6207]) ).

cnf(c_0_6208_0,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6208]) ).

cnf(c_0_6208_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6208]) ).

cnf(c_0_6208_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6208]) ).

cnf(c_0_6209_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6209]) ).

cnf(c_0_6209_1,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6209]) ).

cnf(c_0_6209_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6209]) ).

cnf(c_0_6210_0,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6210]) ).

cnf(c_0_6210_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6210]) ).

cnf(c_0_6210_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6210]) ).

cnf(c_0_6211_0,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6211]) ).

cnf(c_0_6211_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6211]) ).

cnf(c_0_6211_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6211]) ).

cnf(c_0_6212_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Nat_OSuc(X1) = X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6212]) ).

cnf(c_0_6212_1,axiom,
    ( c_Nat_OSuc(X1) = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6212]) ).

cnf(c_0_6212_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Nat_OSuc(X1) = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6212]) ).

cnf(c_0_6213_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6213]) ).

cnf(c_0_6213_1,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6213]) ).

cnf(c_0_6214_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6214]) ).

cnf(c_0_6214_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1))
    | X2 != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6214]) ).

cnf(c_0_6214_2,axiom,
    ( X2 != X1
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6214]) ).

cnf(c_0_6215_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6215]) ).

cnf(c_0_6215_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6215]) ).

cnf(c_0_6216_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6216]) ).

cnf(c_0_6216_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6216]) ).

cnf(c_0_6217_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6217]) ).

cnf(c_0_6217_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6217]) ).

cnf(c_0_6218_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6218]) ).

cnf(c_0_6218_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6218]) ).

cnf(c_0_6219_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6219]) ).

cnf(c_0_6219_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6219]) ).

cnf(c_0_6220_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6220]) ).

cnf(c_0_6220_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6220]) ).

cnf(c_0_6221_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6221]) ).

cnf(c_0_6221_1,axiom,
    ( X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6221]) ).

cnf(c_0_6222_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6222]) ).

cnf(c_0_6222_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6222]) ).

cnf(c_0_6223_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6223]) ).

cnf(c_0_6223_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6223]) ).

cnf(c_0_6224_0,axiom,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_6224]) ).

cnf(c_0_6224_1,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_6224]) ).

cnf(c_0_6224_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6224]) ).

cnf(c_0_6225_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6225]) ).

cnf(c_0_6225_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6225]) ).

cnf(c_0_6226_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6226]) ).

cnf(c_0_6226_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6226]) ).

cnf(c_0_6227_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6227]) ).

cnf(c_0_6227_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6227]) ).

cnf(c_0_6228_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6228]) ).

cnf(c_0_6228_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6228]) ).

cnf(c_0_6229_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6229]) ).

cnf(c_0_6229_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6229]) ).

cnf(c_0_6230_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6230]) ).

cnf(c_0_6230_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6230]) ).

cnf(c_0_6231_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6231]) ).

cnf(c_0_6231_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6231]) ).

cnf(c_0_6232_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6232]) ).

cnf(c_0_6232_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6232]) ).

cnf(c_0_6233_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6233]) ).

cnf(c_0_6233_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6233]) ).

cnf(c_0_6234_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6234]) ).

cnf(c_0_6234_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6234]) ).

cnf(c_0_6235_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6235]) ).

cnf(c_0_6235_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6235]) ).

cnf(c_0_6236_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6236]) ).

cnf(c_0_6236_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6236]) ).

cnf(c_0_6237_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6237]) ).

cnf(c_0_6237_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6237]) ).

cnf(c_0_6238_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6238]) ).

cnf(c_0_6238_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6238]) ).

cnf(c_0_6239_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6239]) ).

cnf(c_0_6239_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6239]) ).

cnf(c_0_6240_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6240]) ).

cnf(c_0_6240_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6240]) ).

cnf(c_0_6241_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6241]) ).

cnf(c_0_6241_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6241]) ).

cnf(c_0_6242_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6242]) ).

cnf(c_0_6242_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6242]) ).

cnf(c_0_6243_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6243]) ).

cnf(c_0_6243_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6243]) ).

cnf(c_0_6244_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6244]) ).

cnf(c_0_6244_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6244]) ).

cnf(c_0_6245_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X1)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6245]) ).

cnf(c_0_6245_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1))
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6245]) ).

cnf(c_0_6246_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6246]) ).

cnf(c_0_6246_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6246]) ).

cnf(c_0_6247_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6247]) ).

cnf(c_0_6247_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6247]) ).

cnf(c_0_6248_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6248]) ).

cnf(c_0_6248_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1))
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6248]) ).

cnf(c_0_6249_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6249]) ).

cnf(c_0_6249_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6249]) ).

cnf(c_0_6250_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6250]) ).

cnf(c_0_6250_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6250]) ).

cnf(c_0_6250_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6250]) ).

cnf(c_0_6251_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6251]) ).

cnf(c_0_6251_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6251]) ).

cnf(c_0_6251_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6251]) ).

cnf(c_0_6252_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6252]) ).

cnf(c_0_6252_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6252]) ).

cnf(c_0_6252_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6252]) ).

cnf(c_0_6253_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6253]) ).

cnf(c_0_6253_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6253]) ).

cnf(c_0_6253_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6253]) ).

cnf(c_0_6254_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6254]) ).

cnf(c_0_6254_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6254]) ).

cnf(c_0_6254_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6254]) ).

cnf(c_0_6255_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6255]) ).

cnf(c_0_6255_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6255]) ).

cnf(c_0_6255_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6255]) ).

cnf(c_0_6256_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6256]) ).

cnf(c_0_6256_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6256]) ).

cnf(c_0_6256_2,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6256]) ).

cnf(c_0_6257_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6257]) ).

cnf(c_0_6257_1,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6257]) ).

cnf(c_0_6258_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6258]) ).

cnf(c_0_6258_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6258]) ).

cnf(c_0_6258_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6258]) ).

cnf(c_0_6259_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6259]) ).

cnf(c_0_6259_1,axiom,
    ( X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6259]) ).

cnf(c_0_6259_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6259]) ).

cnf(c_0_6260_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6260]) ).

cnf(c_0_6260_1,axiom,
    ( X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6260]) ).

cnf(c_0_6260_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6260]) ).

cnf(c_0_6261_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6261]) ).

cnf(c_0_6261_1,axiom,
    ( X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6261]) ).

cnf(c_0_6261_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6261]) ).

cnf(c_0_6262_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X3 != X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6262]) ).

cnf(c_0_6262_1,axiom,
    ( X3 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6262]) ).

cnf(c_0_6262_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
    | X3 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6262]) ).

cnf(c_0_6263_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | X1 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6263]) ).

cnf(c_0_6263_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6263]) ).

cnf(c_0_6263_2,axiom,
    ( X1 != X3
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6263]) ).

cnf(c_0_6264_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X2 != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6264]) ).

cnf(c_0_6264_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X2 != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6264]) ).

cnf(c_0_6264_2,axiom,
    ( X2 != X1
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6264]) ).

cnf(c_0_6265_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X2 != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6265]) ).

cnf(c_0_6265_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X2 != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6265]) ).

cnf(c_0_6265_2,axiom,
    ( X2 != X1
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6265]) ).

cnf(c_0_6266_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6266]) ).

cnf(c_0_6266_1,axiom,
    ( X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6266]) ).

cnf(c_0_6267_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X1 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6267]) ).

cnf(c_0_6267_1,axiom,
    ( X1 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6267]) ).

cnf(c_0_6268_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6268]) ).

cnf(c_0_6268_1,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6268]) ).

cnf(c_0_6268_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6268]) ).

cnf(c_0_6269_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6269]) ).

cnf(c_0_6269_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6269]) ).

cnf(c_0_6270_0,axiom,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6270]) ).

cnf(c_0_6270_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6270]) ).

cnf(c_0_6271_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6271]) ).

cnf(c_0_6271_1,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6271]) ).

cnf(c_0_6271_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6271]) ).

cnf(c_0_6272_0,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6272]) ).

cnf(c_0_6272_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6272]) ).

cnf(c_0_6272_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6272]) ).

cnf(c_0_6273_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6273]) ).

cnf(c_0_6273_1,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6273]) ).

cnf(c_0_6273_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6273]) ).

cnf(c_0_6274_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6274]) ).

cnf(c_0_6274_1,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6274]) ).

cnf(c_0_6274_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | X1 = X2
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6274]) ).

cnf(c_0_6275_0,axiom,
    ( X1 = X2
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6275]) ).

cnf(c_0_6275_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | X1 = X2
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6275]) ).

cnf(c_0_6275_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6275]) ).

cnf(c_0_6276_0,axiom,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6276]) ).

cnf(c_0_6276_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6276]) ).

cnf(c_0_6276_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6276]) ).

cnf(c_0_6277_0,axiom,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6277]) ).

cnf(c_0_6277_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6277]) ).

cnf(c_0_6277_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6277]) ).

cnf(c_0_6278_0,axiom,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6278]) ).

cnf(c_0_6278_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6278]) ).

cnf(c_0_6278_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6278]) ).

cnf(c_0_6279_0,axiom,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6279]) ).

cnf(c_0_6279_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6279]) ).

cnf(c_0_6279_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6279]) ).

cnf(c_0_6280_0,axiom,
    ( X1 = X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6280]) ).

cnf(c_0_6280_1,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6280]) ).

cnf(c_0_6280_2,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6280]) ).

cnf(c_0_6281_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6281]) ).

cnf(c_0_6281_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6281]) ).

cnf(c_0_6282_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6282]) ).

cnf(c_0_6282_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6282]) ).

cnf(c_0_6283_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6283]) ).

cnf(c_0_6283_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6283]) ).

cnf(c_0_6284_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6284]) ).

cnf(c_0_6284_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6284]) ).

cnf(c_0_6285_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6285]) ).

cnf(c_0_6285_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6285]) ).

cnf(c_0_6286_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6286]) ).

cnf(c_0_6286_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6286]) ).

cnf(c_0_6287_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6287]) ).

cnf(c_0_6287_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6287]) ).

cnf(c_0_6288_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6288]) ).

cnf(c_0_6288_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OMin)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6288]) ).

cnf(c_0_6289_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6289]) ).

cnf(c_0_6289_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6289]) ).

cnf(c_0_6290_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6290]) ).

cnf(c_0_6290_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6290]) ).

cnf(c_0_6291_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6291]) ).

cnf(c_0_6291_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6291]) ).

cnf(c_0_6292_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6292]) ).

cnf(c_0_6292_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6292]) ).

cnf(c_0_6293_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6293]) ).

cnf(c_0_6293_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6293]) ).

cnf(c_0_6294_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6294]) ).

cnf(c_0_6294_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6294]) ).

cnf(c_0_6295_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6295]) ).

cnf(c_0_6295_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6295]) ).

cnf(c_0_6296_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6296]) ).

cnf(c_0_6296_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6296]) ).

cnf(c_0_6297_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6297]) ).

cnf(c_0_6297_1,axiom,
    ( X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6297]) ).

cnf(c_0_6298_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6298]) ).

cnf(c_0_6298_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6298]) ).

cnf(c_0_6299_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6299]) ).

cnf(c_0_6299_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6299]) ).

cnf(c_0_6300_0,axiom,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_6300]) ).

cnf(c_0_6300_1,axiom,
    ( ~ class_Int_Oring__char__0(X1)
    | c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_6300]) ).

cnf(c_0_6300_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_6300]) ).

cnf(c_0_6300_3,axiom,
    ( ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6300]) ).

cnf(c_0_6301_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6301]) ).

cnf(c_0_6301_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6301]) ).

cnf(c_0_6302_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6302]) ).

cnf(c_0_6302_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6302]) ).

cnf(c_0_6303_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6303]) ).

cnf(c_0_6303_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6303]) ).

cnf(c_0_6304_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6304]) ).

cnf(c_0_6304_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6304]) ).

cnf(c_0_6305_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6305]) ).

cnf(c_0_6305_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6305]) ).

cnf(c_0_6306_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6306]) ).

cnf(c_0_6306_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6306]) ).

cnf(c_0_6307_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6307]) ).

cnf(c_0_6307_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6307]) ).

cnf(c_0_6308_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6308]) ).

cnf(c_0_6308_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6308]) ).

cnf(c_0_6309_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6309]) ).

cnf(c_0_6309_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6309]) ).

cnf(c_0_6310_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6310]) ).

cnf(c_0_6310_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6310]) ).

cnf(c_0_6311_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6311]) ).

cnf(c_0_6311_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6311]) ).

cnf(c_0_6312_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6312]) ).

cnf(c_0_6312_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6312]) ).

cnf(c_0_6313_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6313]) ).

cnf(c_0_6313_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6313]) ).

cnf(c_0_6314_0,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6314]) ).

cnf(c_0_6314_1,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6314]) ).

cnf(c_0_6314_2,axiom,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6314]) ).

cnf(c_0_6314_3,axiom,
    ( ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6314]) ).

cnf(c_0_6314_4,axiom,
    ( ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6314]) ).

cnf(c_0_6314_5,axiom,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) = c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6314]) ).

cnf(c_0_6314_6,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6314]) ).

cnf(c_0_6315_0,axiom,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)))
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6315]) ).

cnf(c_0_6315_1,axiom,
    ( ~ class_Int_Oring__char__0(X1)
    | c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)))
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6315]) ).

cnf(c_0_6315_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)))
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6315]) ).

cnf(c_0_6315_3,axiom,
    ( ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_6315]) ).

cnf(c_0_6316_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Nat_OSuc(sk1_esk9_2(X2,X1)) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6316]) ).

cnf(c_0_6316_1,axiom,
    ( c_Nat_OSuc(sk1_esk9_2(X2,X1)) = X1
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6316]) ).

cnf(c_0_6316_2,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Nat_OSuc(sk1_esk9_2(X2,X1)) = X1
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6316]) ).

cnf(c_0_6317_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sk1_esk4_1(X1)) = X1
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6317]) ).

cnf(c_0_6317_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sk1_esk4_1(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6317]) ).

cnf(c_0_6318_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sk1_esk2_1(X1)) = X1
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6318]) ).

cnf(c_0_6318_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sk1_esk2_1(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6318]) ).

cnf(c_0_6319_0,axiom,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6319]) ).

cnf(c_0_6319_1,axiom,
    ( ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6319]) ).

cnf(c_0_6319_2,axiom,
    ( ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6319]) ).

cnf(c_0_6319_3,axiom,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6319]) ).

cnf(c_0_6319_4,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6319]) ).

cnf(c_0_6319_5,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6319]) ).

cnf(c_0_6320_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6320]) ).

cnf(c_0_6320_1,axiom,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6320]) ).

cnf(c_0_6320_2,axiom,
    ( ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6320]) ).

cnf(c_0_6320_3,axiom,
    ( ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6320]) ).

cnf(c_0_6320_4,axiom,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6320]) ).

cnf(c_0_6320_5,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6320]) ).

cnf(c_0_6321_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6321]) ).

cnf(c_0_6321_1,axiom,
    ( ~ class_Rings_Osemiring__0(X1)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6321]) ).

cnf(c_0_6321_2,axiom,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Oone__class_Oone(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6321]) ).

cnf(c_0_6321_3,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Power_Opower(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6321]) ).

cnf(c_0_6322_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6322]) ).

cnf(c_0_6322_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6322]) ).

cnf(c_0_6324_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6324]) ).

cnf(c_0_6324_1,axiom,
    ( X2 != X3
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6324]) ).

cnf(c_0_6325_0,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6325]) ).

cnf(c_0_6325_1,axiom,
    ( ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6325]) ).

cnf(c_0_6325_2,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6325]) ).

cnf(c_0_6326_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6326]) ).

cnf(c_0_6326_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
    | c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6326]) ).

cnf(c_0_6327_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6327]) ).

cnf(c_0_6327_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6327]) ).

cnf(c_0_6328_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X4,X3)
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | X2 != X4 ),
    inference(literals_permutation,[status(thm)],[c_0_6328]) ).

cnf(c_0_6328_1,axiom,
    ( ~ class_Groups_Ocancel__semigroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X4,X3)
    | X2 != X4 ),
    inference(literals_permutation,[status(thm)],[c_0_6328]) ).

cnf(c_0_6328_2,axiom,
    ( X2 != X4
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X4,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6328]) ).

cnf(c_0_6329_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,X4)
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | X3 != X4 ),
    inference(literals_permutation,[status(thm)],[c_0_6329]) ).

cnf(c_0_6329_1,axiom,
    ( ~ class_Groups_Ocancel__semigroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,X4)
    | X3 != X4 ),
    inference(literals_permutation,[status(thm)],[c_0_6329]) ).

cnf(c_0_6329_2,axiom,
    ( X3 != X4
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_6329]) ).

cnf(c_0_6330_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6330]) ).

cnf(c_0_6330_1,axiom,
    ( ~ class_Rings_Osemiring__1(X1)
    | c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6330]) ).

cnf(c_0_6331_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6331]) ).

cnf(c_0_6331_1,axiom,
    ( ~ class_Rings_Osemiring__1(X1)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6331]) ).

cnf(c_0_6332_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X2,X3)
    | c_Orderings_Oord__class_Oless(X1,X3,X2)
    | X3 = X2
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6332]) ).

cnf(c_0_6332_1,axiom,
    ( c_Orderings_Oord__class_Oless(X1,X3,X2)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | X3 = X2
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6332]) ).

cnf(c_0_6332_2,axiom,
    ( X3 = X2
    | c_Orderings_Oord__class_Oless(X1,X3,X2)
    | c_Orderings_Oord__class_Oless(X1,X2,X3)
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6332]) ).

cnf(c_0_6332_3,axiom,
    ( ~ class_Rings_Olinordered__idom(X1)
    | X3 = X2
    | c_Orderings_Oord__class_Oless(X1,X3,X2)
    | c_Orderings_Oord__class_Oless(X1,X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6332]) ).

cnf(c_0_6335_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Ozero__class_Ozero(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6335]) ).

cnf(c_0_6335_1,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6335]) ).

cnf(c_0_6335_2,axiom,
    ( ~ class_Rings_Osemiring__0(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6335]) ).

cnf(c_0_6335_3,axiom,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6335]) ).

cnf(c_0_6336_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6336]) ).

cnf(c_0_6336_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6336]) ).

cnf(c_0_6336_2,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6336]) ).

cnf(c_0_6337_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6337]) ).

cnf(c_0_6337_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6337]) ).

cnf(c_0_6338_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Otimes__class_Otimes(X1,X3,X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6338]) ).

cnf(c_0_6338_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Otimes__class_Otimes(X1,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6338]) ).

cnf(c_0_6339_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6339]) ).

cnf(c_0_6339_1,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3)
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6339]) ).

cnf(c_0_6339_2,axiom,
    ( X2 != X3
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3)
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_6339]) ).

cnf(c_0_6340_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6340]) ).

cnf(c_0_6340_1,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6340]) ).

cnf(c_0_6340_2,axiom,
    ( X2 != X3
    | c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1)
    | X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(literals_permutation,[status(thm)],[c_0_6340]) ).

cnf(c_0_6341_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6341]) ).

cnf(c_0_6341_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6341]) ).

cnf(c_0_6342_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6342]) ).

cnf(c_0_6342_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6342]) ).

cnf(c_0_6343_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6343]) ).

cnf(c_0_6343_1,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6343]) ).

cnf(c_0_6344_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6344]) ).

cnf(c_0_6344_1,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6344]) ).

cnf(c_0_6345_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6345]) ).

cnf(c_0_6345_1,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6345]) ).

cnf(c_0_6346_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6346]) ).

cnf(c_0_6346_1,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6346]) ).

cnf(c_0_6347_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6347]) ).

cnf(c_0_6347_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6347]) ).

cnf(c_0_6348_0,axiom,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6348]) ).

cnf(c_0_6348_1,axiom,
    ( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6348]) ).

cnf(c_0_6348_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6348]) ).

cnf(c_0_6349_0,axiom,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6349]) ).

cnf(c_0_6349_1,axiom,
    ( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6349]) ).

cnf(c_0_6349_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6349]) ).

cnf(c_0_6350_0,axiom,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(literals_permutation,[status(thm)],[c_0_6350]) ).

cnf(c_0_6350_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6350]) ).

cnf(c_0_6351_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),sk1_esk6_1(X1)) = X1
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6351]) ).

cnf(c_0_6351_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),sk1_esk6_1(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6351]) ).

cnf(c_0_6354_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6354]) ).

cnf(c_0_6354_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6354]) ).

cnf(c_0_6354_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6354]) ).

cnf(c_0_6355_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6355]) ).

cnf(c_0_6355_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6355]) ).

cnf(c_0_6355_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6355]) ).

cnf(c_0_6356_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | X3 = c_Groups_Ozero__class_Ozero(X2)
    | c_Groups_Otimes__class_Otimes(X2,X3,X1) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Ono__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6356]) ).

cnf(c_0_6356_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(X2)
    | X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Groups_Otimes__class_Otimes(X2,X3,X1) != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Ono__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6356]) ).

cnf(c_0_6356_2,axiom,
    ( c_Groups_Otimes__class_Otimes(X2,X3,X1) != c_Groups_Ozero__class_Ozero(X2)
    | X3 = c_Groups_Ozero__class_Ozero(X2)
    | X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Ono__zero__divisors(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6356]) ).

cnf(c_0_6356_3,axiom,
    ( ~ class_Rings_Ono__zero__divisors(X2)
    | c_Groups_Otimes__class_Otimes(X2,X3,X1) != c_Groups_Ozero__class_Ozero(X2)
    | X3 = c_Groups_Ozero__class_Ozero(X2)
    | X1 = c_Groups_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6356]) ).

cnf(c_0_6357_0,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6357]) ).

cnf(c_0_6357_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6357]) ).

cnf(c_0_6357_2,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6357]) ).

cnf(c_0_6357_3,axiom,
    ( ~ class_Rings_Ono__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6357]) ).

cnf(c_0_6358_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6358]) ).

cnf(c_0_6358_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6358]) ).

cnf(c_0_6358_2,axiom,
    ( ~ class_Rings_Oring__no__zero__divisors(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Otimes__class_Otimes(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6358]) ).

cnf(c_0_6358_3,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X3,X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6358]) ).

cnf(c_0_6359_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
    | X1 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6359]) ).

cnf(c_0_6359_1,axiom,
    ( X1 != X3
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6359]) ).

cnf(c_0_6360_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6360]) ).

cnf(c_0_6360_1,axiom,
    ( X2 != X3
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6360]) ).

cnf(c_0_6361_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6361]) ).

cnf(c_0_6361_1,axiom,
    ( X2 != X3
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6361]) ).

cnf(c_0_6362_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6362]) ).

cnf(c_0_6362_1,axiom,
    ( X2 != X3
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6362]) ).

cnf(c_0_6363_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)
    | X1 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6363]) ).

cnf(c_0_6363_1,axiom,
    ( X1 != X3
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6363]) ).

cnf(c_0_6364_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6364]) ).

cnf(c_0_6364_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6364]) ).

cnf(c_0_6364_2,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Int_Onumber__ring(X1)
    | c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6364]) ).

cnf(c_0_6365_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6365]) ).

cnf(c_0_6365_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6365]) ).

cnf(c_0_6365_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
    | c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6365]) ).

cnf(c_0_6366_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6366]) ).

cnf(c_0_6366_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6366]) ).

cnf(c_0_6366_2,axiom,
    ( X2 = X1
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6366]) ).

cnf(c_0_6367_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6367]) ).

cnf(c_0_6367_1,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6367]) ).

cnf(c_0_6367_2,axiom,
    ( X2 = X1
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6367]) ).

cnf(c_0_6368_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X2 = X1
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6368]) ).

cnf(c_0_6368_1,axiom,
    ( X2 = X1
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6368]) ).

cnf(c_0_6368_2,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
    | X2 = X1
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6368]) ).

cnf(c_0_6369_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ozero__class_Ozero(X2),X1)
    | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6369]) ).

cnf(c_0_6369_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ozero__class_Ozero(X2),X1)
    | X1 = c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6369]) ).

cnf(c_0_6369_2,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X2)
    | ~ c_Rings_Odvd__class_Odvd(X2,c_Groups_Ozero__class_Ozero(X2),X1)
    | X1 = c_Groups_Ozero__class_Ozero(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6369]) ).

cnf(c_0_6371_0,axiom,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6371]) ).

cnf(c_0_6371_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6371]) ).

cnf(c_0_6371_2,axiom,
    ( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6371]) ).

cnf(c_0_6372_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(literals_permutation,[status(thm)],[c_0_6372]) ).

cnf(c_0_6372_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6372]) ).

cnf(c_0_6373_0,axiom,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6373]) ).

cnf(c_0_6373_1,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6373]) ).

cnf(c_0_6373_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6373]) ).

cnf(c_0_6374_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6374]) ).

cnf(c_0_6374_1,axiom,
    ( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6374]) ).

cnf(c_0_6374_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6374]) ).

cnf(c_0_6375_0,axiom,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6375]) ).

cnf(c_0_6375_1,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6375]) ).

cnf(c_0_6375_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6375]) ).

cnf(c_0_6376_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6376]) ).

cnf(c_0_6376_1,axiom,
    ( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6376]) ).

cnf(c_0_6376_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6376]) ).

cnf(c_0_6377_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6377]) ).

cnf(c_0_6377_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6377]) ).

cnf(c_0_6378_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6378]) ).

cnf(c_0_6378_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6378]) ).

cnf(c_0_6379_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6379]) ).

cnf(c_0_6379_1,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6379]) ).

cnf(c_0_6380_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6380]) ).

cnf(c_0_6380_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6380]) ).

cnf(c_0_6381_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6381]) ).

cnf(c_0_6381_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6381]) ).

cnf(c_0_6387_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6387]) ).

cnf(c_0_6387_1,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6387]) ).

cnf(c_0_6387_2,axiom,
    ( ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6387]) ).

cnf(c_0_6388_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6388]) ).

cnf(c_0_6388_1,axiom,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6388]) ).

cnf(c_0_6388_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6388]) ).

cnf(c_0_6389_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6389]) ).

cnf(c_0_6389_1,axiom,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6389]) ).

cnf(c_0_6389_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6389]) ).

cnf(c_0_6390_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6390]) ).

cnf(c_0_6390_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6390]) ).

cnf(c_0_6391_0,axiom,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6391]) ).

cnf(c_0_6391_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6391]) ).

cnf(c_0_6395_0,axiom,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6395]) ).

cnf(c_0_6395_1,axiom,
    ( X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6395]) ).

cnf(c_0_6395_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6395]) ).

cnf(c_0_6396_0,axiom,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6396]) ).

cnf(c_0_6396_1,axiom,
    ( X2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6396]) ).

cnf(c_0_6396_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6396]) ).

cnf(c_0_6397_0,axiom,
    ( X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6397]) ).

cnf(c_0_6397_1,axiom,
    ( X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6397]) ).

cnf(c_0_6397_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6397]) ).

cnf(c_0_6398_0,axiom,
    ( X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6398]) ).

cnf(c_0_6398_1,axiom,
    ( X2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6398]) ).

cnf(c_0_6398_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6398]) ).

cnf(c_0_6399_0,axiom,
    ( X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6399]) ).

cnf(c_0_6399_1,axiom,
    ( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6399]) ).

cnf(c_0_6399_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6399]) ).

cnf(c_0_6400_0,axiom,
    ( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6400]) ).

cnf(c_0_6400_1,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6400]) ).

cnf(c_0_6401_0,axiom,
    ( X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6401]) ).

cnf(c_0_6401_1,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6401]) ).

cnf(c_0_6402_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6402]) ).

cnf(c_0_6402_1,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6402]) ).

cnf(c_0_6402_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6402]) ).

cnf(c_0_6403_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6403]) ).

cnf(c_0_6403_1,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6403]) ).

cnf(c_0_6403_2,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6403]) ).

cnf(c_0_6404_0,axiom,
    ( X2 = X3
    | ~ class_Groups_Oab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6404]) ).

cnf(c_0_6404_1,axiom,
    ( ~ class_Groups_Oab__group__add(X1)
    | X2 = X3
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6404]) ).

cnf(c_0_6404_2,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oab__group__add(X1)
    | X2 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6404]) ).

cnf(c_0_6405_0,axiom,
    ( X2 = X3
    | ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6405]) ).

cnf(c_0_6405_1,axiom,
    ( ~ class_Groups_Ogroup__add(X1)
    | X2 = X3
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6405]) ).

cnf(c_0_6405_2,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1)
    | X2 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6405]) ).

cnf(c_0_6406_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6406]) ).

cnf(c_0_6406_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    inference(literals_permutation,[status(thm)],[c_0_6406]) ).

cnf(c_0_6407_0,axiom,
    ( c_Nat_OSuc(sk1_esk10_1(X1)) = X1
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6407]) ).

cnf(c_0_6407_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Nat_OSuc(sk1_esk10_1(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6407]) ).

cnf(c_0_6408_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,X3,X2) != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6408]) ).

cnf(c_0_6408_1,axiom,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Oplus__class_Oplus(X1,X3,X2) != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6408]) ).

cnf(c_0_6408_2,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X3,X2) != X3
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6408]) ).

cnf(c_0_6409_0,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6409]) ).

cnf(c_0_6409_1,axiom,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6409]) ).

cnf(c_0_6409_2,axiom,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6409]) ).

cnf(c_0_6409_3,axiom,
    ( ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6409]) ).

cnf(c_0_6409_4,axiom,
    ( ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6409]) ).

cnf(c_0_6409_5,axiom,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6409]) ).

cnf(c_0_6409_6,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1)
    | ~ class_Rings_Omult__zero(X1)
    | ~ class_Rings_Ono__zero__divisors(X1)
    | ~ class_Rings_Ozero__neq__one(X1)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6409]) ).

cnf(c_0_6411_0,axiom,
    ( ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2)))
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6411]) ).

cnf(c_0_6411_1,axiom,
    ( ~ class_Int_Oring__char__0(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6411]) ).

cnf(c_0_6411_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_6411]) ).

cnf(c_0_6412_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6412]) ).

cnf(c_0_6412_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6412]) ).

cnf(c_0_6413_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6413]) ).

cnf(c_0_6413_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6413]) ).

cnf(c_0_6414_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6414]) ).

cnf(c_0_6414_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6414]) ).

cnf(c_0_6414_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6414]) ).

cnf(c_0_6415_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)),X2) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6415]) ).

cnf(c_0_6415_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)),X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6415]) ).

cnf(c_0_6416_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6416]) ).

cnf(c_0_6416_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6416]) ).

cnf(c_0_6417_0,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6417]) ).

cnf(c_0_6417_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6417]) ).

cnf(c_0_6418_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X1 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6418]) ).

cnf(c_0_6418_1,axiom,
    ( X2 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ),
    inference(literals_permutation,[status(thm)],[c_0_6418]) ).

cnf(c_0_6418_2,axiom,
    ( X1 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | X2 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6418]) ).

cnf(c_0_6420_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6420]) ).

cnf(c_0_6420_1,axiom,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6420]) ).

cnf(c_0_6420_2,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != X1
    | X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6420]) ).

cnf(c_0_6421_0,axiom,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6421]) ).

cnf(c_0_6421_1,axiom,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6421]) ).

cnf(c_0_6422_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6422]) ).

cnf(c_0_6422_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6422]) ).

cnf(c_0_6423_0,axiom,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6423]) ).

cnf(c_0_6423_1,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6423]) ).

cnf(c_0_6424_0,axiom,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6424]) ).

cnf(c_0_6424_1,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6424]) ).

cnf(c_0_6425_0,axiom,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6425]) ).

cnf(c_0_6425_1,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6425]) ).

cnf(c_0_6426_0,axiom,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6426]) ).

cnf(c_0_6426_1,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6426]) ).

cnf(c_0_6427_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6427]) ).

cnf(c_0_6427_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6427]) ).

cnf(c_0_6428_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6428]) ).

cnf(c_0_6428_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6428]) ).

cnf(c_0_6429_0,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6429]) ).

cnf(c_0_6429_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6429]) ).

cnf(c_0_6430_0,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6430]) ).

cnf(c_0_6430_1,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6430]) ).

cnf(c_0_6434_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6434]) ).

cnf(c_0_6434_1,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6434]) ).

cnf(c_0_6435_0,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6435]) ).

cnf(c_0_6435_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6435]) ).

cnf(c_0_6436_0,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6436]) ).

cnf(c_0_6436_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6436]) ).

cnf(c_0_6437_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6437]) ).

cnf(c_0_6437_1,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6437]) ).

cnf(c_0_6438_0,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6438]) ).

cnf(c_0_6438_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6438]) ).

cnf(c_0_6439_0,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6439]) ).

cnf(c_0_6439_1,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6439]) ).

cnf(c_0_6440_0,axiom,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6440]) ).

cnf(c_0_6440_1,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6440]) ).

cnf(c_0_6441_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6441]) ).

cnf(c_0_6441_1,axiom,
    ( X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6441]) ).

cnf(c_0_6441_2,axiom,
    ( X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6441]) ).

cnf(c_0_6443_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X2) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6443]) ).

cnf(c_0_6443_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6443]) ).

cnf(c_0_6444_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) = X2
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6444]) ).

cnf(c_0_6444_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6444]) ).

cnf(c_0_6445_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Nat_OSuc(X2)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6445]) ).

cnf(c_0_6445_1,axiom,
    ( ~ class_Rings_Osemiring__0(X1)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Nat_OSuc(X2)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6445]) ).

cnf(c_0_6445_2,axiom,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Nat_OSuc(X2)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6445]) ).

cnf(c_0_6446_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6446]) ).

cnf(c_0_6446_1,axiom,
    ( ~ class_Rings_Osemiring__0(X1)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6446]) ).

cnf(c_0_6446_2,axiom,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Oone__class_Oone(X1)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6446]) ).

cnf(c_0_6446_3,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Power_Opower(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6446]) ).

cnf(c_0_6450_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6450]) ).

cnf(c_0_6450_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | ~ class_Power_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6450]) ).

cnf(c_0_6450_2,axiom,
    ( ~ class_Rings_Osemiring__0(X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Power_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6450]) ).

cnf(c_0_6450_3,axiom,
    ( ~ class_Power_Opower(X1)
    | ~ class_Rings_Osemiring__0(X1)
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6450]) ).

cnf(c_0_6451_0,axiom,
    ( ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6451]) ).

cnf(c_0_6451_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) ),
    inference(literals_permutation,[status(thm)],[c_0_6451]) ).

cnf(c_0_6452_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6452]) ).

cnf(c_0_6452_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6452]) ).

cnf(c_0_6452_2,axiom,
    ( X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6452]) ).

cnf(c_0_6453_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6453]) ).

cnf(c_0_6453_1,axiom,
    ( X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6453]) ).

cnf(c_0_6453_2,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6453]) ).

cnf(c_0_6454_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6454]) ).

cnf(c_0_6454_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6454]) ).

cnf(c_0_6454_2,axiom,
    ( X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6454]) ).

cnf(c_0_6455_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6455]) ).

cnf(c_0_6455_1,axiom,
    ( X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6455]) ).

cnf(c_0_6455_2,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6455]) ).

cnf(c_0_6460_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6460]) ).

cnf(c_0_6460_1,axiom,
    ( X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(literals_permutation,[status(thm)],[c_0_6460]) ).

cnf(c_0_6462_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6462]) ).

cnf(c_0_6462_1,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6462]) ).

cnf(c_0_6463_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
    | c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6463]) ).

cnf(c_0_6463_1,axiom,
    ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
    inference(literals_permutation,[status(thm)],[c_0_6463]) ).

cnf(c_0_6465_0,axiom,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6465]) ).

cnf(c_0_6465_1,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6465]) ).

cnf(c_0_6466_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6466]) ).

cnf(c_0_6466_1,axiom,
    ( ~ class_Rings_Olinordered__semidom(X1)
    | c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6466]) ).

cnf(c_0_6467_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6467]) ).

cnf(c_0_6467_1,axiom,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6467]) ).

cnf(c_0_6467_2,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6467]) ).

cnf(c_0_6468_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6468]) ).

cnf(c_0_6468_1,axiom,
    ( ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6468]) ).

cnf(c_0_6468_2,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6468]) ).

cnf(c_0_6469_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6469]) ).

cnf(c_0_6469_1,axiom,
    ( ~ class_Rings_Oring__no__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6469]) ).

cnf(c_0_6469_2,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6469]) ).

cnf(c_0_6470_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6470]) ).

cnf(c_0_6470_1,axiom,
    ( ~ class_Rings_Oring__no__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6470]) ).

cnf(c_0_6470_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6470]) ).

cnf(c_0_6471_0,axiom,
    ( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6471]) ).

cnf(c_0_6471_1,axiom,
    ( X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6471]) ).

cnf(c_0_6473_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6473]) ).

cnf(c_0_6473_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6473]) ).

cnf(c_0_6474_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6474]) ).

cnf(c_0_6474_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6474]) ).

cnf(c_0_6475_0,axiom,
    ( c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6475]) ).

cnf(c_0_6475_1,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),X2) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6475]) ).

cnf(c_0_6476_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6476]) ).

cnf(c_0_6476_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6476]) ).

cnf(c_0_6477_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6477]) ).

cnf(c_0_6477_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6477]) ).

cnf(c_0_6478_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6478]) ).

cnf(c_0_6478_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6478]) ).

cnf(c_0_6479_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6479]) ).

cnf(c_0_6479_1,axiom,
    ( ~ class_Rings_Omult__zero(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6479]) ).

cnf(c_0_6480_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6480]) ).

cnf(c_0_6480_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6480]) ).

cnf(c_0_6481_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_RealVector_Oreal__normed__algebra(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6481]) ).

cnf(c_0_6481_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6481]) ).

cnf(c_0_6482_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6482]) ).

cnf(c_0_6482_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6482]) ).

cnf(c_0_6483_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Omult__zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6483]) ).

cnf(c_0_6483_1,axiom,
    ( ~ class_Rings_Omult__zero(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6483]) ).

cnf(c_0_6484_0,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6484]) ).

cnf(c_0_6484_1,axiom,
    ( ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Oone__class_Oone(X1)
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6484]) ).

cnf(c_0_6484_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,X3) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6484]) ).

cnf(c_0_6485_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6485]) ).

cnf(c_0_6485_1,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(literals_permutation,[status(thm)],[c_0_6485]) ).

cnf(c_0_6486_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6486]) ).

cnf(c_0_6486_1,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6486]) ).

cnf(c_0_6486_2,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6486]) ).

cnf(c_0_6487_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,X3) = X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6487]) ).

cnf(c_0_6487_1,axiom,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) = X2
    | X3 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6487]) ).

cnf(c_0_6487_2,axiom,
    ( X3 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,X3) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6487]) ).

cnf(c_0_6488_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Oab__group__add(X1)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6488]) ).

cnf(c_0_6488_1,axiom,
    ( ~ class_Groups_Oab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6488]) ).

cnf(c_0_6488_2,axiom,
    ( X2 != X3
    | ~ class_Groups_Oab__group__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6488]) ).

cnf(c_0_6489_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6489]) ).

cnf(c_0_6489_1,axiom,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6489]) ).

cnf(c_0_6489_2,axiom,
    ( X2 != X3
    | ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X3) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6489]) ).

cnf(c_0_6490_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6490]) ).

cnf(c_0_6490_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6490]) ).

cnf(c_0_6491_0,axiom,
    ( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6491]) ).

cnf(c_0_6491_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6491]) ).

cnf(c_0_6492_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6492]) ).

cnf(c_0_6492_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6492]) ).

cnf(c_0_6493_0,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Power_Opower(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6493]) ).

cnf(c_0_6493_1,axiom,
    ( ~ class_Power_Opower(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6493]) ).

cnf(c_0_6494_0,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6494]) ).

cnf(c_0_6494_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6494]) ).

cnf(c_0_6495_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6495]) ).

cnf(c_0_6495_1,axiom,
    ( ~ class_Groups_Ocomm__monoid__mult(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6495]) ).

cnf(c_0_6496_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6496]) ).

cnf(c_0_6496_1,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6496]) ).

cnf(c_0_6497_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
    | ~ class_Groups_Ocomm__monoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6497]) ).

cnf(c_0_6497_1,axiom,
    ( ~ class_Groups_Ocomm__monoid__mult(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6497]) ).

cnf(c_0_6498_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6498]) ).

cnf(c_0_6498_1,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6498]) ).

cnf(c_0_6499_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6499]) ).

cnf(c_0_6499_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6499]) ).

cnf(c_0_6500_0,axiom,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6500]) ).

cnf(c_0_6500_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6500]) ).

cnf(c_0_6501_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6501]) ).

cnf(c_0_6501_1,axiom,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6501]) ).

cnf(c_0_6502_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6502]) ).

cnf(c_0_6502_1,axiom,
    ( ~ class_Groups_Ocomm__monoid__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6502]) ).

cnf(c_0_6503_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6503]) ).

cnf(c_0_6503_1,axiom,
    ( ~ class_Groups_Omonoid__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6503]) ).

cnf(c_0_6504_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6504]) ).

cnf(c_0_6504_1,axiom,
    ( ~ class_Groups_Ocomm__monoid__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6504]) ).

cnf(c_0_6505_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
    | ~ class_Groups_Omonoid__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6505]) ).

cnf(c_0_6505_1,axiom,
    ( ~ class_Groups_Omonoid__add(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6505]) ).

cnf(c_0_6506_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6506]) ).

cnf(c_0_6506_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6506]) ).

cnf(c_0_6507_0,axiom,
    ( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6507]) ).

cnf(c_0_6507_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6507]) ).

cnf(c_0_6508_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6508]) ).

cnf(c_0_6508_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6508]) ).

cnf(c_0_6509_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6509]) ).

cnf(c_0_6509_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6509]) ).

cnf(c_0_6511_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != c_Nat_OSuc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6511]) ).

cnf(c_0_6511_1,axiom,
    ( X1 != c_Nat_OSuc(X2)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6511]) ).

cnf(c_0_6512_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6512]) ).

cnf(c_0_6512_1,axiom,
    ( X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6512]) ).

cnf(c_0_6512_2,axiom,
    ( X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6512]) ).

cnf(c_0_6513_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6513]) ).

cnf(c_0_6513_1,axiom,
    ( X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6513]) ).

cnf(c_0_6513_2,axiom,
    ( X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6513]) ).

cnf(c_0_6514_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6514]) ).

cnf(c_0_6514_1,axiom,
    ( X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6514]) ).

cnf(c_0_6514_2,axiom,
    ( X1 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6514]) ).

cnf(c_0_6515_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6515]) ).

cnf(c_0_6515_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6515]) ).

cnf(c_0_6515_2,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6515]) ).

cnf(c_0_6516_0,axiom,
    ( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6516]) ).

cnf(c_0_6516_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6516]) ).

cnf(c_0_6517_0,axiom,
    ( c_Divides_Odiv__class_Omod(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6517]) ).

cnf(c_0_6517_1,axiom,
    ( ~ class_Divides_Osemiring__div(X1)
    | c_Divides_Odiv__class_Omod(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6517]) ).

cnf(c_0_6518_0,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
    | ~ class_Groups_Omonoid__mult(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6518]) ).

cnf(c_0_6518_1,axiom,
    ( ~ class_Groups_Omonoid__mult(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6518]) ).

cnf(c_0_6519_0,axiom,
    ( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6519]) ).

cnf(c_0_6519_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Power_Opower__class_Opower(X1,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6519]) ).

cnf(c_0_6520_0,axiom,
    ( ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6520]) ).

cnf(c_0_6520_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)) ),
    inference(literals_permutation,[status(thm)],[c_0_6520]) ).

cnf(c_0_6521_0,axiom,
    ( c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ogroup__add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6521]) ).

cnf(c_0_6521_1,axiom,
    ( ~ class_Groups_Ogroup__add(X1)
    | c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6521]) ).

cnf(c_0_6523_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6523]) ).

cnf(c_0_6523_1,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6523]) ).

cnf(c_0_6524_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X1 != c_Nat_OSuc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6524]) ).

cnf(c_0_6524_1,axiom,
    ( X1 != c_Nat_OSuc(X2)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6524]) ).

cnf(c_0_6526_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6526]) ).

cnf(c_0_6526_1,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_6526]) ).

cnf(c_0_6528_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6528]) ).

cnf(c_0_6528_1,axiom,
    ( X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6528]) ).

cnf(c_0_6529_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6529]) ).

cnf(c_0_6529_1,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(literals_permutation,[status(thm)],[c_0_6529]) ).

cnf(c_0_6530_0,axiom,
    ( c_Rings_Odvd__class_Odvd(X1,X2,X2)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6530]) ).

cnf(c_0_6530_1,axiom,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | c_Rings_Odvd__class_Odvd(X1,X2,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6530]) ).

cnf(c_0_6531_0,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6531]) ).

cnf(c_0_6531_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6531]) ).

cnf(c_0_6532_0,axiom,
    ( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6532]) ).

cnf(c_0_6532_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6532]) ).

cnf(c_0_6533_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6533]) ).

cnf(c_0_6533_1,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6533]) ).

cnf(c_0_6534_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6534]) ).

cnf(c_0_6534_1,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6534]) ).

cnf(c_0_6535_0,axiom,
    ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6535]) ).

cnf(c_0_6535_1,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6535]) ).

cnf(c_0_6536_0,axiom,
    ( X2 = X3
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | c_Int_Onumber__class_Onumber__of(X1,X2) != c_Int_Onumber__class_Onumber__of(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6536]) ).

cnf(c_0_6536_1,axiom,
    ( ~ class_Int_Oring__char__0(X1)
    | X2 = X3
    | ~ class_Int_Onumber__ring(X1)
    | c_Int_Onumber__class_Onumber__of(X1,X2) != c_Int_Onumber__class_Onumber__of(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6536]) ).

cnf(c_0_6536_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | X2 = X3
    | c_Int_Onumber__class_Onumber__of(X1,X2) != c_Int_Onumber__class_Onumber__of(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6536]) ).

cnf(c_0_6536_3,axiom,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) != c_Int_Onumber__class_Onumber__of(X1,X3)
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | X2 = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6536]) ).

cnf(c_0_6539_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6539]) ).

cnf(c_0_6539_1,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6539]) ).

cnf(c_0_6540_0,axiom,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6540]) ).

cnf(c_0_6540_1,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6540]) ).

cnf(c_0_6541_0,axiom,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X2
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(literals_permutation,[status(thm)],[c_0_6541]) ).

cnf(c_0_6541_1,axiom,
    ( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6541]) ).

cnf(c_0_6542_0,axiom,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6542]) ).

cnf(c_0_6542_1,axiom,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(literals_permutation,[status(thm)],[c_0_6542]) ).

cnf(c_0_6565_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6565]) ).

cnf(c_0_6565_1,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6565]) ).

cnf(c_0_6566_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6566]) ).

cnf(c_0_6566_1,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6566]) ).

cnf(c_0_6567_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6567]) ).

cnf(c_0_6567_1,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6567]) ).

cnf(c_0_6568_0,axiom,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6568]) ).

cnf(c_0_6568_1,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6568]) ).

cnf(c_0_6569_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6569]) ).

cnf(c_0_6569_1,axiom,
    ( X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6569]) ).

cnf(c_0_6570_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6570]) ).

cnf(c_0_6570_1,axiom,
    ( X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6570]) ).

cnf(c_0_6571_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6571]) ).

cnf(c_0_6571_1,axiom,
    ( X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6571]) ).

cnf(c_0_6572_0,axiom,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6572]) ).

cnf(c_0_6572_1,axiom,
    ( X1 != X2
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6572]) ).

cnf(c_0_6592_0,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6592]) ).

cnf(c_0_6592_1,axiom,
    ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X1))
    | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6592]) ).

cnf(c_0_6593_0,axiom,
    ( X2 = c_Int_Onumber__class_Onumber__of(X1,X3)
    | ~ class_Int_Onumber(X1)
    | c_Int_Onumber__class_Onumber__of(X1,X3) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6593]) ).

cnf(c_0_6593_1,axiom,
    ( ~ class_Int_Onumber(X1)
    | X2 = c_Int_Onumber__class_Onumber__of(X1,X3)
    | c_Int_Onumber__class_Onumber__of(X1,X3) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6593]) ).

cnf(c_0_6593_2,axiom,
    ( c_Int_Onumber__class_Onumber__of(X1,X3) != X2
    | ~ class_Int_Onumber(X1)
    | X2 = c_Int_Onumber__class_Onumber__of(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6593]) ).

cnf(c_0_6594_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) = X3
    | ~ class_Int_Onumber(X1)
    | X3 != c_Int_Onumber__class_Onumber__of(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6594]) ).

cnf(c_0_6594_1,axiom,
    ( ~ class_Int_Onumber(X1)
    | c_Int_Onumber__class_Onumber__of(X1,X2) = X3
    | X3 != c_Int_Onumber__class_Onumber__of(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6594]) ).

cnf(c_0_6594_2,axiom,
    ( X3 != c_Int_Onumber__class_Onumber__of(X1,X2)
    | ~ class_Int_Onumber(X1)
    | c_Int_Onumber__class_Onumber__of(X1,X2) = X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6594]) ).

cnf(c_0_6595_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Int_Onumber__class_Onumber__of(X1,X3)
    | ~ class_Int_Oring__char__0(X1)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6595]) ).

cnf(c_0_6595_1,axiom,
    ( ~ class_Int_Oring__char__0(X1)
    | c_Int_Onumber__class_Onumber__of(X1,X2) = c_Int_Onumber__class_Onumber__of(X1,X3)
    | ~ class_Int_Onumber__ring(X1)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6595]) ).

cnf(c_0_6595_2,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | c_Int_Onumber__class_Onumber__of(X1,X2) = c_Int_Onumber__class_Onumber__of(X1,X3)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_6595]) ).

cnf(c_0_6595_3,axiom,
    ( X2 != X3
    | ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | c_Int_Onumber__class_Onumber__of(X1,X2) = c_Int_Onumber__class_Onumber__of(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_6595]) ).

cnf(c_0_6596_0,axiom,
    ( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6596]) ).

cnf(c_0_6596_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) ),
    inference(literals_permutation,[status(thm)],[c_0_6596]) ).

cnf(c_0_6599_0,axiom,
    ( ~ c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6599]) ).

cnf(c_0_6599_1,axiom,
    ( ~ class_Rings_Osemiring__1(X1)
    | ~ c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6599]) ).

cnf(c_0_6600_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__1(X1)
    | ~ c_Int_Oiszero(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6600]) ).

cnf(c_0_6600_1,axiom,
    ( ~ class_Rings_Osemiring__1(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ c_Int_Oiszero(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6600]) ).

cnf(c_0_6600_2,axiom,
    ( ~ c_Int_Oiszero(X1,X2)
    | ~ class_Rings_Osemiring__1(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6600]) ).

cnf(c_0_6602_0,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X1))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6602]) ).

cnf(c_0_6602_1,axiom,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6602]) ).

cnf(c_0_6603_0,axiom,
    ( c_Int_Oiszero(X1,X2)
    | ~ class_Rings_Osemiring__1(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6603]) ).

cnf(c_0_6603_1,axiom,
    ( ~ class_Rings_Osemiring__1(X1)
    | c_Int_Oiszero(X1,X2)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6603]) ).

cnf(c_0_6603_2,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Osemiring__1(X1)
    | c_Int_Oiszero(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6603]) ).

cnf(c_0_6604_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6604]) ).

cnf(c_0_6604_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6604]) ).

cnf(c_0_6605_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6605]) ).

cnf(c_0_6605_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6605]) ).

cnf(c_0_6606_0,axiom,
    ( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6606]) ).

cnf(c_0_6606_1,axiom,
    ( ~ class_Rings_Osemiring__1(X1)
    | c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_6606]) ).

cnf(c_0_6609_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6609]) ).

cnf(c_0_6609_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6609]) ).

cnf(c_0_6610_0,axiom,
    ( c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6610]) ).

cnf(c_0_6610_1,axiom,
    ( ~ class_Int_Onumber__ring(X1)
    | c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6610]) ).

cnf(c_0_6612_0,axiom,
    ( X2 = c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Oone(X1)
    | c_Groups_Oone__class_Oone(X1) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6612]) ).

cnf(c_0_6612_1,axiom,
    ( ~ class_Groups_Oone(X1)
    | X2 = c_Groups_Oone__class_Oone(X1)
    | c_Groups_Oone__class_Oone(X1) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6612]) ).

cnf(c_0_6612_2,axiom,
    ( c_Groups_Oone__class_Oone(X1) != X2
    | ~ class_Groups_Oone(X1)
    | X2 = c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6612]) ).

cnf(c_0_6613_0,axiom,
    ( c_Groups_Oone__class_Oone(X1) = X2
    | ~ class_Groups_Oone(X1)
    | X2 != c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6613]) ).

cnf(c_0_6613_1,axiom,
    ( ~ class_Groups_Oone(X1)
    | c_Groups_Oone__class_Oone(X1) = X2
    | X2 != c_Groups_Oone__class_Oone(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6613]) ).

cnf(c_0_6613_2,axiom,
    ( X2 != c_Groups_Oone__class_Oone(X1)
    | ~ class_Groups_Oone(X1)
    | c_Groups_Oone__class_Oone(X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6613]) ).

cnf(c_0_6614_0,axiom,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ozero(X1)
    | c_Groups_Ozero__class_Ozero(X1) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6614]) ).

cnf(c_0_6614_1,axiom,
    ( ~ class_Groups_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | c_Groups_Ozero__class_Ozero(X1) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6614]) ).

cnf(c_0_6614_2,axiom,
    ( c_Groups_Ozero__class_Ozero(X1) != X2
    | ~ class_Groups_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6614]) ).

cnf(c_0_6615_0,axiom,
    ( c_Groups_Ozero__class_Ozero(X1) = X2
    | ~ class_Groups_Ozero(X1)
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6615]) ).

cnf(c_0_6615_1,axiom,
    ( ~ class_Groups_Ozero(X1)
    | c_Groups_Ozero__class_Ozero(X1) = X2
    | X2 != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6615]) ).

cnf(c_0_6615_2,axiom,
    ( X2 != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ozero(X1)
    | c_Groups_Ozero__class_Ozero(X1) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6615]) ).

cnf(c_0_6616_0,axiom,
    ( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6616]) ).

cnf(c_0_6616_1,axiom,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6616]) ).

cnf(c_0_6617_0,axiom,
    ( c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ozero__neq__one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6617]) ).

cnf(c_0_6617_1,axiom,
    ( ~ class_Rings_Ozero__neq__one(X1)
    | c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_6617]) ).

cnf(c_0_6623_0,axiom,
    ( X1 = X2
    | c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6623]) ).

cnf(c_0_6623_1,axiom,
    ( c_Nat_OSuc(X1) != c_Nat_OSuc(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6623]) ).

cnf(c_0_6624_0,axiom,
    ( X1 = X2
    | c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6624]) ).

cnf(c_0_6624_1,axiom,
    ( c_Nat_OSuc(X1) != c_Nat_OSuc(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6624]) ).

cnf(c_0_6625_0,axiom,
    ( X1 = X2
    | c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6625]) ).

cnf(c_0_6625_1,axiom,
    ( c_Int_OBit0(X1) != c_Int_OBit0(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6625]) ).

cnf(c_0_6626_0,axiom,
    ( X1 = X2
    | c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6626]) ).

cnf(c_0_6626_1,axiom,
    ( c_Int_OBit1(X1) != c_Int_OBit1(X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6626]) ).

cnf(c_0_6633_0,axiom,
    ( c_Nat_OSuc(X1) = c_Nat_OSuc(X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6633]) ).

cnf(c_0_6633_1,axiom,
    ( X1 != X2
    | c_Nat_OSuc(X1) = c_Nat_OSuc(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6633]) ).

cnf(c_0_6634_0,axiom,
    ( c_Int_OBit0(X1) = c_Int_OBit0(X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6634]) ).

cnf(c_0_6634_1,axiom,
    ( X1 != X2
    | c_Int_OBit0(X1) = c_Int_OBit0(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6634]) ).

cnf(c_0_6635_0,axiom,
    ( c_Int_OBit1(X1) = c_Int_OBit1(X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_6635]) ).

cnf(c_0_6635_1,axiom,
    ( X1 != X2
    | c_Int_OBit1(X1) = c_Int_OBit1(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_6635]) ).

cnf(c_0_6644_0,axiom,
    ( X1 = c_Int_OMin
    | c_Int_OBit1(X1) != c_Int_OMin ),
    inference(literals_permutation,[status(thm)],[c_0_6644]) ).

cnf(c_0_6644_1,axiom,
    ( c_Int_OBit1(X1) != c_Int_OMin
    | X1 = c_Int_OMin ),
    inference(literals_permutation,[status(thm)],[c_0_6644]) ).

cnf(c_0_6645_0,axiom,
    ( c_Int_OMin = X1
    | c_Int_OBit1(X1) != c_Int_OMin ),
    inference(literals_permutation,[status(thm)],[c_0_6645]) ).

cnf(c_0_6645_1,axiom,
    ( c_Int_OBit1(X1) != c_Int_OMin
    | c_Int_OMin = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6645]) ).

cnf(c_0_6646_0,axiom,
    ( X1 = c_Int_OPls
    | c_Int_OBit0(X1) != c_Int_OPls ),
    inference(literals_permutation,[status(thm)],[c_0_6646]) ).

cnf(c_0_6646_1,axiom,
    ( c_Int_OBit0(X1) != c_Int_OPls
    | X1 = c_Int_OPls ),
    inference(literals_permutation,[status(thm)],[c_0_6646]) ).

cnf(c_0_6647_0,axiom,
    ( c_Int_OPls = X1
    | c_Int_OBit0(X1) != c_Int_OPls ),
    inference(literals_permutation,[status(thm)],[c_0_6647]) ).

cnf(c_0_6647_1,axiom,
    ( c_Int_OBit0(X1) != c_Int_OPls
    | c_Int_OPls = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6647]) ).

cnf(c_0_6656_0,axiom,
    ( c_Int_OBit1(X1) = c_Int_OMin
    | X1 != c_Int_OMin ),
    inference(literals_permutation,[status(thm)],[c_0_6656]) ).

cnf(c_0_6656_1,axiom,
    ( X1 != c_Int_OMin
    | c_Int_OBit1(X1) = c_Int_OMin ),
    inference(literals_permutation,[status(thm)],[c_0_6656]) ).

cnf(c_0_6657_0,axiom,
    ( c_Int_OBit1(X1) = c_Int_OMin
    | c_Int_OMin != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6657]) ).

cnf(c_0_6657_1,axiom,
    ( c_Int_OMin != X1
    | c_Int_OBit1(X1) = c_Int_OMin ),
    inference(literals_permutation,[status(thm)],[c_0_6657]) ).

cnf(c_0_6658_0,axiom,
    ( c_Int_OBit0(X1) = c_Int_OPls
    | X1 != c_Int_OPls ),
    inference(literals_permutation,[status(thm)],[c_0_6658]) ).

cnf(c_0_6658_1,axiom,
    ( X1 != c_Int_OPls
    | c_Int_OBit0(X1) = c_Int_OPls ),
    inference(literals_permutation,[status(thm)],[c_0_6658]) ).

cnf(c_0_6659_0,axiom,
    ( c_Int_OBit0(X1) = c_Int_OPls
    | c_Int_OPls != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_6659]) ).

cnf(c_0_6659_1,axiom,
    ( c_Int_OPls != X1
    | c_Int_OBit0(X1) = c_Int_OPls ),
    inference(literals_permutation,[status(thm)],[c_0_6659]) ).

cnf(c_0_5867_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_5867]) ).

cnf(c_0_5901_0,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
    inference(literals_permutation,[status(thm)],[c_0_5901]) ).

cnf(c_0_5902_0,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
    inference(literals_permutation,[status(thm)],[c_0_5902]) ).

cnf(c_0_6419_0,axiom,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1),
    inference(literals_permutation,[status(thm)],[c_0_6419]) ).

cnf(c_0_6431_0,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(literals_permutation,[status(thm)],[c_0_6431]) ).

cnf(c_0_6432_0,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(literals_permutation,[status(thm)],[c_0_6432]) ).

cnf(c_0_6433_0,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(literals_permutation,[status(thm)],[c_0_6433]) ).

cnf(c_0_6442_0,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_6442]) ).

cnf(c_0_6448_0,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    inference(literals_permutation,[status(thm)],[c_0_6448]) ).

cnf(c_0_6449_0,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
    inference(literals_permutation,[status(thm)],[c_0_6449]) ).

cnf(c_0_6456_0,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
    inference(literals_permutation,[status(thm)],[c_0_6456]) ).

cnf(c_0_6457_0,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
    inference(literals_permutation,[status(thm)],[c_0_6457]) ).

cnf(c_0_6458_0,axiom,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
    inference(literals_permutation,[status(thm)],[c_0_6458]) ).

cnf(c_0_6459_0,axiom,
    ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(literals_permutation,[status(thm)],[c_0_6459]) ).

cnf(c_0_6601_0,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
    inference(literals_permutation,[status(thm)],[c_0_6601]) ).

cnf(c_0_6607_0,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(literals_permutation,[status(thm)],[c_0_6607]) ).

cnf(c_0_6608_0,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_6608]) ).

cnf(c_0_6631_0,axiom,
    c_Int_OBit1(X1) != c_Int_OBit0(X2),
    inference(literals_permutation,[status(thm)],[c_0_6631]) ).

cnf(c_0_6632_0,axiom,
    c_Int_OBit0(X1) != c_Int_OBit1(X2),
    inference(literals_permutation,[status(thm)],[c_0_6632]) ).

cnf(c_0_6637_0,axiom,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6637]) ).

cnf(c_0_6638_0,axiom,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6638]) ).

cnf(c_0_6639_0,axiom,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6639]) ).

cnf(c_0_6640_0,axiom,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6640]) ).

cnf(c_0_6641_0,axiom,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6641]) ).

cnf(c_0_6642_0,axiom,
    c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6642]) ).

cnf(c_0_6648_0,axiom,
    c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6648]) ).

cnf(c_0_6649_0,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6649]) ).

cnf(c_0_6650_0,axiom,
    c_Nat_OSuc(X1) != X1,
    inference(literals_permutation,[status(thm)],[c_0_6650]) ).

cnf(c_0_6651_0,axiom,
    c_Nat_OSuc(X1) != X1,
    inference(literals_permutation,[status(thm)],[c_0_6651]) ).

cnf(c_0_6652_0,axiom,
    c_Int_OBit0(X1) != c_Int_OMin,
    inference(literals_permutation,[status(thm)],[c_0_6652]) ).

cnf(c_0_6653_0,axiom,
    c_Int_OBit0(X1) != c_Int_OMin,
    inference(literals_permutation,[status(thm)],[c_0_6653]) ).

cnf(c_0_6654_0,axiom,
    c_Int_OBit1(X1) != c_Int_OPls,
    inference(literals_permutation,[status(thm)],[c_0_6654]) ).

cnf(c_0_6655_0,axiom,
    c_Int_OBit1(X1) != c_Int_OPls,
    inference(literals_permutation,[status(thm)],[c_0_6655]) ).

cnf(c_0_6660_0,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != v_n,
    inference(literals_permutation,[status(thm)],[c_0_6660]) ).

cnf(c_0_6661_0,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != v_na____,
    inference(literals_permutation,[status(thm)],[c_0_6661]) ).

cnf(c_0_6843_0,axiom,
    c_Int_OMin != c_Int_OPls,
    inference(literals_permutation,[status(thm)],[c_0_6843]) ).

cnf(c_0_6844_0,axiom,
    c_Int_OMin != c_Int_OPls,
    inference(literals_permutation,[status(thm)],[c_0_6844]) ).

cnf(c_0_5196_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3),
    inference(literals_permutation,[status(thm)],[c_0_5196]) ).

cnf(c_0_5200_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),X2)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(literals_permutation,[status(thm)],[c_0_5200]) ).

cnf(c_0_5259_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2),X4),
    inference(literals_permutation,[status(thm)],[c_0_5259]) ).

cnf(c_0_5267_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X3),X2),
    inference(literals_permutation,[status(thm)],[c_0_5267]) ).

cnf(c_0_5296_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(literals_permutation,[status(thm)],[c_0_5296]) ).

cnf(c_0_5386_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3),
    inference(literals_permutation,[status(thm)],[c_0_5386]) ).

cnf(c_0_5387_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3),
    inference(literals_permutation,[status(thm)],[c_0_5387]) ).

cnf(c_0_5388_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),X3),
    inference(literals_permutation,[status(thm)],[c_0_5388]) ).

cnf(c_0_5389_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3),X2),
    inference(literals_permutation,[status(thm)],[c_0_5389]) ).

cnf(c_0_5390_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3),X2),
    inference(literals_permutation,[status(thm)],[c_0_5390]) ).

cnf(c_0_5542_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2))),
    inference(literals_permutation,[status(thm)],[c_0_5542]) ).

cnf(c_0_5545_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2),
    inference(literals_permutation,[status(thm)],[c_0_5545]) ).

cnf(c_0_5546_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X3),
    inference(literals_permutation,[status(thm)],[c_0_5546]) ).

cnf(c_0_5547_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5547]) ).

cnf(c_0_5548_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3),
    inference(literals_permutation,[status(thm)],[c_0_5548]) ).

cnf(c_0_5549_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
    inference(literals_permutation,[status(thm)],[c_0_5549]) ).

cnf(c_0_5550_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5550]) ).

cnf(c_0_5551_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5551]) ).

cnf(c_0_5552_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),X3),
    inference(literals_permutation,[status(thm)],[c_0_5552]) ).

cnf(c_0_5553_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3),
    inference(literals_permutation,[status(thm)],[c_0_5553]) ).

cnf(c_0_5554_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5554]) ).

cnf(c_0_5555_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),
    inference(literals_permutation,[status(thm)],[c_0_5555]) ).

cnf(c_0_5556_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5556]) ).

cnf(c_0_5557_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2),c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3)) = c_Power_Opower__class_Opower(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5557]) ).

cnf(c_0_5637_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X1))),
    inference(literals_permutation,[status(thm)],[c_0_5637]) ).

cnf(c_0_5719_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Nat_OSuc(X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
    inference(literals_permutation,[status(thm)],[c_0_5719]) ).

cnf(c_0_5739_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2),
    inference(literals_permutation,[status(thm)],[c_0_5739]) ).

cnf(c_0_5740_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),X2) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X1),X2),
    inference(literals_permutation,[status(thm)],[c_0_5740]) ).

cnf(c_0_5755_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2),
    inference(literals_permutation,[status(thm)],[c_0_5755]) ).

cnf(c_0_5756_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),X3) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5756]) ).

cnf(c_0_5757_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),
    inference(literals_permutation,[status(thm)],[c_0_5757]) ).

cnf(c_0_5758_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_5758]) ).

cnf(c_0_5759_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5759]) ).

cnf(c_0_5760_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5760]) ).

cnf(c_0_5761_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5761]) ).

cnf(c_0_5762_0,axiom,
    c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2),X3) = c_Power_Opower__class_Opower(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5762]) ).

cnf(c_0_5763_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5763]) ).

cnf(c_0_5764_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5764]) ).

cnf(c_0_5765_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5765]) ).

cnf(c_0_5766_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),
    inference(literals_permutation,[status(thm)],[c_0_5766]) ).

cnf(c_0_5857_0,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
    inference(literals_permutation,[status(thm)],[c_0_5857]) ).

cnf(c_0_5858_0,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
    inference(literals_permutation,[status(thm)],[c_0_5858]) ).

cnf(c_0_5880_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),
    inference(literals_permutation,[status(thm)],[c_0_5880]) ).

cnf(c_0_5966_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
    inference(literals_permutation,[status(thm)],[c_0_5966]) ).

cnf(c_0_5994_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),
    inference(literals_permutation,[status(thm)],[c_0_5994]) ).

cnf(c_0_5995_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
    inference(literals_permutation,[status(thm)],[c_0_5995]) ).

cnf(c_0_5997_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(literals_permutation,[status(thm)],[c_0_5997]) ).

cnf(c_0_5998_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),
    inference(literals_permutation,[status(thm)],[c_0_5998]) ).

cnf(c_0_6079_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    inference(literals_permutation,[status(thm)],[c_0_6079]) ).

cnf(c_0_6080_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    inference(literals_permutation,[status(thm)],[c_0_6080]) ).

cnf(c_0_6081_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
    inference(literals_permutation,[status(thm)],[c_0_6081]) ).

cnf(c_0_6082_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(literals_permutation,[status(thm)],[c_0_6082]) ).

cnf(c_0_6083_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(literals_permutation,[status(thm)],[c_0_6083]) ).

cnf(c_0_6084_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
    inference(literals_permutation,[status(thm)],[c_0_6084]) ).

cnf(c_0_6119_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) = c_Int_OBit1(X1),
    inference(literals_permutation,[status(thm)],[c_0_6119]) ).

cnf(c_0_6120_0,axiom,
    c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),
    inference(literals_permutation,[status(thm)],[c_0_6120]) ).

cnf(c_0_6121_0,axiom,
    c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
    inference(literals_permutation,[status(thm)],[c_0_6121]) ).

cnf(c_0_6122_0,axiom,
    c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X1),X2),
    inference(literals_permutation,[status(thm)],[c_0_6122]) ).

cnf(c_0_6132_0,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Nat_OSuc(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6132]) ).

cnf(c_0_6134_0,axiom,
    c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6134]) ).

cnf(c_0_6135_0,axiom,
    c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6135]) ).

cnf(c_0_6136_0,axiom,
    c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6136]) ).

cnf(c_0_6137_0,axiom,
    c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6137]) ).

cnf(c_0_6140_0,axiom,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6140]) ).

cnf(c_0_6141_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6141]) ).

cnf(c_0_6142_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
    inference(literals_permutation,[status(thm)],[c_0_6142]) ).

cnf(c_0_6143_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6143]) ).

cnf(c_0_6151_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X1),
    inference(literals_permutation,[status(thm)],[c_0_6151]) ).

cnf(c_0_6152_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
    inference(literals_permutation,[status(thm)],[c_0_6152]) ).

cnf(c_0_6153_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X1)),
    inference(literals_permutation,[status(thm)],[c_0_6153]) ).

cnf(c_0_6154_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
    inference(literals_permutation,[status(thm)],[c_0_6154]) ).

cnf(c_0_6155_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
    inference(literals_permutation,[status(thm)],[c_0_6155]) ).

cnf(c_0_6179_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),
    inference(literals_permutation,[status(thm)],[c_0_6179]) ).

cnf(c_0_6180_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),
    inference(literals_permutation,[status(thm)],[c_0_6180]) ).

cnf(c_0_6323_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X1) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X1))),
    inference(literals_permutation,[status(thm)],[c_0_6323]) ).

cnf(c_0_6333_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_6333]) ).

cnf(c_0_6334_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
    inference(literals_permutation,[status(thm)],[c_0_6334]) ).

cnf(c_0_6352_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) = c_Nat_OSuc(c_Nat_OSuc(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6352]) ).

cnf(c_0_6353_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6353]) ).

cnf(c_0_6370_0,axiom,
    c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6370]) ).

cnf(c_0_6382_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),
    inference(literals_permutation,[status(thm)],[c_0_6382]) ).

cnf(c_0_6383_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
    inference(literals_permutation,[status(thm)],[c_0_6383]) ).

cnf(c_0_6384_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
    inference(literals_permutation,[status(thm)],[c_0_6384]) ).

cnf(c_0_6385_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),
    inference(literals_permutation,[status(thm)],[c_0_6385]) ).

cnf(c_0_6386_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),
    inference(literals_permutation,[status(thm)],[c_0_6386]) ).

cnf(c_0_6392_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(literals_permutation,[status(thm)],[c_0_6392]) ).

cnf(c_0_6393_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(literals_permutation,[status(thm)],[c_0_6393]) ).

cnf(c_0_6394_0,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(literals_permutation,[status(thm)],[c_0_6394]) ).

cnf(c_0_6410_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sk1_esk1_0) = v_na____,
    inference(literals_permutation,[status(thm)],[c_0_6410]) ).

cnf(c_0_6447_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(literals_permutation,[status(thm)],[c_0_6447]) ).

cnf(c_0_6461_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
    inference(literals_permutation,[status(thm)],[c_0_6461]) ).

cnf(c_0_6464_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6464]) ).

cnf(c_0_6472_0,axiom,
    c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(literals_permutation,[status(thm)],[c_0_6472]) ).

cnf(c_0_6510_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6510]) ).

cnf(c_0_6522_0,axiom,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
    inference(literals_permutation,[status(thm)],[c_0_6522]) ).

cnf(c_0_6525_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6525]) ).

cnf(c_0_6527_0,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6527]) ).

cnf(c_0_6537_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = c_Nat_OSuc(X1),
    inference(literals_permutation,[status(thm)],[c_0_6537]) ).

cnf(c_0_6538_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_OSuc(X1),
    inference(literals_permutation,[status(thm)],[c_0_6538]) ).

cnf(c_0_6543_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_6543]) ).

cnf(c_0_6544_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_6544]) ).

cnf(c_0_6545_0,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_6545]) ).

cnf(c_0_6546_0,axiom,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1)),
    inference(literals_permutation,[status(thm)],[c_0_6546]) ).

cnf(c_0_6547_0,axiom,
    c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),
    inference(literals_permutation,[status(thm)],[c_0_6547]) ).

cnf(c_0_6548_0,axiom,
    c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6548]) ).

cnf(c_0_6549_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6549]) ).

cnf(c_0_6550_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6550]) ).

cnf(c_0_6551_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6551]) ).

cnf(c_0_6552_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6552]) ).

cnf(c_0_6553_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6553]) ).

cnf(c_0_6554_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6554]) ).

cnf(c_0_6555_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6555]) ).

cnf(c_0_6556_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6556]) ).

cnf(c_0_6557_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6557]) ).

cnf(c_0_6558_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6558]) ).

cnf(c_0_6559_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6559]) ).

cnf(c_0_6560_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) = c_Int_OBit0(X1),
    inference(literals_permutation,[status(thm)],[c_0_6560]) ).

cnf(c_0_6561_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6561]) ).

cnf(c_0_6562_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6562]) ).

cnf(c_0_6563_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6563]) ).

cnf(c_0_6564_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6564]) ).

cnf(c_0_6573_0,axiom,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
    inference(literals_permutation,[status(thm)],[c_0_6573]) ).

cnf(c_0_6574_0,axiom,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(literals_permutation,[status(thm)],[c_0_6574]) ).

cnf(c_0_6575_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
    inference(literals_permutation,[status(thm)],[c_0_6575]) ).

cnf(c_0_6576_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
    inference(literals_permutation,[status(thm)],[c_0_6576]) ).

cnf(c_0_6577_0,axiom,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6577]) ).

cnf(c_0_6578_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6578]) ).

cnf(c_0_6579_0,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_6579]) ).

cnf(c_0_6580_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
    inference(literals_permutation,[status(thm)],[c_0_6580]) ).

cnf(c_0_6581_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
    inference(literals_permutation,[status(thm)],[c_0_6581]) ).

cnf(c_0_6582_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
    inference(literals_permutation,[status(thm)],[c_0_6582]) ).

cnf(c_0_6583_0,axiom,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
    inference(literals_permutation,[status(thm)],[c_0_6583]) ).

cnf(c_0_6584_0,axiom,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6584]) ).

cnf(c_0_6585_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6585]) ).

cnf(c_0_6586_0,axiom,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6586]) ).

cnf(c_0_6587_0,axiom,
    c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,X1) = c_Int_OPls,
    inference(literals_permutation,[status(thm)],[c_0_6587]) ).

cnf(c_0_6588_0,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
    inference(literals_permutation,[status(thm)],[c_0_6588]) ).

cnf(c_0_6589_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
    inference(literals_permutation,[status(thm)],[c_0_6589]) ).

cnf(c_0_6590_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
    inference(literals_permutation,[status(thm)],[c_0_6590]) ).

cnf(c_0_6591_0,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
    inference(literals_permutation,[status(thm)],[c_0_6591]) ).

cnf(c_0_6597_0,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(literals_permutation,[status(thm)],[c_0_6597]) ).

cnf(c_0_6598_0,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(literals_permutation,[status(thm)],[c_0_6598]) ).

cnf(c_0_6611_0,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(literals_permutation,[status(thm)],[c_0_6611]) ).

cnf(c_0_6618_0,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6618]) ).

cnf(c_0_6619_0,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6619]) ).

cnf(c_0_6620_0,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6620]) ).

cnf(c_0_6621_0,axiom,
    c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(literals_permutation,[status(thm)],[c_0_6621]) ).

cnf(c_0_6622_0,axiom,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(literals_permutation,[status(thm)],[c_0_6622]) ).

cnf(c_0_6627_0,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6627]) ).

cnf(c_0_6628_0,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) = X1,
    inference(literals_permutation,[status(thm)],[c_0_6628]) ).

cnf(c_0_6629_0,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6629]) ).

cnf(c_0_6630_0,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6630]) ).

cnf(c_0_6636_0,axiom,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    inference(literals_permutation,[status(thm)],[c_0_6636]) ).

cnf(c_0_6643_0,axiom,
    c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6643]) ).

cnf(c_0_6662_0,axiom,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6662]) ).

cnf(c_0_6663_0,axiom,
    class_Groups_Oone(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6663]) ).

cnf(c_0_6664_0,axiom,
    class_Int_Onumber(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6664]) ).

cnf(c_0_6665_0,axiom,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6665]) ).

cnf(c_0_6666_0,axiom,
    class_Rings_Oring(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6666]) ).

cnf(c_0_6667_0,axiom,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6667]) ).

cnf(c_0_6668_0,axiom,
    class_Power_Opower(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6668]) ).

cnf(c_0_6669_0,axiom,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6669]) ).

cnf(c_0_6670_0,axiom,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6670]) ).

cnf(c_0_6671_0,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6671]) ).

cnf(c_0_6672_0,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6672]) ).

cnf(c_0_6673_0,axiom,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6673]) ).

cnf(c_0_6674_0,axiom,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6674]) ).

cnf(c_0_6675_0,axiom,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6675]) ).

cnf(c_0_6676_0,axiom,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6676]) ).

cnf(c_0_6677_0,axiom,
    class_Rings_Osemiring__1(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6677]) ).

cnf(c_0_6678_0,axiom,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6678]) ).

cnf(c_0_6679_0,axiom,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6679]) ).

cnf(c_0_6680_0,axiom,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6680]) ).

cnf(c_0_6681_0,axiom,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6681]) ).

cnf(c_0_6682_0,axiom,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6682]) ).

cnf(c_0_6683_0,axiom,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6683]) ).

cnf(c_0_6684_0,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6684]) ).

cnf(c_0_6685_0,axiom,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6685]) ).

cnf(c_0_6686_0,axiom,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6686]) ).

cnf(c_0_6687_0,axiom,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6687]) ).

cnf(c_0_6688_0,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6688]) ).

cnf(c_0_6689_0,axiom,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6689]) ).

cnf(c_0_6690_0,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6690]) ).

cnf(c_0_6691_0,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6691]) ).

cnf(c_0_6692_0,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6692]) ).

cnf(c_0_6693_0,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6693]) ).

cnf(c_0_6694_0,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6694]) ).

cnf(c_0_6695_0,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    inference(literals_permutation,[status(thm)],[c_0_6695]) ).

cnf(c_0_6696_0,axiom,
    class_Rings_Odvd(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6696]) ).

cnf(c_0_6697_0,axiom,
    class_Groups_Oone(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6697]) ).

cnf(c_0_6698_0,axiom,
    class_Int_Onumber(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6698]) ).

cnf(c_0_6699_0,axiom,
    class_Rings_Oidom(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6699]) ).

cnf(c_0_6700_0,axiom,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6700]) ).

cnf(c_0_6701_0,axiom,
    class_Groups_Ozero(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6701]) ).

cnf(c_0_6702_0,axiom,
    class_Power_Opower(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6702]) ).

cnf(c_0_6703_0,axiom,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6703]) ).

cnf(c_0_6704_0,axiom,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6704]) ).

cnf(c_0_6705_0,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6705]) ).

cnf(c_0_6706_0,axiom,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6706]) ).

cnf(c_0_6707_0,axiom,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6707]) ).

cnf(c_0_6708_0,axiom,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6708]) ).

cnf(c_0_6709_0,axiom,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6709]) ).

cnf(c_0_6710_0,axiom,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6710]) ).

cnf(c_0_6711_0,axiom,
    class_Rings_Osemiring__1(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6711]) ).

cnf(c_0_6712_0,axiom,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6712]) ).

cnf(c_0_6713_0,axiom,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6713]) ).

cnf(c_0_6714_0,axiom,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6714]) ).

cnf(c_0_6715_0,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6715]) ).

cnf(c_0_6716_0,axiom,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6716]) ).

cnf(c_0_6717_0,axiom,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6717]) ).

cnf(c_0_6718_0,axiom,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6718]) ).

cnf(c_0_6719_0,axiom,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6719]) ).

cnf(c_0_6720_0,axiom,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6720]) ).

cnf(c_0_6721_0,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6721]) ).

cnf(c_0_6722_0,axiom,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6722]) ).

cnf(c_0_6723_0,axiom,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6723]) ).

cnf(c_0_6724_0,axiom,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6724]) ).

cnf(c_0_6725_0,axiom,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6725]) ).

cnf(c_0_6726_0,axiom,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6726]) ).

cnf(c_0_6727_0,axiom,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6727]) ).

cnf(c_0_6728_0,axiom,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6728]) ).

cnf(c_0_6729_0,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6729]) ).

cnf(c_0_6730_0,axiom,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6730]) ).

cnf(c_0_6731_0,axiom,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6731]) ).

cnf(c_0_6732_0,axiom,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6732]) ).

cnf(c_0_6733_0,axiom,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6733]) ).

cnf(c_0_6734_0,axiom,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6734]) ).

cnf(c_0_6735_0,axiom,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6735]) ).

cnf(c_0_6736_0,axiom,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6736]) ).

cnf(c_0_6737_0,axiom,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6737]) ).

cnf(c_0_6738_0,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6738]) ).

cnf(c_0_6739_0,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6739]) ).

cnf(c_0_6740_0,axiom,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6740]) ).

cnf(c_0_6741_0,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6741]) ).

cnf(c_0_6742_0,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6742]) ).

cnf(c_0_6743_0,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6743]) ).

cnf(c_0_6744_0,axiom,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6744]) ).

cnf(c_0_6745_0,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6745]) ).

cnf(c_0_6746_0,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6746]) ).

cnf(c_0_6747_0,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6747]) ).

cnf(c_0_6748_0,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6748]) ).

cnf(c_0_6749_0,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    inference(literals_permutation,[status(thm)],[c_0_6749]) ).

cnf(c_0_6750_0,axiom,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6750]) ).

cnf(c_0_6751_0,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6751]) ).

cnf(c_0_6752_0,axiom,
    class_Int_Onumber(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6752]) ).

cnf(c_0_6753_0,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6753]) ).

cnf(c_0_6754_0,axiom,
    class_Power_Opower(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6754]) ).

cnf(c_0_6755_0,axiom,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6755]) ).

cnf(c_0_6756_0,axiom,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6756]) ).

cnf(c_0_6757_0,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6757]) ).

cnf(c_0_6758_0,axiom,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6758]) ).

cnf(c_0_6759_0,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6759]) ).

cnf(c_0_6760_0,axiom,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6760]) ).

cnf(c_0_6761_0,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6761]) ).

cnf(c_0_6762_0,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6762]) ).

cnf(c_0_6763_0,axiom,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6763]) ).

cnf(c_0_6764_0,axiom,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6764]) ).

cnf(c_0_6765_0,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6765]) ).

cnf(c_0_6766_0,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6766]) ).

cnf(c_0_6767_0,axiom,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6767]) ).

cnf(c_0_6768_0,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6768]) ).

cnf(c_0_6769_0,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6769]) ).

cnf(c_0_6770_0,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6770]) ).

cnf(c_0_6771_0,axiom,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6771]) ).

cnf(c_0_6772_0,axiom,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6772]) ).

cnf(c_0_6773_0,axiom,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6773]) ).

cnf(c_0_6774_0,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6774]) ).

cnf(c_0_6775_0,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6775]) ).

cnf(c_0_6776_0,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6776]) ).

cnf(c_0_6777_0,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6777]) ).

cnf(c_0_6778_0,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6778]) ).

cnf(c_0_6779_0,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6779]) ).

cnf(c_0_6780_0,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6780]) ).

cnf(c_0_6781_0,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6781]) ).

cnf(c_0_6782_0,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6782]) ).

cnf(c_0_6783_0,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6783]) ).

cnf(c_0_6784_0,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(literals_permutation,[status(thm)],[c_0_6784]) ).

cnf(c_0_6785_0,axiom,
    class_Rings_Odvd(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6785]) ).

cnf(c_0_6786_0,axiom,
    class_Groups_Oone(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6786]) ).

cnf(c_0_6787_0,axiom,
    class_Int_Onumber(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6787]) ).

cnf(c_0_6788_0,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6788]) ).

cnf(c_0_6789_0,axiom,
    class_Rings_Oring(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6789]) ).

cnf(c_0_6790_0,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6790]) ).

cnf(c_0_6791_0,axiom,
    class_Power_Opower(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6791]) ).

cnf(c_0_6792_0,axiom,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6792]) ).

cnf(c_0_6793_0,axiom,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6793]) ).

cnf(c_0_6794_0,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6794]) ).

cnf(c_0_6795_0,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6795]) ).

cnf(c_0_6796_0,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6796]) ).

cnf(c_0_6797_0,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6797]) ).

cnf(c_0_6798_0,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6798]) ).

cnf(c_0_6799_0,axiom,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6799]) ).

cnf(c_0_6800_0,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6800]) ).

cnf(c_0_6801_0,axiom,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6801]) ).

cnf(c_0_6802_0,axiom,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6802]) ).

cnf(c_0_6803_0,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6803]) ).

cnf(c_0_6804_0,axiom,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6804]) ).

cnf(c_0_6805_0,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6805]) ).

cnf(c_0_6806_0,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6806]) ).

cnf(c_0_6807_0,axiom,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6807]) ).

cnf(c_0_6808_0,axiom,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6808]) ).

cnf(c_0_6809_0,axiom,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6809]) ).

cnf(c_0_6810_0,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6810]) ).

cnf(c_0_6811_0,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6811]) ).

cnf(c_0_6812_0,axiom,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6812]) ).

cnf(c_0_6813_0,axiom,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6813]) ).

cnf(c_0_6814_0,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6814]) ).

cnf(c_0_6815_0,axiom,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6815]) ).

cnf(c_0_6816_0,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6816]) ).

cnf(c_0_6817_0,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6817]) ).

cnf(c_0_6818_0,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6818]) ).

cnf(c_0_6819_0,axiom,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6819]) ).

cnf(c_0_6820_0,axiom,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6820]) ).

cnf(c_0_6821_0,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6821]) ).

cnf(c_0_6822_0,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6822]) ).

cnf(c_0_6823_0,axiom,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6823]) ).

cnf(c_0_6824_0,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6824]) ).

cnf(c_0_6825_0,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6825]) ).

cnf(c_0_6826_0,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6826]) ).

cnf(c_0_6827_0,axiom,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6827]) ).

cnf(c_0_6828_0,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6828]) ).

cnf(c_0_6829_0,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6829]) ).

cnf(c_0_6830_0,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6830]) ).

cnf(c_0_6831_0,axiom,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6831]) ).

cnf(c_0_6832_0,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6832]) ).

cnf(c_0_6833_0,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6833]) ).

cnf(c_0_6834_0,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6834]) ).

cnf(c_0_6835_0,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6835]) ).

cnf(c_0_6836_0,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6836]) ).

cnf(c_0_6837_0,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6837]) ).

cnf(c_0_6838_0,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6838]) ).

cnf(c_0_6839_0,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(literals_permutation,[status(thm)],[c_0_6839]) ).

cnf(c_0_6840_0,axiom,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(literals_permutation,[status(thm)],[c_0_6840]) ).

cnf(c_0_6841_0,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
    inference(literals_permutation,[status(thm)],[c_0_6841]) ).

cnf(c_0_6842_0,axiom,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(literals_permutation,[status(thm)],[c_0_6842]) ).

% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,hypothesis,
    ( ? [X1] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
   => v_thesis____ ),
    file('<stdin>',conj_0) ).

fof(c_0_1_002,conjecture,
    v_thesis____,
    file('<stdin>',conj_1) ).

fof(c_0_2_003,hypothesis,
    ( ? [X1] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
   => v_thesis____ ),
    c_0_0 ).

fof(c_0_3_004,negated_conjecture,
    ~ v_thesis____,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[c_0_1])]) ).

fof(c_0_4_005,hypothesis,
    ! [X2] :
      ( v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)
      | v_thesis____ ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).

fof(c_0_5_006,negated_conjecture,
    ~ v_thesis____,
    c_0_3 ).

cnf(c_0_6_007,hypothesis,
    ( v_thesis____
    | v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7_008,negated_conjecture,
    ~ v_thesis____,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8_009,hypothesis,
    ( v_thesis____
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) != v_na____ ),
    c_0_6,
    [final] ).

cnf(c_0_9_010,negated_conjecture,
    ~ v_thesis____,
    c_0_7,
    [final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_4079,plain,
    ( v_thesis____
    | c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) != v_na____ ),
    file('/export/starexec/sandbox/tmp/iprover_modulo_db5cba.p',c_0_8) ).

cnf(c_4080,negated_conjecture,
    ~ v_thesis____,
    file('/export/starexec/sandbox/tmp/iprover_modulo_db5cba.p',c_0_9) ).

cnf(c_5130,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) != v_na____,
    inference(global_propositional_subsumption,[status(thm)],[c_4079,c_4080]) ).

cnf(c_5132,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) != v_na____,
    inference(copy,[status(esa)],[c_5130]) ).

cnf(c_5139,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) != v_na____,
    inference(copy,[status(esa)],[c_5132]) ).

cnf(c_5140,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) != v_na____,
    inference(copy,[status(esa)],[c_5139]) ).

cnf(c_5143,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) != v_na____,
    inference(copy,[status(esa)],[c_5140]) ).

cnf(c_9224,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) != v_na____,
    inference(copy,[status(esa)],[c_5143]) ).

cnf(c_89305,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sk1_esk1_0) != v_na____,
    inference(instantiation,[status(thm)],[c_9224]) ).

cnf(c_246,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sk1_esk1_0) = v_na____,
    file('/export/starexec/sandbox/tmp/iprover_modulo_db5cba.p',c_0_6410_0) ).

cnf(contradiction,plain,
    $false,
    inference(minisat,[status(thm)],[c_89305,c_246]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW196+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13  % Command  : iprover_modulo %s %d
% 0.14/0.34  % Computer : n017.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 Jun  6 01:13:31 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running in mono-core mode
% 0.51/0.68  % Orienting using strategy Equiv(ClausalAll)
% 0.51/0.68  % FOF problem with conjecture
% 0.51/0.68  % 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_bf605d.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_db5cba.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_6b596a | grep -v "SZS"
% 0.51/0.70  
% 0.51/0.70  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.51/0.70  
% 0.51/0.70  % 
% 0.51/0.70  % ------  iProver source info 
% 0.51/0.70  
% 0.51/0.70  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.51/0.70  % git: non_committed_changes: true
% 0.51/0.70  % git: last_make_outside_of_git: true
% 0.51/0.70  
% 0.51/0.70  % 
% 0.51/0.70  % ------ Input Options
% 0.51/0.70  
% 0.51/0.70  % --out_options                         all
% 0.51/0.70  % --tptp_safe_out                       true
% 0.51/0.70  % --problem_path                        ""
% 0.51/0.70  % --include_path                        ""
% 0.51/0.70  % --clausifier                          .//eprover
% 0.51/0.70  % --clausifier_options                  --tstp-format  
% 0.51/0.70  % --stdin                               false
% 0.51/0.70  % --dbg_backtrace                       false
% 0.51/0.70  % --dbg_dump_prop_clauses               false
% 0.51/0.70  % --dbg_dump_prop_clauses_file          -
% 0.51/0.70  % --dbg_out_stat                        false
% 0.51/0.70  
% 0.51/0.70  % ------ General Options
% 0.51/0.70  
% 0.51/0.70  % --fof                                 false
% 0.51/0.70  % --time_out_real                       150.
% 0.51/0.70  % --time_out_prep_mult                  0.2
% 0.51/0.70  % --time_out_virtual                    -1.
% 0.51/0.70  % --schedule                            none
% 0.51/0.70  % --ground_splitting                    input
% 0.51/0.70  % --splitting_nvd                       16
% 0.51/0.70  % --non_eq_to_eq                        false
% 0.51/0.70  % --prep_gs_sim                         true
% 0.51/0.70  % --prep_unflatten                      false
% 0.51/0.70  % --prep_res_sim                        true
% 0.51/0.70  % --prep_upred                          true
% 0.51/0.70  % --res_sim_input                       true
% 0.51/0.70  % --clause_weak_htbl                    true
% 0.51/0.70  % --gc_record_bc_elim                   false
% 0.51/0.70  % --symbol_type_check                   false
% 0.51/0.70  % --clausify_out                        false
% 0.51/0.70  % --large_theory_mode                   false
% 0.51/0.70  % --prep_sem_filter                     none
% 0.51/0.70  % --prep_sem_filter_out                 false
% 0.51/0.70  % --preprocessed_out                    false
% 0.51/0.70  % --sub_typing                          false
% 0.51/0.70  % --brand_transform                     false
% 0.51/0.70  % --pure_diseq_elim                     true
% 0.51/0.70  % --min_unsat_core                      false
% 0.51/0.70  % --pred_elim                           true
% 0.51/0.70  % --add_important_lit                   false
% 0.51/0.70  % --soft_assumptions                    false
% 0.51/0.70  % --reset_solvers                       false
% 0.51/0.70  % --bc_imp_inh                          []
% 0.51/0.70  % --conj_cone_tolerance                 1.5
% 0.51/0.70  % --prolific_symb_bound                 500
% 0.51/0.70  % --lt_threshold                        2000
% 0.51/0.70  
% 0.51/0.70  % ------ SAT Options
% 0.51/0.70  
% 0.51/0.70  % --sat_mode                            false
% 0.51/0.70  % --sat_fm_restart_options              ""
% 0.51/0.70  % --sat_gr_def                          false
% 0.51/0.70  % --sat_epr_types                       true
% 0.51/0.70  % --sat_non_cyclic_types                false
% 0.51/0.70  % --sat_finite_models                   false
% 0.51/0.70  % --sat_fm_lemmas                       false
% 0.51/0.70  % --sat_fm_prep                         false
% 0.51/0.70  % --sat_fm_uc_incr                      true
% 0.51/0.70  % --sat_out_model                       small
% 0.51/0.70  % --sat_out_clauses                     false
% 0.51/0.70  
% 0.51/0.70  % ------ QBF Options
% 0.51/0.70  
% 0.51/0.70  % --qbf_mode                            false
% 0.51/0.70  % --qbf_elim_univ                       true
% 0.51/0.70  % --qbf_sk_in                           true
% 0.51/0.70  % --qbf_pred_elim                       true
% 0.51/0.70  % --qbf_split                           32
% 0.51/0.70  
% 0.51/0.70  % ------ BMC1 Options
% 0.51/0.70  
% 0.51/0.70  % --bmc1_incremental                    false
% 0.51/0.70  % --bmc1_axioms                         reachable_all
% 0.51/0.70  % --bmc1_min_bound                      0
% 0.51/0.70  % --bmc1_max_bound                      -1
% 0.51/0.70  % --bmc1_max_bound_default              -1
% 0.51/0.70  % --bmc1_symbol_reachability            true
% 0.51/0.70  % --bmc1_property_lemmas                false
% 0.51/0.70  % --bmc1_k_induction                    false
% 0.51/0.70  % --bmc1_non_equiv_states               false
% 0.51/0.70  % --bmc1_deadlock                       false
% 0.51/0.70  % --bmc1_ucm                            false
% 0.51/0.70  % --bmc1_add_unsat_core                 none
% 0.51/0.70  % --bmc1_unsat_core_children            false
% 0.51/0.70  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.51/0.70  % --bmc1_out_stat                       full
% 0.51/0.70  % --bmc1_ground_init                    false
% 0.51/0.70  % --bmc1_pre_inst_next_state            false
% 0.51/0.70  % --bmc1_pre_inst_state                 false
% 0.51/0.70  % --bmc1_pre_inst_reach_state           false
% 0.51/0.70  % --bmc1_out_unsat_core                 false
% 0.51/0.70  % --bmc1_aig_witness_out                false
% 0.51/0.70  % --bmc1_verbose                        false
% 0.51/0.70  % --bmc1_dump_clauses_tptp              false
% 0.51/0.74  % --bmc1_dump_unsat_core_tptp           false
% 0.51/0.74  % --bmc1_dump_file                      -
% 0.51/0.74  % --bmc1_ucm_expand_uc_limit            128
% 0.51/0.74  % --bmc1_ucm_n_expand_iterations        6
% 0.51/0.74  % --bmc1_ucm_extend_mode                1
% 0.51/0.74  % --bmc1_ucm_init_mode                  2
% 0.51/0.74  % --bmc1_ucm_cone_mode                  none
% 0.51/0.74  % --bmc1_ucm_reduced_relation_type      0
% 0.51/0.74  % --bmc1_ucm_relax_model                4
% 0.51/0.74  % --bmc1_ucm_full_tr_after_sat          true
% 0.51/0.74  % --bmc1_ucm_expand_neg_assumptions     false
% 0.51/0.74  % --bmc1_ucm_layered_model              none
% 0.51/0.74  % --bmc1_ucm_max_lemma_size             10
% 0.51/0.74  
% 0.51/0.74  % ------ AIG Options
% 0.51/0.74  
% 0.51/0.74  % --aig_mode                            false
% 0.51/0.74  
% 0.51/0.74  % ------ Instantiation Options
% 0.51/0.74  
% 0.51/0.74  % --instantiation_flag                  true
% 0.51/0.74  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 0.51/0.74  % --inst_solver_per_active              750
% 0.51/0.74  % --inst_solver_calls_frac              0.5
% 0.51/0.74  % --inst_passive_queue_type             priority_queues
% 0.51/0.74  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.51/0.74  % --inst_passive_queues_freq            [25;2]
% 0.51/0.74  % --inst_dismatching                    true
% 0.51/0.74  % --inst_eager_unprocessed_to_passive   true
% 0.51/0.74  % --inst_prop_sim_given                 true
% 0.51/0.74  % --inst_prop_sim_new                   false
% 0.51/0.74  % --inst_orphan_elimination             true
% 0.51/0.74  % --inst_learning_loop_flag             true
% 0.51/0.74  % --inst_learning_start                 3000
% 0.51/0.74  % --inst_learning_factor                2
% 0.51/0.74  % --inst_start_prop_sim_after_learn     3
% 0.51/0.74  % --inst_sel_renew                      solver
% 0.51/0.74  % --inst_lit_activity_flag              true
% 0.51/0.74  % --inst_out_proof                      true
% 0.51/0.74  
% 0.51/0.74  % ------ Resolution Options
% 0.51/0.74  
% 0.51/0.74  % --resolution_flag                     true
% 0.51/0.74  % --res_lit_sel                         kbo_max
% 0.51/0.74  % --res_to_prop_solver                  none
% 0.51/0.74  % --res_prop_simpl_new                  false
% 0.51/0.74  % --res_prop_simpl_given                false
% 0.51/0.74  % --res_passive_queue_type              priority_queues
% 0.51/0.74  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.51/0.74  % --res_passive_queues_freq             [15;5]
% 0.51/0.74  % --res_forward_subs                    full
% 0.51/0.74  % --res_backward_subs                   full
% 0.51/0.74  % --res_forward_subs_resolution         true
% 0.51/0.74  % --res_backward_subs_resolution        true
% 0.51/0.74  % --res_orphan_elimination              false
% 0.51/0.74  % --res_time_limit                      1000.
% 0.51/0.74  % --res_out_proof                       true
% 0.51/0.74  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_bf605d.s
% 0.51/0.74  % --modulo                              true
% 0.51/0.74  
% 0.51/0.74  % ------ Combination Options
% 0.51/0.74  
% 0.51/0.74  % --comb_res_mult                       1000
% 0.51/0.74  % --comb_inst_mult                      300
% 0.51/0.74  % ------ 
% 0.51/0.74  
% 0.51/0.74  % ------ Parsing...% 
% 0.51/0.74  
% 0.51/0.74  
% 0.51/0.74  % ------                             Statistics
% 0.51/0.74  
% 0.51/0.74  % ------ General
% 0.51/0.74  
% 0.51/0.74  % num_of_input_clauses:                 857
% 0.51/0.74  % num_of_input_neg_conjectures:         0
% 0.51/0.74  % num_of_splits:                        0
% 0.51/0.74  % num_of_split_atoms:                   0
% 0.51/0.74  % num_of_sem_filtered_clauses:          0
% 0.51/0.74  % num_of_subtypes:                      0
% 0.51/0.74  % monotx_restored_types:                0
% 0.51/0.74  % sat_num_of_epr_types:                 0
% 0.51/0.74  % sat_num_of_non_cyclic_types:          0
% 0.51/0.74  % sat_guarded_non_collapsed_types:      0
% 0.51/0.74  % is_epr:                               0
% 0.51/0.74  % is_horn:                              0
% 0.51/0.74  % has_eq:                               0
% 0.51/0.74  % num_pure_diseq_elim:                  0
% 0.51/0.74  % simp_replaced_by:                     0
% 0.51/0.74  % res_preprocessed:                     0
% 0.51/0.74  % prep_upred:                           0
% 0.51/0.74  % prep_unflattend:                      0
% 0.51/0.74  % pred_elim_cands:                      0
% 0.51/0.74  % pred_elim:                            0
% 0.51/0.74  % pred_elim_cl:                         0
% 0.51/0.74  % pred_elim_cycles:                     0
% 0.51/0.74  % forced_gc_time:                       0
% 0.51/0.74  % gc_basic_clause_elim:                 0
% 0.51/0.74  % parsing_time:                         0.
% 0.51/0.74  % sem_filter_time:                      0.
% 0.51/0.74  % pred_elim_time:                       0.
% 0.51/0.74  % out_proof_time:                       0.
% 0.51/0.74  % monotx_time:                          0.
% 0.51/0.74  % subtype_inf_time:                     0.
% 0.51/0.74  % unif_index_cands_time:                0.
% 0.51/0.74  % uFatal error: exception Failure("Parse error in: /export/starexec/sandbox/tmp/iprover_modulo_db5cba.p line: 860 near token: '!='")
% 0.51/0.74  nif_index_add_time:                  0.
% 0.51/0.74  % total_time:                           0.052
% 0.51/0.74  % num_of_symbols:                       114
% 0.51/0.74  % num_of_terms:                         1573
% 0.51/0.74  
% 0.51/0.74  % ------ Propositional Solver
% 0.51/0.74  
% 0.51/0.74  % prop_solver_calls:                    0
% 0.51/0.74  % prop_fast_solver_calls:               0
% 0.51/0.74  % prop_num_of_clauses:                  0
% 0.51/0.74  % prop_preprocess_simplified:           0
% 0.51/0.74  % prop_fo_subsumed:                     0
% 0.51/0.74  % prop_solver_time:                     0.
% 0.51/0.74  % prop_fast_solver_time:                0.
% 0.51/0.74  % prop_unsat_core_time:                 0.
% 0.51/0.74  
% 0.51/0.74  % ------ QBF 
% 0.51/0.74  
% 0.51/0.74  % qbf_q_res:                            0
% 0.51/0.74  % qbf_num_tautologies:                  0
% 0.51/0.74  % qbf_prep_cycles:                      0
% 0.51/0.74  
% 0.51/0.74  % ------ BMC1
% 0.51/0.74  
% 0.51/0.74  % bmc1_current_bound:                   -1
% 0.51/0.74  % bmc1_last_solved_bound:               -1
% 0.51/0.74  % bmc1_unsat_core_size:                 -1
% 0.51/0.74  % bmc1_unsat_core_parents_size:         -1
% 0.51/0.74  % bmc1_merge_next_fun:                  0
% 0.51/0.74  % bmc1_unsat_core_clauses_time:         0.
% 0.51/0.74  
% 0.51/0.74  % ------ Instantiation
% 0.51/0.74  
% 0.51/0.74  % inst_num_of_clauses:                  undef
% 0.51/0.74  % inst_num_in_passive:                  undef
% 0.51/0.74  % inst_num_in_active:                   0
% 0.51/0.74  % inst_num_in_unprocessed:              0
% 0.51/0.74  % inst_num_of_loops:                    0
% 0.51/0.74  % inst_num_of_learning_restarts:        0
% 0.51/0.74  % inst_num_moves_active_passive:        0
% 0.51/0.74  % inst_lit_activity:                    0
% 0.51/0.74  % inst_lit_activity_moves:              0
% 0.51/0.74  % inst_num_tautologies:                 0
% 0.51/0.74  % inst_num_prop_implied:                0
% 0.51/0.74  % inst_num_existing_simplified:         0
% 0.51/0.74  % inst_num_eq_res_simplified:           0
% 0.51/0.74  % inst_num_child_elim:                  0
% 0.51/0.74  % inst_num_of_dismatching_blockings:    0
% 0.51/0.74  % inst_num_of_non_proper_insts:         0
% 0.51/0.74  % inst_num_of_duplicates:               0
% 0.51/0.74  % inst_inst_num_from_inst_to_res:       0
% 0.51/0.74  % inst_dismatching_checking_time:       0.
% 0.51/0.74  
% 0.51/0.74  % ------ Resolution
% 0.51/0.74  
% 0.51/0.74  % res_num_of_clauses:                   undef
% 0.51/0.74  % res_num_in_passive:                   undef
% 0.51/0.74  % res_num_in_active:                    0
% 0.51/0.74  % res_num_of_loops:                     0
% 0.51/0.74  % res_forward_subset_subsumed:          0
% 0.51/0.74  % res_backward_subset_subsumed:         0
% 0.51/0.74  % res_forward_subsumed:                 0
% 0.51/0.74  % res_backward_subsumed:                0
% 0.51/0.74  % res_forward_subsumption_resolution:   0
% 0.51/0.74  % res_backward_subsumption_resolution:  0
% 0.51/0.74  % res_clause_to_clause_subsumption:     0
% 0.51/0.74  % res_orphan_elimination:               0
% 0.51/0.74  % res_tautology_del:                    0
% 0.51/0.74  % res_num_eq_res_simplified:            0
% 0.51/0.74  % res_num_sel_changes:                  0
% 0.51/0.74  % res_moves_from_active_to_pass:        0
% 0.51/0.74  
% 0.51/0.74  % Status Unknown
% 0.61/1.03  % Orienting using strategy ClausalAll
% 0.61/1.03  % FOF problem with conjecture
% 0.61/1.03  % 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_bf605d.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_db5cba.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_a17f47 | grep -v "SZS"
% 0.91/1.05  
% 0.91/1.05  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.91/1.05  
% 0.91/1.05  % 
% 0.91/1.05  % ------  iProver source info 
% 0.91/1.05  
% 0.91/1.05  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.91/1.05  % git: non_committed_changes: true
% 0.91/1.05  % git: last_make_outside_of_git: true
% 0.91/1.05  
% 0.91/1.05  % 
% 0.91/1.05  % ------ Input Options
% 0.91/1.05  
% 0.91/1.05  % --out_options                         all
% 0.91/1.05  % --tptp_safe_out                       true
% 0.91/1.05  % --problem_path                        ""
% 0.91/1.05  % --include_path                        ""
% 0.91/1.05  % --clausifier                          .//eprover
% 0.91/1.05  % --clausifier_options                  --tstp-format  
% 0.91/1.05  % --stdin                               false
% 0.91/1.05  % --dbg_backtrace                       false
% 0.91/1.05  % --dbg_dump_prop_clauses               false
% 0.91/1.05  % --dbg_dump_prop_clauses_file          -
% 0.91/1.05  % --dbg_out_stat                        false
% 0.91/1.05  
% 0.91/1.05  % ------ General Options
% 0.91/1.05  
% 0.91/1.05  % --fof                                 false
% 0.91/1.05  % --time_out_real                       150.
% 0.91/1.05  % --time_out_prep_mult                  0.2
% 0.91/1.05  % --time_out_virtual                    -1.
% 0.91/1.05  % --schedule                            none
% 0.91/1.05  % --ground_splitting                    input
% 0.91/1.05  % --splitting_nvd                       16
% 0.91/1.05  % --non_eq_to_eq                        false
% 0.91/1.05  % --prep_gs_sim                         true
% 0.91/1.05  % --prep_unflatten                      false
% 0.91/1.05  % --prep_res_sim                        true
% 0.91/1.05  % --prep_upred                          true
% 0.91/1.05  % --res_sim_input                       true
% 0.91/1.05  % --clause_weak_htbl                    true
% 0.91/1.05  % --gc_record_bc_elim                   false
% 0.91/1.05  % --symbol_type_check                   false
% 0.91/1.05  % --clausify_out                        false
% 0.91/1.05  % --large_theory_mode                   false
% 0.91/1.05  % --prep_sem_filter                     none
% 0.91/1.05  % --prep_sem_filter_out                 false
% 0.91/1.05  % --preprocessed_out                    false
% 0.91/1.05  % --sub_typing                          false
% 0.91/1.05  % --brand_transform                     false
% 0.91/1.05  % --pure_diseq_elim                     true
% 0.91/1.05  % --min_unsat_core                      false
% 0.91/1.05  % --pred_elim                           true
% 0.91/1.05  % --add_important_lit                   false
% 0.91/1.05  % --soft_assumptions                    false
% 0.91/1.05  % --reset_solvers                       false
% 0.91/1.05  % --bc_imp_inh                          []
% 0.91/1.05  % --conj_cone_tolerance                 1.5
% 0.91/1.05  % --prolific_symb_bound                 500
% 0.91/1.05  % --lt_threshold                        2000
% 0.91/1.05  
% 0.91/1.05  % ------ SAT Options
% 0.91/1.05  
% 0.91/1.05  % --sat_mode                            false
% 0.91/1.05  % --sat_fm_restart_options              ""
% 0.91/1.05  % --sat_gr_def                          false
% 0.91/1.05  % --sat_epr_types                       true
% 0.91/1.05  % --sat_non_cyclic_types                false
% 0.91/1.05  % --sat_finite_models                   false
% 0.91/1.05  % --sat_fm_lemmas                       false
% 0.91/1.05  % --sat_fm_prep                         false
% 0.91/1.05  % --sat_fm_uc_incr                      true
% 0.91/1.05  % --sat_out_model                       small
% 0.91/1.05  % --sat_out_clauses                     false
% 0.91/1.05  
% 0.91/1.05  % ------ QBF Options
% 0.91/1.05  
% 0.91/1.05  % --qbf_mode                            false
% 0.91/1.05  % --qbf_elim_univ                       true
% 0.91/1.05  % --qbf_sk_in                           true
% 0.91/1.05  % --qbf_pred_elim                       true
% 0.91/1.05  % --qbf_split                           32
% 0.91/1.05  
% 0.91/1.05  % ------ BMC1 Options
% 0.91/1.05  
% 0.91/1.05  % --bmc1_incremental                    false
% 0.91/1.05  % --bmc1_axioms                         reachable_all
% 0.91/1.05  % --bmc1_min_bound                      0
% 0.91/1.05  % --bmc1_max_bound                      -1
% 0.91/1.05  % --bmc1_max_bound_default              -1
% 0.91/1.05  % --bmc1_symbol_reachability            true
% 0.91/1.05  % --bmc1_property_lemmas                false
% 0.91/1.05  % --bmc1_k_induction                    false
% 0.91/1.05  % --bmc1_non_equiv_states               false
% 0.91/1.05  % --bmc1_deadlock                       false
% 0.91/1.05  % --bmc1_ucm                            false
% 0.91/1.05  % --bmc1_add_unsat_core                 none
% 0.91/1.05  % --bmc1_unsat_core_children            false
% 0.91/1.05  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.91/1.05  % --bmc1_out_stat                       full
% 0.91/1.05  % --bmc1_ground_init                    false
% 0.91/1.05  % --bmc1_pre_inst_next_state            false
% 0.91/1.05  % --bmc1_pre_inst_state                 false
% 0.91/1.05  % --bmc1_pre_inst_reach_state           false
% 0.91/1.05  % --bmc1_out_unsat_core                 false
% 0.91/1.05  % --bmc1_aig_witness_out                false
% 0.91/1.05  % --bmc1_verbose                        false
% 0.91/1.05  % --bmc1_dump_clauses_tptp              false
% 4.65/4.85  % --bmc1_dump_unsat_core_tptp           false
% 4.65/4.85  % --bmc1_dump_file                      -
% 4.65/4.85  % --bmc1_ucm_expand_uc_limit            128
% 4.65/4.85  % --bmc1_ucm_n_expand_iterations        6
% 4.65/4.85  % --bmc1_ucm_extend_mode                1
% 4.65/4.85  % --bmc1_ucm_init_mode                  2
% 4.65/4.85  % --bmc1_ucm_cone_mode                  none
% 4.65/4.85  % --bmc1_ucm_reduced_relation_type      0
% 4.65/4.85  % --bmc1_ucm_relax_model                4
% 4.65/4.85  % --bmc1_ucm_full_tr_after_sat          true
% 4.65/4.85  % --bmc1_ucm_expand_neg_assumptions     false
% 4.65/4.85  % --bmc1_ucm_layered_model              none
% 4.65/4.85  % --bmc1_ucm_max_lemma_size             10
% 4.65/4.85  
% 4.65/4.85  % ------ AIG Options
% 4.65/4.85  
% 4.65/4.85  % --aig_mode                            false
% 4.65/4.85  
% 4.65/4.85  % ------ Instantiation Options
% 4.65/4.85  
% 4.65/4.85  % --instantiation_flag                  true
% 4.65/4.85  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 4.65/4.85  % --inst_solver_per_active              750
% 4.65/4.85  % --inst_solver_calls_frac              0.5
% 4.65/4.85  % --inst_passive_queue_type             priority_queues
% 4.65/4.85  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 4.65/4.85  % --inst_passive_queues_freq            [25;2]
% 4.65/4.85  % --inst_dismatching                    true
% 4.65/4.85  % --inst_eager_unprocessed_to_passive   true
% 4.65/4.85  % --inst_prop_sim_given                 true
% 4.65/4.85  % --inst_prop_sim_new                   false
% 4.65/4.85  % --inst_orphan_elimination             true
% 4.65/4.85  % --inst_learning_loop_flag             true
% 4.65/4.85  % --inst_learning_start                 3000
% 4.65/4.85  % --inst_learning_factor                2
% 4.65/4.85  % --inst_start_prop_sim_after_learn     3
% 4.65/4.85  % --inst_sel_renew                      solver
% 4.65/4.85  % --inst_lit_activity_flag              true
% 4.65/4.85  % --inst_out_proof                      true
% 4.65/4.85  
% 4.65/4.85  % ------ Resolution Options
% 4.65/4.85  
% 4.65/4.85  % --resolution_flag                     true
% 4.65/4.85  % --res_lit_sel                         kbo_max
% 4.65/4.85  % --res_to_prop_solver                  none
% 4.65/4.85  % --res_prop_simpl_new                  false
% 4.65/4.85  % --res_prop_simpl_given                false
% 4.65/4.85  % --res_passive_queue_type              priority_queues
% 4.65/4.85  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 4.65/4.85  % --res_passive_queues_freq             [15;5]
% 4.65/4.85  % --res_forward_subs                    full
% 4.65/4.85  % --res_backward_subs                   full
% 4.65/4.85  % --res_forward_subs_resolution         true
% 4.65/4.85  % --res_backward_subs_resolution        true
% 4.65/4.85  % --res_orphan_elimination              false
% 4.65/4.85  % --res_time_limit                      1000.
% 4.65/4.85  % --res_out_proof                       true
% 4.65/4.85  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_bf605d.s
% 4.65/4.85  % --modulo                              true
% 4.65/4.85  
% 4.65/4.85  % ------ Combination Options
% 4.65/4.85  
% 4.65/4.85  % --comb_res_mult                       1000
% 4.65/4.85  % --comb_inst_mult                      300
% 4.65/4.85  % ------ 
% 4.65/4.85  
% 4.65/4.85  % ------ Parsing...% successful
% 4.65/4.85  
% 4.65/4.85  % ------ 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 % 
% 4.65/4.85  
% 4.65/4.85  % ------ Proving...
% 4.65/4.85  % ------ Problem Properties 
% 4.65/4.85  
% 4.65/4.85  % 
% 4.65/4.85  % EPR                                   false
% 4.65/4.85  % Horn                                  false
% 4.65/4.85  % Has equality                          true
% 4.65/4.85  
% 4.65/4.85  % % ------ Input Options Time Limit: Unbounded
% 4.65/4.85  
% 4.65/4.85  
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  Compiling...
% 4.65/4.85  Loading plugin: done.
% 4.65/4.85  % % ------ Current options:
% 4.65/4.85  
% 4.65/4.85  % ------ Input Options
% 4.65/4.85  
% 4.65/4.85  % --out_options                         all
% 4.65/4.85  % --tptp_safe_out                       true
% 4.65/4.85  % --problem_path                        ""
% 4.65/4.85  % --include_path                        ""
% 4.65/4.85  % --clausifier                          .//eprover
% 4.65/4.85  % --clausifier_options                  --tstp-format  
% 4.65/4.85  % --stdin                               false
% 4.65/4.85  % --dbg_backtrace                       false
% 4.65/4.85  % --dbg_dump_prop_clauses               false
% 4.65/4.85  % --dbg_dump_prop_clauses_file          -
% 4.65/4.85  % --dbg_out_stat                        false
% 4.65/4.85  
% 4.65/4.85  % ------ General Options
% 4.65/4.85  
% 4.65/4.85  % --fof                                 false
% 4.65/4.85  % --time_out_real                       150.
% 4.65/4.85  % --time_out_prep_mult                  0.2
% 4.65/4.85  % --time_out_virtual                    -1.
% 4.65/4.85  % --schedule                            none
% 4.65/4.85  % --ground_splitting                    input
% 4.65/4.85  % --splitting_nvd                       16
% 4.65/4.85  % --non_eq_to_eq                        false
% 4.65/4.85  % --prep_gs_sim                         true
% 4.65/4.85  % --prep_unflatten                      false
% 4.65/4.85  % --prep_res_sim                        true
% 4.65/4.85  % --prep_upred                          true
% 4.65/4.85  % --res_sim_input                       true
% 4.65/4.85  % --clause_weak_htbl                    true
% 4.65/4.85  % --gc_record_bc_elim                   false
% 4.65/4.85  % --symbol_type_check                   false
% 4.65/4.85  % --clausify_out                        false
% 4.65/4.85  % --large_theory_mode                   false
% 4.65/4.85  % --prep_sem_filter                     none
% 4.65/4.85  % --prep_sem_filter_out                 false
% 4.65/4.85  % --preprocessed_out                    false
% 4.65/4.85  % --sub_typing                          false
% 4.65/4.85  % --brand_transform                     false
% 4.65/4.85  % --pure_diseq_elim                     true
% 4.65/4.85  % --min_unsat_core                      false
% 4.65/4.85  % --pred_elim                           true
% 4.65/4.85  % --add_important_lit                   false
% 4.65/4.85  % --soft_assumptions                    false
% 4.65/4.85  % --reset_solvers                       false
% 4.65/4.85  % --bc_imp_inh                          []
% 4.65/4.85  % --conj_cone_tolerance                 1.5
% 4.65/4.85  % --prolific_symb_bound                 500
% 4.65/4.85  % --lt_threshold                        2000
% 4.65/4.85  
% 4.65/4.85  % ------ SAT Options
% 4.65/4.85  
% 4.65/4.85  % --sat_mode                            false
% 4.65/4.85  % --sat_fm_restart_options              ""
% 4.65/4.85  % --sat_gr_def                          false
% 4.65/4.85  % --sat_epr_types                       true
% 4.65/4.85  % --sat_non_cyclic_types                false
% 4.65/4.85  % --sat_finite_models                   false
% 4.65/4.85  % --sat_fm_lemmas                       false
% 4.65/4.85  % --sat_fm_prep                         false
% 4.65/4.85  % --sat_fm_uc_incr                      true
% 4.65/4.85  % --sat_out_model                       small
% 4.65/4.85  % --sat_out_clauses                     false
% 4.65/4.85  
% 4.65/4.85  % ------ QBF Options
% 4.65/4.85  
% 4.65/4.85  % --qbf_mode                            false
% 4.65/4.85  % --qbf_elim_univ                       true
% 4.65/4.85  % --qbf_sk_in                           true
% 4.65/4.85  % --qbf_pred_elim                       true
% 4.65/4.85  % --qbf_split                           32
% 4.65/4.85  
% 4.65/4.85  % ------ BMC1 Options
% 4.65/4.85  
% 4.65/4.85  % --bmc1_incremental                    false
% 4.65/4.85  % --bmc1_axioms                         reachable_all
% 4.65/4.85  % --bmc1_min_bound                      0
% 4.65/4.85  % --bmc1_max_bound                      -1
% 4.65/4.85  % --bmc1_max_bound_default              -1
% 4.65/4.85  % --bmc1_symbol_reachability            true
% 4.65/4.85  % --bmc1_property_lemmas                false
% 4.65/4.85  % --bmc1_k_induction                    false
% 4.65/4.85  % --bmc1_non_equiv_states               false
% 4.65/4.85  % --bmc1_deadlock                       false
% 4.65/4.85  % --bmc1_ucm                            false
% 4.65/4.85  % --bmc1_add_unsat_core                 none
% 4.65/4.85  % --bmc1_unsat_core_children            false
% 4.65/4.85  % --bmc1_unsat_core_extrapolate_axioms  false
% 4.65/4.85  % --bmc1_out_stat                       full
% 4.65/4.85  % --bmc1_ground_init                    false
% 4.65/4.85  % --bmc1_pre_inst_next_state            false
% 4.65/4.85  % --bmc1_pre_inst_state                 false
% 4.65/4.85  % --bmc1_pre_inst_reach_state           false
% 4.65/4.85  % --bmc1_out_unsat_core                 false
% 4.65/4.85  % --bmc1_aig_witness_out                false
% 4.65/4.85  % --bmc1_verbose                        false
% 4.65/4.85  % --bmc1_dump_clauses_tptp              false
% 4.65/4.85  % --bmc1_dump_unsat_core_tptp           false
% 4.65/4.85  % --bmc1_dump_file                      -
% 4.65/4.85  % --bmc1_ucm_expand_uc_limit            128
% 4.65/4.85  % --bmc1_ucm_n_expand_iterations        6
% 4.65/4.85  % --bmc1_ucm_extend_mode                1
% 4.65/4.85  % --bmc1_ucm_init_mode                  2
% 4.65/4.85  % --bmc1_ucm_cone_mode                  none
% 4.65/4.85  % --bmc1_ucm_reduced_relation_type      0
% 4.65/4.85  % --bmc1_ucm_relax_model                4
% 4.65/4.85  % --bmc1_ucm_full_tr_after_sat          true
% 4.65/4.85  % --bmc1_ucm_expand_neg_assumptions     false
% 4.65/4.85  % --bmc1_ucm_layered_model              none
% 5.86/6.06  % --bmc1_ucm_max_lemma_size             10
% 5.86/6.06  
% 5.86/6.06  % ------ AIG Options
% 5.86/6.06  
% 5.86/6.06  % --aig_mode                            false
% 5.86/6.06  
% 5.86/6.06  % ------ Instantiation Options
% 5.86/6.06  
% 5.86/6.06  % --instantiation_flag                  true
% 5.86/6.06  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 5.86/6.06  % --inst_solver_per_active              750
% 5.86/6.06  % --inst_solver_calls_frac              0.5
% 5.86/6.06  % --inst_passive_queue_type             priority_queues
% 5.86/6.06  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 5.86/6.06  % --inst_passive_queues_freq            [25;2]
% 5.86/6.06  % --inst_dismatching                    true
% 5.86/6.06  % --inst_eager_unprocessed_to_passive   true
% 5.86/6.06  % --inst_prop_sim_given                 true
% 5.86/6.06  % --inst_prop_sim_new                   false
% 5.86/6.06  % --inst_orphan_elimination             true
% 5.86/6.06  % --inst_learning_loop_flag             true
% 5.86/6.06  % --inst_learning_start                 3000
% 5.86/6.06  % --inst_learning_factor                2
% 5.86/6.06  % --inst_start_prop_sim_after_learn     3
% 5.86/6.06  % --inst_sel_renew                      solver
% 5.86/6.06  % --inst_lit_activity_flag              true
% 5.86/6.06  % --inst_out_proof                      true
% 5.86/6.06  
% 5.86/6.06  % ------ Resolution Options
% 5.86/6.06  
% 5.86/6.06  % --resolution_flag                     true
% 5.86/6.06  % --res_lit_sel                         kbo_max
% 5.86/6.06  % --res_to_prop_solver                  none
% 5.86/6.06  % --res_prop_simpl_new                  false
% 5.86/6.06  % --res_prop_simpl_given                false
% 5.86/6.06  % --res_passive_queue_type              priority_queues
% 5.86/6.06  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 5.86/6.06  % --res_passive_queues_freq             [15;5]
% 5.86/6.06  % --res_forward_subs                    full
% 5.86/6.06  % --res_backward_subs                   full
% 5.86/6.06  % --res_forward_subs_resolution         true
% 5.86/6.06  % --res_backward_subs_resolution        true
% 5.86/6.06  % --res_orphan_elimination              false
% 5.86/6.06  % --res_time_limit                      1000.
% 5.86/6.06  % --res_out_proof                       true
% 5.86/6.06  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_bf605d.s
% 5.86/6.06  % --modulo                              true
% 5.86/6.06  
% 5.86/6.06  % ------ Combination Options
% 5.86/6.06  
% 5.86/6.06  % --comb_res_mult                       1000
% 5.86/6.06  % --comb_inst_mult                      300
% 5.86/6.06  % ------ 
% 5.86/6.06  
% 5.86/6.06  
% 5.86/6.06  
% 5.86/6.06  % ------ Proving...
% 5.86/6.06  % 
% 5.86/6.06  
% 5.86/6.06  
% 5.86/6.06  % ------                             Statistics
% 5.86/6.06  
% 5.86/6.06  % ------ General
% 5.86/6.06  
% 5.86/6.06  % num_of_input_clauses:                 4081
% 5.86/6.06  % num_of_input_neg_conjectures:         1
% 5.86/6.06  % num_of_splits:                        0
% 5.86/6.06  % num_of_split_atoms:                   0
% 5.86/6.06  % num_of_sem_filtered_clauses:          0
% 5.86/6.06  % num_of_subtypes:                      0
% 5.86/6.06  % monotx_restored_types:                0
% 5.86/6.06  % sat_num_of_epr_types:                 0
% 5.86/6.06  % sat_num_of_non_cyclic_types:          0
% 5.86/6.06  % sat_guarded_non_collapsed_types:      0
% 5.86/6.06  % is_epr:                               0
% 5.86/6.06  % is_horn:                              0
% 5.86/6.06  % has_eq:                               1
% 5.86/6.06  % num_pure_diseq_elim:                  0
% 5.86/6.06  % simp_replaced_by:                     0
% 5.86/6.06  % res_preprocessed:                     3
% 5.86/6.06  % prep_upred:                           0
% 5.86/6.06  % prep_unflattend:                      0
% 5.86/6.06  % pred_elim_cands:                      0
% 5.86/6.06  % pred_elim:                            0
% 5.86/6.06  % pred_elim_cl:                         0
% 5.86/6.06  % pred_elim_cycles:                     0
% 5.86/6.06  % forced_gc_time:                       0
% 5.86/6.06  % gc_basic_clause_elim:                 0
% 5.86/6.06  % parsing_time:                         0.171
% 5.86/6.06  % sem_filter_time:                      0.
% 5.86/6.06  % pred_elim_time:                       0.
% 5.86/6.06  % out_proof_time:                       0.001
% 5.86/6.06  % monotx_time:                          0.
% 5.86/6.06  % subtype_inf_time:                     0.
% 5.86/6.06  % unif_index_cands_time:                0.004
% 5.86/6.06  % unif_index_add_time:                  0.006
% 5.86/6.06  % total_time:                           5.023
% 5.86/6.06  % num_of_symbols:                       132
% 5.86/6.06  % num_of_terms:                         68259
% 5.86/6.06  
% 5.86/6.06  % ------ Propositional Solver
% 5.86/6.06  
% 5.86/6.06  % prop_solver_calls:                    2
% 5.86/6.06  % prop_fast_solver_calls:               7
% 5.86/6.06  % prop_num_of_clauses:                  3073
% 5.86/6.06  % prop_preprocess_simplified:           20763
% 5.86/6.06  % prop_fo_subsumed:                     1
% 5.86/6.06  % prop_solver_time:                     0.001
% 5.86/6.06  % prop_fast_solver_time:                0.
% 5.86/6.06  % prop_unsat_core_time:                 0.
% 5.86/6.06  
% 5.86/6.06  % ------ QBF 
% 5.86/6.06  
% 5.86/6.06  % qbf_q_res:                            0
% 5.86/6.06  % qbf_num_tautologies:                  0
% 5.86/6.06  % qbf_prep_cycles:                      0
% 5.86/6.06  
% 5.86/6.06  % ------ BMC1
% 5.86/6.06  
% 5.86/6.06  % bmc1_current_bound:                   -1
% 5.86/6.06  % bmc1_last_solved_bound:               -1
% 5.86/6.06  % bmc1_unsat_core_size:                 -1
% 5.86/6.06  % bmc1_unsat_core_parents_size:         -1
% 5.86/6.06  % bmc1_merge_next_fun:                  0
% 5.86/6.06  % bmc1_unsat_core_clauses_time:         0.
% 5.86/6.06  
% 5.86/6.06  % ------ Instantiation
% 5.86/6.06  
% 5.86/6.06  % inst_num_of_clauses:                  3682
% 5.86/6.06  % inst_num_in_passive:                  3437
% 5.86/6.06  % inst_num_in_active:                   243
% 5.86/6.06  % inst_num_in_unprocessed:              0
% 5.86/6.06  % inst_num_of_loops:                    245
% 5.86/6.06  % inst_num_of_learning_restarts:        0
% 5.86/6.06  % inst_num_moves_active_passive:        0
% 5.86/6.06  % inst_lit_activity:                    2
% 5.86/6.06  % inst_lit_activity_moves:              0
% 5.86/6.06  % inst_num_tautologies:                 0
% 5.86/6.06  % inst_num_prop_implied:                0
% 5.86/6.06  % inst_num_existing_simplified:         0
% 5.86/6.06  % inst_num_eq_res_simplified:           0
% 5.86/6.06  % inst_num_child_elim:                  0
% 5.86/6.06  % inst_num_of_dismatching_blockings:    0
% 5.86/6.06  % inst_num_of_non_proper_insts:         1
% 5.86/6.06  % inst_num_of_duplicates:               0
% 5.86/6.06  % inst_inst_num_from_inst_to_res:       0
% 5.86/6.06  % inst_dismatching_checking_time:       0.
% 5.86/6.06  
% 5.86/6.06  % ------ Resolution
% 5.86/6.06  
% 5.86/6.06  % res_num_of_clauses:                   32132
% 5.86/6.06  % res_num_in_passive:                   27207
% 5.86/6.06  % res_num_in_active:                    2304
% 5.86/6.06  % res_num_of_loops:                     1000
% 5.86/6.06  % res_forward_subset_subsumed:          9154
% 5.86/6.06  % res_backward_subset_subsumed:         120
% 5.86/6.06  % res_forward_subsumed:                 187
% 5.86/6.06  % res_backward_subsumed:                9
% 5.86/6.06  % res_forward_subsumption_resolution:   10
% 5.86/6.06  % res_backward_subsumption_resolution:  0
% 5.86/6.06  % res_clause_to_clause_subsumption:     3569
% 5.86/6.06  % res_orphan_elimination:               0
% 5.86/6.06  % res_tautology_del:                    181
% 5.86/6.06  % res_num_eq_res_simplified:            19
% 5.86/6.06  % res_num_sel_changes:                  0
% 5.86/6.06  % res_moves_from_active_to_pass:        0
% 5.86/6.06  
% 5.86/6.06  % Status Unsatisfiable
% 5.86/6.06  % SZS status Theorem
% 5.86/6.06  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------