TSTP Solution File: SWW203+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW203+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 : 0s
% DateTime : Wed Jul 20 23:21:12 EDT 2022
% Result : Timeout 300.03s 300.51s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW203+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon Jun 6 10:15:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.89/1.46 *** allocated 10000 integers for termspace/termends
% 0.89/1.46 *** allocated 10000 integers for clauses
% 0.89/1.46 *** allocated 10000 integers for justifications
% 0.89/1.46 *** allocated 15000 integers for termspace/termends
% 0.89/1.46 *** allocated 22500 integers for termspace/termends
% 0.89/1.46 *** allocated 33750 integers for termspace/termends
% 0.89/1.46 Bliksem 1.12
% 0.89/1.46
% 0.89/1.46
% 0.89/1.46 Automatic Strategy Selection
% 0.89/1.46
% 0.89/1.46 *** allocated 50625 integers for termspace/termends
% 0.89/1.46 *** allocated 75937 integers for termspace/termends
% 0.89/1.46 *** allocated 113905 integers for termspace/termends
% 0.89/1.46
% 0.89/1.46 Clauses:
% 0.89/1.46
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_Complex_ORe( v_x ),
% 0.89/1.46 c_Complex_ORe( v_y ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.89/1.46 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.89/1.46 ( c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_Complex_OIm( v_x ),
% 0.89/1.46 c_Complex_OIm( v_y ) ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.89/1.46 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_Complex_ORe( v_x ),
% 0.89/1.46 c_Complex_ORe( v_y ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.89/1.46 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ), c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_RealDef_Oreal, c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_Complex_OIm( v_x ),
% 0.89/1.46 c_Complex_OIm( v_y ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.89/1.46 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), c_NthRoot_Osqrt(
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), c_NthRoot_Osqrt(
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, T,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ), c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_RealDef_Oreal, c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.89/1.46 { c_NthRoot_Osqrt( c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }
% 0.89/1.46 .
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.89/1.46 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.89/1.46 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), c_Power_Opower__class_Opower( X,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, Y ), c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.89/1.46 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.89/1.46 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.89/1.46 ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.89/1.46 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.89/1.46 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.89/1.46 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.89/1.46 Y ) ) ) ) }.
% 0.89/1.46 { c_Complex_OIm( c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X )
% 0.89/1.46 ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_Complex_OIm( Y )
% 0.89/1.46 , c_Complex_OIm( X ) ) }.
% 0.89/1.46 { c_Complex_ORe( c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X )
% 0.89/1.46 ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_Complex_ORe( Y )
% 0.89/1.46 , c_Complex_ORe( X ) ) }.
% 0.89/1.46 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.89/1.46 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.89/1.46 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.89/1.46 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.89/1.46 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.89/1.46 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.89/1.46 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.89/1.46 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.89/1.46 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.89/1.46 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.89/1.46 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.89/1.46 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.89/1.46 ) }.
% 0.89/1.46 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.89/1.46 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.89/1.46 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.89/1.46 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.89/1.46 { ! c_NthRoot_Osqrt( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.89/1.46 , X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X
% 0.89/1.46 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { c_NthRoot_Osqrt( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.46 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.46 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.46 ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.46 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 Z, Y ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.46 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 Y, Z ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.46 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.46 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.46 .
% 0.89/1.46 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.46 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.46 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.46 .
% 0.89/1.46 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.46 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.46 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.89/1.46 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.46 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.46 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.89/1.46 ) }.
% 0.89/1.46 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.89/1.46 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.46 ) }.
% 0.89/1.46 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.46 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.89/1.46 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.46 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.46 ) }.
% 0.89/1.46 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.46 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.46 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.89/1.46 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.89/1.46 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.46 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.46 }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.46 { c_Complex_ORe( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) )
% 0.89/1.46 = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Complex_ORe( Y ),
% 0.89/1.46 c_Complex_ORe( X ) ) }.
% 0.89/1.46 { c_Complex_OIm( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) )
% 0.89/1.46 = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Complex_OIm( Y ),
% 0.89/1.46 c_Complex_OIm( X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 0.89/1.46 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.89/1.46 .
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.89/1.46 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.89/1.46 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.89/1.46 .
% 0.89/1.46 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 Y, T ), Z = Y }.
% 0.89/1.46 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 T, Y ), Z = Y }.
% 0.89/1.46 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 T, Y ), Z = Y }.
% 0.89/1.46 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 Y, Z ), T = Y }.
% 0.89/1.46 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 Y, Z ) }.
% 0.89/1.46 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 T, Y ), Z = Y }.
% 0.89/1.46 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 T, Y ) }.
% 0.89/1.46 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.89/1.46 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.89/1.46 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.89/1.46 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.89/1.46 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.89/1.46 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.89/1.46 { ! c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ), Y = X }.
% 0.89/1.46 { ! Y = X, c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ) }.
% 0.89/1.46 { ! class_Rings_Oring__1__no__zero__divisors( X ), !
% 0.89/1.46 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.46 .
% 0.89/1.46 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Rings_Osemiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__semidom( X ), ! c_Power_Opower__class_Opower(
% 0.89/1.46 X, Z, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.89/1.46 c_Int_OBit1( c_Int_OPls ) ) ) ) = c_Power_Opower__class_Opower( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.46 ), Z = Y }.
% 0.89/1.46 { ! class_Rings_Olinordered__semidom( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Z
% 0.89/1.46 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.89/1.46 ( c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.89/1.46 ( X, Z, Y ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.46 X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.89/1.46 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.46 .
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.89/1.46 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.46 .
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.89/1.46 X ), ! Y = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus
% 0.89/1.46 ( X, c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.89/1.46 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.89/1.46 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.46 ( X, c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ), Z =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.46 ( X, c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.89/1.46 X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.89/1.46 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.46 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.89/1.46 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.89/1.46 { ! c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) = X, ! c_Orderings_Oord__class_Oless__eq(
% 0.89/1.46 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.89/1.46 c_NthRoot_Osqrt( X ) = Y }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) = X }.
% 0.89/1.46 { ! c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) = X, c_Orderings_Oord__class_Oless__eq(
% 0.89/1.46 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }
% 0.89/1.46 .
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) = X }.
% 0.89/1.46 { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ) = Y, X = c_Groups_Ozero__class_Ozero(
% 0.89/1.46 tc_RealDef_Oreal ) }.
% 0.89/1.46 { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ) = Y, X = c_Groups_Ozero__class_Ozero(
% 0.89/1.46 tc_RealDef_Oreal ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.46 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.89/1.46 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.89/1.46 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.46 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.89/1.46 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.46 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.46 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.46 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.46 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.89/1.46 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.89/1.46 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.89/1.46 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.89/1.46 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.46 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.89/1.46 ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.89/1.46 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.89/1.46 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.89/1.46 ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.89/1.46 , c_NthRoot_Osqrt( X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y
% 0.89/1.46 ), c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.46 tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.89/1.46 , c_NthRoot_Osqrt( X ) ) }.
% 0.89/1.46 { c_NthRoot_Osqrt( c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y, X ) )
% 0.89/1.46 = c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.89/1.46 X ) }.
% 0.89/1.46 { ! c_Complex_ORe( Y ) = c_Complex_ORe( X ), ! c_Complex_OIm( Y ) =
% 0.89/1.46 c_Complex_OIm( X ), Y = X }.
% 0.89/1.46 { ! Y = X, c_Complex_ORe( Y ) = c_Complex_ORe( X ) }.
% 0.89/1.46 { ! Y = X, c_Complex_OIm( Y ) = c_Complex_OIm( X ) }.
% 0.89/1.46 { ! c_Complex_ORe( Y ) = c_Complex_ORe( X ), ! c_Complex_OIm( Y ) =
% 0.89/1.46 c_Complex_OIm( X ), Y = X }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.46 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.89/1.46 ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.89/1.46 ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.89/1.46 ) }.
% 0.89/1.46 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.89/1.46 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y
% 0.89/1.46 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X
% 0.89/1.46 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }
% 0.89/1.46 .
% 0.89/1.46 { c_Power_Opower__class_Opower( tc_Complex_Ocomplex,
% 0.89/1.46 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( X ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) = X }.
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.46 X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( X, Z ), Y ) ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.46 c_Int_OBit0( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.89/1.46 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.89/1.46 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.46 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.89/1.46 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.89/1.46 , ! c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.89/1.46 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.89/1.46 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.89/1.46 , ! c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.89/1.46 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ), !
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.89/1.46 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.89/1.46 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.89/1.46 ( X, Z, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ), Y ) = Y }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) = Y }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.89/1.46 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.46 c_Int_OPls ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Power_Opower__class_Opower
% 0.89/1.46 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ), X ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.89/1.46 tc_Int_Oint ), X ) = X }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.89/1.46 ( tc_Int_Oint ) ) = X }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.89/1.46 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.89/1.46 { c_Complex_ORe( c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex, X )
% 0.89/1.46 ) = c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ) }.
% 0.89/1.46 { c_Int_OPls = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.89/1.46 { c_Complex_OIm( c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex, X )
% 0.89/1.46 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) }.
% 0.89/1.46 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.89/1.46 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { c_Complex_ORe( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { c_Complex_OIm( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 0.89/1.46 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 0.89/1.46 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 0.89/1.46 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 0.89/1.46 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.89/1.46 { ! c_Int_OBit1( Y ) = c_Int_OBit1( X ), Y = X }.
% 0.89/1.46 { ! Y = X, c_Int_OBit1( Y ) = c_Int_OBit1( X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.89/1.46 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.89/1.46 ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.89/1.46 c_Int_OBit1( X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.89/1.46 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.89/1.46 ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.89/1.46 c_Int_OBit1( X ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OPls )
% 0.89/1.46 }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OPls, X ) = X }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.89/1.46 { ! c_Int_OBit0( Y ) = c_Int_OBit0( X ), Y = X }.
% 0.89/1.46 { ! Y = X, c_Int_OBit0( Y ) = c_Int_OBit0( X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.89/1.46 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.89/1.46 ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.89/1.46 c_Int_OBit0( X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.89/1.46 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.89/1.46 ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.89/1.46 c_Int_OBit0( X ) ) }.
% 0.89/1.46 { c_Int_OBit0( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, X ) }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0(
% 0.89/1.46 X ) ) = c_Int_OBit0( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.89/1.46 .
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.89/1.46 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.89/1.46 ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.46 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.89/1.46 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.46 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.89/1.46 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.89/1.46 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.89/1.46 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 0.89/1.46 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Int_Oint, Z, Y ) ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.46 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.89/1.46 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), ! c_Power_Opower__class_Opower( X, Y, Z
% 0.89/1.46 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.89/1.46 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.89/1.46 , ! c_Power_Opower__class_Opower( X, Z, Y ) = c_Groups_Ozero__class_Ozero
% 0.89/1.46 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.89/1.46 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.89/1.46 , ! c_Power_Opower__class_Opower( X, Z, Y ) = c_Groups_Ozero__class_Ozero
% 0.89/1.46 ( X ), ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.89/1.46 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.89/1.46 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.89/1.46 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( X, Z, Y ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.89/1.46 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.89/1.46 { ! c_Int_OPls = c_Int_OBit1( X ) }.
% 0.89/1.46 { ! c_Int_OBit1( X ) = c_Int_OPls }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1
% 0.89/1.46 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.89/1.46 }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1(
% 0.89/1.46 X ) ) }.
% 0.89/1.46 { ! c_Int_OBit0( Y ) = c_Int_OBit1( X ) }.
% 0.89/1.46 { ! c_Int_OBit1( Y ) = c_Int_OBit0( X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.89/1.46 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.89/1.46 ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.89/1.46 c_Int_OBit1( X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.89/1.46 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.89/1.46 ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.89/1.46 c_Int_OBit1( X ) ) }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1(
% 0.89/1.46 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.89/1.46 .
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0(
% 0.89/1.46 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.89/1.46 .
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.89/1.46 ( X ) ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.89/1.46 ) }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.89/1.46 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.89/1.46 ) }.
% 0.89/1.46 { c_Int_OBit0( c_Int_OPls ) = c_Int_OPls }.
% 0.89/1.46 { ! c_Int_OPls = c_Int_OBit0( X ), c_Int_OPls = X }.
% 0.89/1.46 { ! c_Int_OPls = X, c_Int_OPls = c_Int_OBit0( X ) }.
% 0.89/1.46 { ! c_Int_OBit0( X ) = c_Int_OPls, X = c_Int_OPls }.
% 0.89/1.46 { ! X = c_Int_OPls, c_Int_OBit0( X ) = c_Int_OPls }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0
% 0.89/1.46 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.89/1.46 }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0(
% 0.89/1.46 X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.89/1.46 c_Int_OPls ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.89/1.46 c_Int_OPls ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.89/1.46 c_Int_OPls ) }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.89/1.46 ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls
% 0.89/1.46 , X ) ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.89/1.46 c_Power_Opower__class_Opower( X, Z, Y ) ) = c_Power_Opower__class_Opower
% 0.89/1.46 ( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__semidom( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.46 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.46 ), c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__semidom( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.46 ), c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X
% 0.89/1.46 , Z, T ), c_Power_Opower__class_Opower( X, Y, T ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( X ) ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( X ) ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, T,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.89/1.46 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 0.89/1.46 c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_Complex_ORe( X ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_Complex_OIm( X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.89/1.46 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.89/1.46 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.89/1.46 , Y ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Power_Opower__class_Opower( X,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, Z, Y ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) = c_Groups_Ominus__class_Ominus( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.46 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ), Z ), Y ) ) }.
% 0.89/1.46 { c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, T,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.89/1.46 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, T,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) ) }.
% 0.89/1.46 { c_Power_Opower__class_Opower( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.89/1.46 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_Int_Oint, Z, Y ),
% 0.89/1.46 c_Power_Opower__class_Opower( tc_Int_Oint, Z, X ) ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.89/1.46 ( tc_Int_Oint, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X )
% 0.89/1.46 ) }.
% 0.89/1.46 { c_Power_Opower__class_Opower( tc_Int_Oint, c_Power_Opower__class_Opower(
% 0.89/1.46 tc_Int_Oint, Z, Y ), X ) = c_Power_Opower__class_Opower( tc_Int_Oint, Z,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.89/1.46 ( tc_Int_Oint, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, Y ), X ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Int_Oint, Z, Y ) ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ) ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.89/1.46 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.89/1.46 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 0.89/1.46 { ! class_Groups_Oab__semigroup__mult( X ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.89/1.46 , Y ) ) }.
% 0.89/1.46 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ), Z = X, Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! Z = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.89/1.46 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.89/1.46 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ), Y = X, Z =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.89/1.46 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.89/1.46 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.46 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Otimes__class_Otimes
% 0.89/1.46 ( tc_Int_Oint, X, Y ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, T ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, X ) ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, X ) ) }.
% 0.89/1.46 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, T,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T, Z )
% 0.89/1.46 , c_Power_Opower__class_Opower( X, T, Y ) ) }.
% 0.89/1.46 { ! class_Groups_Ocomm__monoid__mult( X ), c_Power_Opower__class_Opower( X
% 0.89/1.46 , c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T, Y )
% 0.89/1.46 , c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.89/1.46 { ! class_Groups_Omonoid__mult( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Power_Opower__class_Opower( X, Z, Y ), Z ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, Z, c_Power_Opower__class_Opower( X, Z,
% 0.89/1.46 Y ) ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Int_OPls, X ) = c_Int_OPls
% 0.89/1.46 }.
% 0.89/1.46 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, T,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) ) =
% 0.89/1.46 c_Power_Opower__class_Opower( X, c_Power_Opower__class_Opower( X, T, Z )
% 0.89/1.46 , Y ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Int_OBit0( Y ), X ) =
% 0.89/1.46 c_Int_OBit0( c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.89/1.46 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ), Z = Y }.
% 0.89/1.46 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.46 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ), Z = Y }.
% 0.89/1.46 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Int_Oint, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ) )
% 0.89/1.46 }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ), X ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.89/1.46 { c_NthRoot_Osqrt( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X )
% 0.89/1.46 ) = c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y
% 0.89/1.46 ), c_NthRoot_Osqrt( X ) ) }.
% 0.89/1.46 { c_Complex_OIm( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, Y, X )
% 0.89/1.46 ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, c_Complex_ORe( Y ),
% 0.89/1.46 c_Complex_OIm( X ) ), c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_Complex_OIm( Y ), c_Complex_ORe( X ) ) ) }.
% 0.89/1.46 { c_Complex_ORe( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, Y, X )
% 0.89/1.46 ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, c_Complex_ORe( Y ),
% 0.89/1.46 c_Complex_ORe( X ) ), c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_Complex_OIm( Y ), c_Complex_OIm( X ) ) ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.89/1.46 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.46 .
% 0.89/1.46 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.89/1.46 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.46 .
% 0.89/1.46 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.46 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.89/1.46 ), c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.89/1.46 , c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Groups_Otimes__class_Otimes
% 0.89/1.46 ( X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.89/1.46 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.89/1.46 ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, T ), Z ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.89/1.46 ), Y ) ) }.
% 0.89/1.46 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, U, c_Groups_Ominus__class_Ominus( X, T
% 0.89/1.46 , Y ) ), c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus
% 0.89/1.46 ( X, U, Z ), Y ) ) }.
% 0.89/1.46 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.89/1.46 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Groups_Otimes__class_Otimes
% 0.89/1.46 ( X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.89/1.46 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.89/1.46 ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, T ), Z ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.89/1.46 ), Y ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Complex_ORe( X ),
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.46 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { c_NthRoot_Osqrt( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X )
% 0.89/1.46 ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ), Z =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.46 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.46 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Y, Y ) ) ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ), Y ) = Y
% 0.89/1.46 }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }
% 0.89/1.46 .
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Complex_ORe( X ) ),
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Complex_OIm( X ) ),
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Int_OBit1( Y ), X ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0(
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ), X ) }.
% 0.89/1.46 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.46 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.46 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.89/1.46 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.89/1.46 hAPP( Y, U ) ) }.
% 0.89/1.46 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.46 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.89/1.46 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.46 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.89/1.46 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.46 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.89/1.46 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.46 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.89/1.46 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.46 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.89/1.46 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.89/1.46 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.89/1.46 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.89/1.46 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.46 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.89/1.46 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.46 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.89/1.46 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.46 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.46 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.89/1.46 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.89/1.46 hAPP( Y, U ) ) }.
% 0.89/1.46 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.46 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.89/1.46 ( X, Z, Y ) }.
% 0.89/1.46 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.89/1.46 ( X, Y, Z ) }.
% 0.89/1.46 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.46 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.89/1.46 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.46 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.46 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.89/1.46 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.89/1.46 hAPP( Y, U ) ) }.
% 0.89/1.46 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.89/1.46 ( Z, skol1( X, Y, Z ) ), hAPP( Y, skol1( X, Y, Z ) ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.46 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.89/1.46 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.89/1.46 ( tc_Nat_Onat ) ) = X }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.46 tc_Nat_Onat ), X ) = X }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.46 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Power_Opower__class_Opower
% 0.89/1.46 ( tc_Int_Oint, X, Y ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.89/1.46 tc_Int_Oint ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.46 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.89/1.46 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.89/1.46 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.89/1.46 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, Z, X ), Y ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.89/1.46 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, Z, Y ), X ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol2( X, Y ) ) }.
% 0.89/1.46 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.89/1.46 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, Y, Y ), Y ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X )
% 0.89/1.46 }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) ) ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.89/1.46 ) ) ), Y ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.89/1.46 ) ) ) ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.89/1.46 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) = c_Groups_Otimes__class_Otimes( X, Y, Y ) }.
% 0.89/1.46 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Z,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ), Y ) ) = c_Power_Opower__class_Opower( X,
% 0.89/1.46 c_Power_Opower__class_Opower( X, Z, Y ), c_Int_Onumber__class_Onumber__of
% 0.89/1.46 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.46 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ) = c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.46 c_Int_OBit1( c_Int_OPls ) ) ), X ), c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.89/1.46 { ! class_Groups_Omonoid__mult( X ), ! class_Int_Onumber( X ),
% 0.89/1.46 c_Power_Opower__class_Opower( X, c_Int_Onumber__class_Onumber__of( X, Y )
% 0.89/1.46 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.89/1.46 ( c_Int_OPls ) ) ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Y ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.89/1.46 { c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) ), c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.46 c_Int_OBit1( c_Int_OPls ) ) ), Y ), X ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.46 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.89/1.46 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), c_Power_Opower__class_Opower( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, Z, Y ), c_Int_Onumber__class_Onumber__of
% 0.89/1.46 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.89/1.46 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.46 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.89/1.46 ) ) ), Z ), Y ) ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.46 X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Z,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ), Y ) ) ) }.
% 0.89/1.46 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.46 ( X, c_Power_Opower__class_Opower( X, Y, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.89/1.46 c_Int_OBit1( c_Int_OPls ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.46 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Int_Oint, X, Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Z
% 0.89/1.46 , c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ), Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Power_Opower__class_Opower( X, Z, Y ), c_Power_Opower__class_Opower( X
% 0.89/1.46 , Z, Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 Y, Y ) = c_Power_Opower__class_Opower( X, Y,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.46 c_Int_OPls ) ) ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.46 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.89/1.46 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.89/1.46 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.89/1.46 ( X, T, Y ) ) ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_RealDef_Oreal, Y, c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Int_Onumber__ring( X ), !
% 0.89/1.46 class_RealVector_Oreal__normed__algebra__1( X ),
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.46 Y ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.46 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, Y ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X,
% 0.89/1.46 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.46 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.89/1.46 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) )
% 0.89/1.46 }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.46 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.89/1.46 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.46 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.89/1.46 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.89/1.46 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.89/1.46 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.89/1.46 ( tc_Int_Oint, Z, Y ), X ) = c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.89/1.46 Z, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.89/1.46 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.89/1.46 Z, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.46 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.46 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.46 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.89/1.46 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.89/1.46 ( tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X )
% 0.89/1.46 ) }.
% 0.89/1.46 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.89/1.46 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, T, Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, U, T
% 0.89/1.46 ), Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X, U,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.89/1.46 , Y ) ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, T, Y
% 0.89/1.46 ), Z ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.89/1.46 , Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.89/1.46 ), Y ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Otimes__class_Otimes( X, T
% 0.89/1.46 , Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 Z, Y ) = c_Groups_Otimes__class_Otimes( X, Y, Z ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.89/1.46 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.89/1.46 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.89/1.46 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.89/1.46 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.89/1.46 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.89/1.46 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.89/1.46 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.89/1.46 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.89/1.46 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.89/1.46 c_Power_Opower__class_Opower( X, T, Z ), Y ) =
% 0.89/1.46 c_Power_Opower__class_Opower( X, T, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, Z, Y ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol3( X, Y ) ) }.
% 0.89/1.46 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.46 }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 Y, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.46 }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.89/1.46 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.89/1.46 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.46 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.46 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.89/1.46 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.89/1.46 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.89/1.46 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.46 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.46 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, T, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, T, Z ) ) }.
% 0.89/1.46 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.46 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 U, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.89/1.46 , c_Groups_Otimes__class_Otimes( X, T, Z ) ), ! U = T }.
% 0.89/1.46 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.46 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 U, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.89/1.46 , c_Groups_Otimes__class_Otimes( X, T, Z ) ), ! Z = Y }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.89/1.46 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.89/1.46 , Y ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.46 , T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.89/1.46 , Y ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.46 , T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, T, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Y, Z ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.89/1.46 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.46 ( X ), ! c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.46 , U, T ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.89/1.46 , c_Groups_Otimes__class_Otimes( X, Z, T ) ), U = Z, T = Y }.
% 0.89/1.46 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.46 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Z, T ) ) }.
% 0.89/1.46 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.46 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Z, T ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Ominus__class_Ominus( X, Z
% 0.89/1.46 , Y ) ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.89/1.46 ( X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Ominus__class_Ominus( X, Z
% 0.89/1.46 , Y ) ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.89/1.46 ( X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.89/1.46 ), Y ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.89/1.46 ( X, T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.89/1.46 ), Y ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.89/1.46 ( X, T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T, Y )
% 0.89/1.46 , c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.89/1.46 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.46 c_Power_Opower__class_Opower( X, T, Z ), c_Power_Opower__class_Opower( X
% 0.89/1.46 , T, Y ) ) = c_Power_Opower__class_Opower( X, T,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.89/1.46 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.89/1.46 ( X, Y, Z ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.89/1.46 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.89/1.46 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.89/1.46 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, W, c_Groups_Otimes__class_Otimes( X, Y, T
% 0.89/1.46 ) ) = c_Groups_Oplus__class_Oplus( X, U, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 X, Y, Z ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, U, T
% 0.89/1.46 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.89/1.46 ), c_Groups_Ominus__class_Ominus( X, T, Y ) ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.89/1.46 ), Y ) ), c_Groups_Otimes__class_Otimes( X, Z,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.46 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.89/1.46 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, c_Groups_Otimes__class_Otimes( X, Z,
% 0.89/1.46 Y ) ) = c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.46 ( X, Y ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, c_Power_Opower__class_Opower( X, Z, Y
% 0.89/1.46 ) ) = c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Z ), Y ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.89/1.46 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.46 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, c_Groups_Otimes__class_Otimes( X, Z,
% 0.89/1.46 Y ) ), c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.46 ( X, Y ) ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.89/1.46 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.46 ( X, Y ) ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.89/1.46 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.46 ( X, Y ) ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, c_Power_Opower__class_Opower( X, Z, Y
% 0.89/1.46 ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Z ), Y ) ) }.
% 0.89/1.46 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.46 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.46 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, Y, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ), T =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.89/1.46 }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.89/1.46 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.89/1.46 ( tc_Nat_Onat, Y, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), T ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, X, U ), Z ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.89/1.46 T, c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.46 ( tc_Nat_Onat, X, Y ), U ), Z ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, Y, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.89/1.46 ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.89/1.46 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, Y, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, X, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), Z ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.89/1.46 = Z }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.89/1.46 = Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, Y, U ), Z ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.46 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.46 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ),
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, Y, U ), Z ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.89/1.46 , Z ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, X, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), Z ) ),
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.89/1.46 , Z ) }.
% 0.89/1.46 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.89/1.46 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.89/1.46 , Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, X, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), Z ) ) }.
% 0.89/1.46 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ), Z =
% 0.89/1.46 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.89/1.46 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.89/1.46 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.89/1.46 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, T, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.46 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ), X ) ) =
% 0.89/1.46 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.89/1.46 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ), Z ), X ) }
% 0.89/1.46 .
% 0.89/1.46 { ! class_Rings_Oordered__ring__abs( X ), alpha95( X, Z ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), c_Groups_Oabs__class_Oabs( X, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.89/1.47 ) ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.89/1.47 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring__abs( X ), alpha95( X, Z ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), c_Groups_Oabs__class_Oabs( X, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.89/1.47 ) ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.89/1.47 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.47 { ! alpha95( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { ! alpha95( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ) ), alpha95( X, Y ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Otimes__class_Otimes
% 0.89/1.47 ( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) = c_Groups_Oabs__class_Oabs(
% 0.89/1.47 X, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U
% 0.89/1.47 ), T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.47 , Z, U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.89/1.47 , Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U
% 0.89/1.47 ), T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.47 , Z, U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , T, c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.89/1.47 , Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.89/1.47 , Y ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ) = Y }.
% 0.89/1.47 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, W, Z
% 0.89/1.47 ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.89/1.47 , Y ) }.
% 0.89/1.47 { ! class_Rings_Omult__zero( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 }.
% 0.89/1.47 { ! class_Rings_Omult__zero( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Rings_Oring__no__zero__divisors( X ), !
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ), Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ) }.
% 0.89/1.47 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.89/1.47 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.89/1.47 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ), Z = c_Groups_Ozero__class_Ozero( X ), !
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) }.
% 0.89/1.47 { ! class_Rings_Ono__zero__divisors( X ), ! c_Groups_Otimes__class_Otimes(
% 0.89/1.47 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.47 .
% 0.89/1.47 { ! class_Rings_Ocomm__semiring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.47 , c_Groups_Otimes__class_Otimes( X, Z, T ), Y ) ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, U, Z ), T ), Y ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.47 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, Y ) }.
% 0.89/1.47 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__semiring( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ), U ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, U ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 X, Y, T ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__semiring( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ), U ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, U ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 X, Y, T ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , c_Groups_Otimes__class_Otimes( X, T, Y ), c_Groups_Otimes__class_Otimes
% 0.89/1.47 ( X, T, Z ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , c_Groups_Otimes__class_Otimes( X, Y, T ), c_Groups_Otimes__class_Otimes
% 0.89/1.47 ( X, Z, T ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.89/1.47 X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__semiring( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.89/1.47 X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__semiring( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.89/1.47 X, Z, T ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , c_Groups_Otimes__class_Otimes( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y, Z
% 0.89/1.47 ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.89/1.47 , Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ), alpha30( X
% 0.89/1.47 , Y, Z ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.89/1.47 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha30( X, Y, Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.89/1.47 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ), Y ), alpha30( X, Y, Z ) }.
% 0.89/1.47 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.89/1.47 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), alpha1( X, Y, Z ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), alpha2( X, Y, Z ), alpha31( X
% 0.89/1.47 , Y, Z ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha31( X, Y, Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.89/1.47 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), alpha31( X, Y, Z ) }.
% 0.89/1.47 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.89/1.47 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y
% 0.89/1.47 , Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.89/1.47 , Y ), T = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes
% 0.89/1.47 ( X, c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) }.
% 0.89/1.47 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, Z, W
% 0.89/1.47 ), U ), Y ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.89/1.47 , Y ) }.
% 0.89/1.47 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_NthRoot_Osqrt(
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.47 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ) ) ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol4 ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_OIm( X ) ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), skol4 ) ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol5 ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, c_Complex_ORe( X ) ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), skol5 ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y
% 0.89/1.47 , c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ), Z ) ) ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, X, c_Complex_Ocnj( X
% 0.89/1.47 ) ) ) = c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ) }.
% 0.89/1.47 { c_Complex_ORe( c_Complex_Ocnj( X ) ) = c_Complex_ORe( X ) }.
% 0.89/1.47 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.89/1.47 ), T = Y }.
% 0.89/1.47 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.89/1.47 ), Z = X }.
% 0.89/1.47 { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Y, X ) }.
% 0.89/1.47 { ! c_Complex_Ocnj( Y ) = c_Complex_Ocnj( X ), Y = X }.
% 0.89/1.47 { ! Y = X, c_Complex_Ocnj( Y ) = c_Complex_Ocnj( X ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_Complex_Ocnj( X ) ) = X }.
% 0.89/1.47 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.89/1.47 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.89/1.47 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.89/1.47 { ! c_Nat_OSuc( X ) = X }.
% 0.89/1.47 { ! X = c_Nat_OSuc( X ) }.
% 0.89/1.47 { c_Complex_OIm( c_Complex_Ocomplex_OComplex( Y, X ) ) = X }.
% 0.89/1.47 { c_Complex_ORe( c_Complex_Ocomplex_OComplex( Y, X ) ) = Y }.
% 0.89/1.47 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.47 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.89/1.47 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.89/1.47 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.89/1.47 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.89/1.47 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ), Y = X }
% 0.89/1.47 .
% 0.89/1.47 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y )
% 0.89/1.47 = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.89/1.47 .
% 0.89/1.47 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.89/1.47 ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.89/1.47 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.89/1.47 , c_Nat_OSuc( X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.89/1.47 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.89/1.47 }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.89/1.47 c_Nat_OSuc( X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.89/1.47 ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.89/1.47 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.89/1.47 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.89/1.47 { c_Power_Opower__class_Opower( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.47 { ! c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.47 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.89/1.47 c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.47 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.89/1.47 c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.47 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.89/1.47 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.89/1.47 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.47 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.47 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.89/1.47 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.47 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, c_Complex_Ocnj( X )
% 0.89/1.47 ) = c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, Y, X
% 0.89/1.47 ) ) = c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, c_Complex_Ocnj
% 0.89/1.47 ( Y ), c_Complex_Ocnj( X ) ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 0.89/1.47 ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, c_Complex_Ocnj( Y
% 0.89/1.47 ), c_Complex_Ocnj( X ) ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.89/1.47 { ! c_Complex_Ocnj( X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex
% 0.89/1.47 ), X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.89/1.47 { ! X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), c_Complex_Ocnj
% 0.89/1.47 ( X ) = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X
% 0.89/1.47 ) ) = c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, c_Complex_Ocnj
% 0.89/1.47 ( Y ), c_Complex_Ocnj( X ) ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex, X
% 0.89/1.47 ) ) = c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex, X ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_Power_Opower__class_Opower( tc_Complex_Ocomplex, Y, X )
% 0.89/1.47 ) = c_Power_Opower__class_Opower( tc_Complex_Ocomplex, c_Complex_Ocnj( Y
% 0.89/1.47 ), X ) }.
% 0.89/1.47 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.89/1.47 c_Power_Opower__class_Opower( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc
% 0.89/1.47 ( Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.89/1.47 c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Z,
% 0.89/1.47 c_Nat_OSuc( Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Power_Opower__class_Opower( X, Z, Y ), Z ) }.
% 0.89/1.47 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Z
% 0.89/1.47 , c_Nat_OSuc( Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.89/1.47 c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 Z, c_Power_Opower__class_Opower( X, Z, Y ) ) =
% 0.89/1.47 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( Y ) ) }.
% 0.89/1.47 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Power_Opower__class_Opower( X, Z, Y ), Z ) =
% 0.89/1.47 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( Y ) ) }.
% 0.89/1.47 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha3( X, Y ), alpha32( X
% 0.89/1.47 , Y ) }.
% 0.89/1.47 { ! alpha3( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.89/1.47 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.47 { ! alpha32( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.89/1.47 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.47 { ! alpha32( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.47 { ! alpha32( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_Nat_Onat ) ) }.
% 0.89/1.47 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha32( X, Y ) }.
% 0.89/1.47 { ! alpha3( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_Nat_Onat ) ) }.
% 0.89/1.47 { ! alpha3( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.47 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha3( X, Y ) }.
% 0.89/1.47 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha4( X, Y ), alpha33
% 0.89/1.47 ( X, Y ) }.
% 0.89/1.47 { ! alpha4( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.89/1.47 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.89/1.47 { ! alpha33( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.89/1.47 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.89/1.47 { ! alpha33( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.47 { ! alpha33( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_Nat_Onat ) ) }.
% 0.89/1.47 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha33( X, Y ) }.
% 0.89/1.47 { ! alpha4( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_Nat_Onat ) ) }.
% 0.89/1.47 { ! alpha4( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.47 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha4( X, Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.89/1.47 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) ) }.
% 0.89/1.47 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.47 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.47 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.89/1.47 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.89/1.47 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.89/1.47 { c_Complex_Ocomplex_OComplex( c_Complex_ORe( X ), c_Complex_OIm( X ) ) = X
% 0.89/1.47 }.
% 0.89/1.47 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.47 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.89/1.47 ) }.
% 0.89/1.47 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.89/1.47 ) }.
% 0.89/1.47 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_Complex_Ocomplex ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.89/1.47 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.89/1.47 ) = c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 0.89/1.47 tc_RealDef_Oreal, T, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.47 Z, X ) ) }.
% 0.89/1.47 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.89/1.47 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.89/1.47 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.89/1.47 tc_RealDef_Oreal, T, Y ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 0.89/1.47 , Z, X ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semidom( X ), ! c_Power_Opower__class_Opower(
% 0.89/1.47 X, Z, c_Nat_OSuc( T ) ) = c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc
% 0.89/1.47 ( T ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), Z = Y }.
% 0.89/1.47 { ! class_Rings_Olinordered__semidom( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Z
% 0.89/1.47 , c_Nat_OSuc( T ) ), c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( T )
% 0.89/1.47 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ), Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.89/1.47 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.89/1.47 { c_Complex_OIm( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, X,
% 0.89/1.47 c_Complex_Ocnj( X ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.89/1.47 }.
% 0.89/1.47 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 0.89/1.47 ( tc_Complex_Ocomplex, X ), Z = c_Int_Onumber__class_Onumber__of(
% 0.89/1.47 tc_RealDef_Oreal, X ) }.
% 0.89/1.47 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 0.89/1.47 ( tc_Complex_Ocomplex, X ), Y = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_RealDef_Oreal ) }.
% 0.89/1.47 { ! Z = c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ), ! Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of(
% 0.89/1.47 tc_Complex_Ocomplex, X ) }.
% 0.89/1.47 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.89/1.47 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.89/1.47 ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.47 { c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc( X ) ) ) = c_Groups_Oplus__class_Oplus
% 0.89/1.47 ( tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1
% 0.89/1.47 ( c_Int_OBit1( c_Int_OPls ) ) ), X ) }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex,
% 0.89/1.47 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.89/1.47 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.89/1.47 tc_RealDef_Oreal, c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, T, Y )
% 0.89/1.47 , c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ) ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, T, X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, Y ) ) ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 0.89/1.47 tc_RealDef_Oreal, c_Complex_ORe( Y ), c_Complex_ORe( X ) ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Complex_OIm( Y ),
% 0.89/1.47 c_Complex_OIm( X ) ) ) }.
% 0.89/1.47 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 0.89/1.47 c_NthRoot_Osqrt( c_Complex_ORe( c_Groups_Otimes__class_Otimes(
% 0.89/1.47 tc_Complex_Ocomplex, X, c_Complex_Ocnj( X ) ) ) ) }.
% 0.89/1.47 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X,
% 0.89/1.47 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ),
% 0.89/1.47 c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.89/1.47 ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.89/1.47 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_Nat_Onat ) ) ) }.
% 0.89/1.47 { c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ), X ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, Y, X ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.89/1.47 tc_RealDef_Oreal, c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.47 c_Complex_ORe( Y ), c_Complex_ORe( X ) ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 tc_RealDef_Oreal, c_Complex_OIm( Y ), c_Complex_OIm( X ) ) ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, c_Complex_ORe( Y ),
% 0.89/1.47 c_Complex_OIm( X ) ), c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.47 c_Complex_OIm( Y ), c_Complex_ORe( X ) ) ) ) }.
% 0.89/1.47 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Z,
% 0.89/1.47 c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ), Y ) ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.89/1.47 c_Power_Opower__class_Opower( X, c_Power_Opower__class_Opower( X, Z, Y )
% 0.89/1.47 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.89/1.47 ( c_Int_OPls ) ) ) ) ) }.
% 0.89/1.47 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Z
% 0.89/1.47 , c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ), Y ) ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, Z, Y )
% 0.89/1.47 , c_Power_Opower__class_Opower( X, Z, Y ) ) ) }.
% 0.89/1.47 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.89/1.47 tc_Nat_Onat, Z, Y ), c_Power_Opower__class_Opower( X, T,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ), T ) }.
% 0.89/1.47 { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) )
% 0.89/1.47 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, X, c_Complex_Ocnj( X
% 0.89/1.47 ) ) = c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.47 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_Complex_ORe( X ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.47 c_Complex_OIm( X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.89/1.47 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.89/1.47 { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex,
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_Nat_Onat ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) ) =
% 0.89/1.47 c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) }.
% 0.89/1.47 { c_Complex_ORe( c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) ) = X }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), ! c_RealVector_Oof__real( X, Z
% 0.89/1.47 ) = c_RealVector_Oof__real( X, Y ), Z = Y }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), ! Z = Y,
% 0.89/1.47 c_RealVector_Oof__real( X, Z ) = c_RealVector_Oof__real( X, Y ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), ! c_RealVector_Oof__real( X, Y
% 0.89/1.47 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_RealDef_Oreal ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), ! Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealVector_Oof__real(
% 0.89/1.47 X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.89/1.47 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, Y ) ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_RealVector_Oof__real( X, Z ),
% 0.89/1.47 c_RealVector_Oof__real( X, Y ) ) }.
% 0.89/1.47 { c_Complex_OIm( c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.47 { ! class_Int_Onumber__ring( X ), ! class_RealVector_Oreal__algebra__1( X )
% 0.89/1.47 , c_RealVector_Oof__real( X, c_Int_Onumber__class_Onumber__of(
% 0.89/1.47 tc_RealDef_Oreal, Y ) ) = c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_RealVector_Oof__real( X, Z ),
% 0.89/1.47 c_RealVector_Oof__real( X, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.89/1.47 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_RealVector_Oof__real( X, Z ),
% 0.89/1.47 c_RealVector_Oof__real( X, Y ) ) }.
% 0.89/1.47 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_RealVector_Oof__real(
% 0.89/1.47 tc_Complex_Ocomplex, X ), Z = X }.
% 0.89/1.47 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_RealVector_Oof__real(
% 0.89/1.47 tc_Complex_Ocomplex, X ), Y = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_RealDef_Oreal ) }.
% 0.89/1.47 { ! Z = X, ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Z, Y ) = c_RealVector_Oof__real(
% 0.89/1.47 tc_Complex_Ocomplex, X ) }.
% 0.89/1.47 { c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_RealDef_Oreal ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.89/1.47 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z, Y ) ) =
% 0.89/1.47 c_Power_Opower__class_Opower( X, c_RealVector_Oof__real( X, Z ), Y ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, c_RealVector_Oof__real( X, Z ),
% 0.89/1.47 c_RealVector_Oof__real( X, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.89/1.47 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, Y ) ) =
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, c_RealVector_Oof__real( X, Z ),
% 0.89/1.47 c_RealVector_Oof__real( X, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, c_RealVector_Oof__real( X, Y ) ) =
% 0.89/1.47 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ) }.
% 0.89/1.47 { c_Power_Opower__class_Opower( tc_Complex_Ocomplex, c_RealVector_Oof__real
% 0.89/1.47 ( tc_Complex_Ocomplex, Y ), X ) = c_RealVector_Oof__real(
% 0.89/1.47 tc_Complex_Ocomplex, c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y, X
% 0.89/1.47 ) ) }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex,
% 0.89/1.47 c_RealVector_Oof__real( tc_Complex_Ocomplex, Z ),
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex(
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, Y ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ) ) }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex,
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Z, Y ), c_RealVector_Oof__real(
% 0.89/1.47 tc_Complex_Ocomplex, X ) ) = c_Complex_Ocomplex_OComplex(
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, c_RealVector_Oof__real
% 0.89/1.47 ( tc_Complex_Ocomplex, Z ), c_Complex_Ocomplex_OComplex( Y, X ) ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 0.89/1.47 tc_RealDef_Oreal, Z, Y ), X ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Z, Y ), c_RealVector_Oof__real(
% 0.89/1.47 tc_Complex_Ocomplex, X ) ) = c_Complex_Ocomplex_OComplex(
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ), Y ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Ocnj( X )
% 0.89/1.47 ) = c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ), c_Complex_ORe( X ) ) ) }.
% 0.89/1.47 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Ocnj( X
% 0.89/1.47 ) ) = c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex,
% 0.89/1.47 c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ), c_Complex_OIm( X ) ) ), c_Complex_Oii ) }
% 0.89/1.47 .
% 0.89/1.47 { ! c_Complex_OIm( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Complex_ORe( X ) ),
% 0.89/1.47 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( X ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( c_NthRoot_Osqrt( c_Complex_ORe( X ) ),
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.47 { ! c_Complex_OIm( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Complex_ORe( X ) ),
% 0.89/1.47 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( X ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_RealDef_Oreal ), c_NthRoot_Osqrt( c_Groups_Ouminus__class_Ouminus(
% 0.89/1.47 tc_RealDef_Oreal, c_Complex_ORe( X ) ) ) ) }.
% 0.89/1.47 { c_Complex_OIm( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( X ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( c_NthRoot_Osqrt(
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), c_Complex_ORe
% 0.89/1.47 ( X ) ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0
% 0.89/1.47 ( c_Int_OBit1( c_Int_OPls ) ) ) ) ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 tc_RealDef_Oreal, c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.89/1.47 c_Complex_OIm( X ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.47 c_Complex_OIm( X ) ) ), c_NthRoot_Osqrt( c_Rings_Oinverse__class_Odivide
% 0.89/1.47 ( tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ), c_Complex_ORe
% 0.89/1.47 ( X ) ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0
% 0.89/1.47 ( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.89/1.47 { c_Complex_Ocomplex_Ocomplex__rec( T, Z, c_Complex_Ocomplex_OComplex( Y, X
% 0.89/1.47 ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.89/1.47 { c_Complex_Ocomplex_Ocomplex__case( T, Z, c_Complex_Ocomplex_OComplex( Y,
% 0.89/1.47 X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), c_Power_Opower__class_Opower(
% 0.89/1.47 X, c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Power_Opower__class_Opower( X, T, Y
% 0.89/1.47 ), c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), c_RealVector_Oof__real( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) =
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__algebra__1( X ), !
% 0.89/1.47 class_RealVector_Oreal__normed__vector( X ), c_RealVector_Oof__real( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) =
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.89/1.47 class_RealVector_Oreal__field( X ), c_RealVector_Oof__real( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Z, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_RealVector_Oof__real( X, Z ),
% 0.89/1.47 c_RealVector_Oof__real( X, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_RealDef_Oreal ), c_RealVector_Oof__real( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Z, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_RealVector_Oof__real( X, Z ),
% 0.89/1.47 c_RealVector_Oof__real( X, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 0.89/1.47 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.89/1.47 ), Y ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.89/1.47 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oidom( X ), ! c_Groups_Otimes__class_Otimes( X, Z, Z ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, Y ), Z = Y, Z =
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.89/1.47 { ! class_Rings_Oidom( X ), ! Z = Y, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.89/1.47 ) = c_Groups_Otimes__class_Otimes( X, Y, Y ) }.
% 0.89/1.47 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Z ) = c_Groups_Otimes__class_Otimes
% 0.89/1.47 ( X, Y, Y ) }.
% 0.89/1.47 { ! class_Rings_Oring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.89/1.47 ( X, Y ) ) = c_Groups_Otimes__class_Otimes( X, Z, Y ) }.
% 0.89/1.47 { ! class_Rings_Oring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 Y ) ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), c_Groups_Otimes__class_Otimes( X, T,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.89/1.47 Z ), Y ) }.
% 0.89/1.47 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.89/1.47 , Y ) }.
% 0.89/1.47 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 Y ) ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.89/1.47 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__field( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.89/1.47 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.47 Z ) ), Y ) = c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, c_Groups_Ouminus__class_Ouminus(
% 0.89/1.47 tc_Int_Oint, Z ) ), Y ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.89/1.47 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.89/1.47 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.89/1.47 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.89/1.47 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.89/1.47 { ! class_Int_Onumber__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, c_Groups_Ouminus__class_Ouminus(
% 0.89/1.47 tc_Int_Oint, Y ) ) }.
% 0.89/1.47 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) =
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.47 Y ) ) }.
% 0.89/1.47 { c_NthRoot_Osqrt( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X
% 0.89/1.47 ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_NthRoot_Osqrt
% 0.89/1.47 ( Y ), c_NthRoot_Osqrt( X ) ) }.
% 0.89/1.47 { c_NthRoot_Osqrt( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) )
% 0.89/1.47 = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.89/1.47 ) ) }.
% 0.89/1.47 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.89/1.47 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.47 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.89/1.47 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.89/1.47 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.89/1.47 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.89/1.47 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.89/1.47 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.89/1.47 Y ) ) = Y }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 Z, Y ) ) = Y }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 Y ) ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes
% 0.89/1.47 ( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 Y ) ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes
% 0.89/1.47 ( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.89/1.47 , Y ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes
% 0.89/1.47 ( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.89/1.47 , Y ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes
% 0.89/1.47 ( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__field( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.89/1.47 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__field( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 0.89/1.47 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 0.89/1.47 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.89/1.47 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.89/1.47 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.89/1.47 = Y }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.89/1.47 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Y ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 = Y }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.89/1.47 ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__field( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.89/1.47 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.89/1.47 class_RealVector_Oreal__normed__field( X ),
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.89/1.47 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.47 ( X, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.89/1.47 ( X, Y ) ) }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, c_Complex_Oii,
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex(
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ) }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex,
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Y, X ), c_Complex_Oii ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( c_Groups_Ouminus__class_Ouminus(
% 0.89/1.47 tc_RealDef_Oreal, X ), Y ) }.
% 0.89/1.47 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , ! c_Groups_Otimes__class_Otimes( X, T, Y ) = Z, T =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , ! T = c_Groups_Otimes__class_Otimes( X, Z, Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , ! T = c_Groups_Otimes__class_Otimes( X, Z, Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, T, Y ) = Z }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , ! c_Groups_Otimes__class_Otimes( X, T, Y ) = Z, T =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.89/1.47 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.89/1.47 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.89/1.47 ( X, Y ), Y ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.89/1.47 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.89/1.47 ( X, Y ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.89/1.47 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 Z ) = Y }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.89/1.47 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.89/1.47 ( X, Z ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Power_Opower__class_Opower( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.89/1.47 ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 c_Power_Opower__class_Opower( X, T, Z ), c_Power_Opower__class_Opower( X
% 0.89/1.47 , Y, Z ) ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.89/1.47 X, Y ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.89/1.47 X, Z, Y ) }.
% 0.89/1.47 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.89/1.47 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.89/1.47 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Y ) ) }.
% 0.89/1.47 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.89/1.47 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.89/1.47 X, Y ) ) }.
% 0.89/1.47 { ! c_Complex_Oii = c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex,
% 0.89/1.47 X ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.47 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.47 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.89/1.47 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.89/1.47 c_Power_Opower__class_Opower( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.89/1.47 , Y ) ) = c_Groups_Oabs__class_Oabs( X, c_Power_Opower__class_Opower( X,
% 0.89/1.47 Z, Y ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha5( X, Y
% 0.89/1.47 ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha34( X,
% 0.89/1.47 Y ) }.
% 0.89/1.47 { ! alpha5( X, Y ), ! alpha34( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 0.89/1.47 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 0.89/1.47 { ! alpha34( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha34( X, Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha34( X, Y ) }.
% 0.89/1.47 { ! alpha5( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 0.89/1.47 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha5( X, Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha5( X, Y ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ) ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) }.
% 0.89/1.47 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.89/1.47 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.47 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.89/1.47 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ) }.
% 0.89/1.47 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.89/1.47 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.89/1.47 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.89/1.47 ( tc_RealDef_Oreal, Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.89/1.47 , X ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.47 { c_Complex_OIm( c_Complex_Ocnj( X ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.89/1.47 tc_RealDef_Oreal, c_Complex_OIm( X ) ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_Complex_Ocomplex_OComplex( Y, X ) ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Y, c_Groups_Ouminus__class_Ouminus(
% 0.89/1.47 tc_RealDef_Oreal, X ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T
% 0.89/1.47 = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 0.89/1.47 ( X, Y ) ), alpha35( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T
% 0.89/1.47 = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 0.89/1.47 ( X, Y ) ), alpha6( X, Y, T ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.89/1.47 alpha35( X, Y, Z, T ), ! alpha6( X, Y, T ), T =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.89/1.47 X, Y ) ) }.
% 0.89/1.47 { ! alpha35( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Y ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, T,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, Y ) ) = Z }.
% 0.89/1.47 { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ), alpha35( X, Y, Z, T ) }.
% 0.89/1.47 { ! c_Groups_Otimes__class_Otimes( X, T, c_Int_Onumber__class_Onumber__of(
% 0.89/1.47 X, Y ) ) = Z, alpha35( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha6( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Y ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.47 .
% 0.89/1.47 { c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ), alpha6( X, Y, Z ) }.
% 0.89/1.47 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha6( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, T ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha36( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, T ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha7( X, Y, T ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.89/1.47 alpha36( X, Y, Z, T ), ! alpha7( X, Y, T ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, T ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.89/1.47 { ! alpha36( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.89/1.47 ), Y ) = Z }.
% 0.89/1.47 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha36( X, Y, Z, T ) }.
% 0.89/1.47 { ! c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.47 T ), Y ) = Z, alpha36( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha7( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) }.
% 0.89/1.47 { Y = c_Groups_Ozero__class_Ozero( X ), alpha7( X, Y, Z ) }.
% 0.89/1.47 { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ), alpha7( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, Y ), alpha37( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, Y ), alpha8( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.89/1.47 alpha37( X, Y, Z, T ), ! alpha8( X, Y, Z ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.89/1.47 { ! alpha37( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.47 ), Z ) }.
% 0.89/1.47 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha37( X, Y, Z, T ) }.
% 0.89/1.47 { ! T = c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of
% 0.89/1.47 ( X, Y ), Z ), alpha37( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha8( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) }.
% 0.89/1.47 { Z = c_Groups_Ozero__class_Ozero( X ), alpha8( X, Y, Z ) }.
% 0.89/1.47 { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ), alpha8( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.89/1.47 X, Z ) ) = Y, alpha38( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.89/1.47 X, Z ) ) = Y, alpha9( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 0.89/1.47 alpha38( X, Y, Z, T ), ! alpha9( X, Y, Z ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.89/1.47 X, Z ) ) = Y }.
% 0.89/1.47 { ! alpha38( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), T = c_Groups_Otimes__class_Otimes( X, Y
% 0.89/1.47 , c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.89/1.47 { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ), alpha38( X, Y, Z, T ) }.
% 0.89/1.47 { ! T = c_Groups_Otimes__class_Otimes( X, Y,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha38( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha9( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.89/1.47 .
% 0.89/1.47 { c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ), alpha9( X, Y, Z ) }.
% 0.89/1.47 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha9( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber__ring( X )
% 0.89/1.47 , c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of
% 0.89/1.47 ( X, c_Int_OPls ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { c_Complex_ORe( c_Complex_Oii ) = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_RealDef_Oreal ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.89/1.47 X, Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , c_Groups_Oabs__class_Oabs( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), ! class_Int_Onumber__ring( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.47 X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), ! class_Int_Onumber__ring( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.47 X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }.
% 0.89/1.47 { ! class_Rings_Oidom( X ), ! c_Power_Opower__class_Opower( X, Z,
% 0.89/1.47 c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) )
% 0.89/1.47 = c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.89/1.47 { ! class_Rings_Oidom( X ), ! Z = Y, c_Power_Opower__class_Opower( X, Z,
% 0.89/1.47 c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) )
% 0.89/1.47 = c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.89/1.47 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.89/1.47 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) =
% 0.89/1.47 c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.89/1.47 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z )
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) ) ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.89/1.47 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ),
% 0.89/1.47 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.89/1.47 ( tc_RealDef_Oreal, Z, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.89/1.47 , X ) ) ) ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.89/1.47 c_Power_Opower__class_Opower( X, Y, c_Groups_Ominus__class_Ominus(
% 0.89/1.47 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 c_Power_Opower__class_Opower( X, Y, Z ), c_Power_Opower__class_Opower( X
% 0.89/1.47 , Y, T ) ) }.
% 0.89/1.47 { c_Complex_Ocnj( X ) = c_Complex_Ocomplex_OComplex( c_Complex_ORe( X ),
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_Complex_OIm( X ) ) )
% 0.89/1.47 }.
% 0.89/1.47 { ! class_Rings_Oring__1( X ), c_Power_Opower__class_Opower( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Int_Onumber__class_Onumber__of
% 0.89/1.47 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.89/1.47 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.47 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.89/1.47 { ! class_Rings_Oring__1( X ), c_Power_Opower__class_Opower( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ), Y ) ) = c_Power_Opower__class_Opower( X, Z
% 0.89/1.47 , c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ), Y ) ) }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, c_Complex_Oii,
% 0.89/1.47 c_RealVector_Oof__real( tc_Complex_Ocomplex, X ) ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_RealDef_Oreal ), X ) }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex,
% 0.89/1.47 c_RealVector_Oof__real( tc_Complex_Ocomplex, X ), c_Complex_Oii ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_RealDef_Oreal ), X ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.89/1.47 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ) ) }.
% 0.89/1.47 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) = c_Rings_Oinverse__class_Odivide(
% 0.89/1.47 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X )
% 0.89/1.47 , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.89/1.47 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ) ), Y ) = c_Rings_Oinverse__class_Odivide(
% 0.89/1.47 tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y )
% 0.89/1.47 , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ) ), c_Rings_Oinverse__class_Odivide(
% 0.89/1.47 tc_RealDef_Oreal, X, c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.89/1.47 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) = X }.
% 0.89/1.47 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.89/1.47 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.89/1.47 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.89/1.47 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.89/1.47 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit0( X ) ) =
% 0.89/1.47 c_Int_OBit0( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.89/1.47 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OPls ) = c_Int_OPls }
% 0.89/1.47 .
% 0.89/1.47 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X )
% 0.89/1.47 ) = c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, c_Complex_Ocnj
% 0.89/1.47 ( X ) ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, Y,
% 0.89/1.47 X ) ) = c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex,
% 0.89/1.47 c_Complex_Ocnj( Y ), c_Complex_Ocnj( X ) ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.89/1.47 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.89/1.47 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.89/1.47 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.89/1.47 { c_Complex_ORe( c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X )
% 0.89/1.47 ) = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_Complex_ORe( X
% 0.89/1.47 ) ) }.
% 0.89/1.47 { c_Complex_OIm( c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X )
% 0.89/1.47 ) = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_Complex_OIm( X
% 0.89/1.47 ) ) }.
% 0.89/1.47 { c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex,
% 0.89/1.47 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex(
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 0.89/1.47 tc_Complex_Ocomplex, c_Complex_Oii ) }.
% 0.89/1.47 { c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, c_Complex_Oii,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, c_Complex_Oii, X ) )
% 0.89/1.47 = c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 0.89/1.47 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.47 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.89/1.47 tc_Int_Oint, Z, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }.
% 0.89/1.47 { c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.89/1.47 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.89/1.47 X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ), Z ) }.
% 0.89/1.47 { c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( c_Groups_Ouminus__class_Ouminus(
% 0.89/1.47 tc_RealDef_Oreal, c_Complex_ORe( X ) ), c_Groups_Ouminus__class_Ouminus(
% 0.89/1.47 tc_RealDef_Oreal, c_Complex_OIm( X ) ) ) }.
% 0.89/1.47 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.89/1.47 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.89/1.47 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.89/1.47 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, Y ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.89/1.47 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ), Y ) ) =
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, hAPP( Z, X ), hAPP( Z, Y
% 0.89/1.47 ) ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X, Y ) ), X ) ) }
% 0.89/1.47 .
% 0.89/1.47 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 0.89/1.47 , c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, W,
% 0.89/1.47 U ), c_Groups_Otimes__class_Otimes( X, T, Z ) ), Y ) =
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.89/1.47 Z ), Y ) ), c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, W,
% 0.89/1.47 T ), Y ), Z ) ) }.
% 0.89/1.47 { ! Z = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ), X ) ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 tc_RealDef_Oreal, c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.89/1.47 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ), Z ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.47 { ! c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ), Z ) = c_Rings_Oinverse__class_Odivide(
% 0.89/1.47 tc_RealDef_Oreal, Y, X ), Z = c_Rings_Oinverse__class_Odivide(
% 0.89/1.47 tc_RealDef_Oreal, Y, c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ), X ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 X, T, Y ) ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.89/1.47 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, T, c_Groups_Otimes__class_Otimes( X, Y
% 0.89/1.47 , Z ) ), Y ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, Y, T
% 0.89/1.47 ), Z ), Y ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), c_Groups_Otimes__class_Otimes
% 0.89/1.47 ( X, c_Rings_Oinverse__class_Odivide( X, U, T ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Otimes__class_Otimes( X, U,
% 0.89/1.47 Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.89/1.47 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 0.89/1.47 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.89/1.47 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z, Y )
% 0.89/1.47 ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.89/1.47 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.89/1.47 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.89/1.47 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.89/1.47 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha10( X, Y, Z ), alpha39
% 0.89/1.47 ( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha10( X, Y, Z
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.89/1.47 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 0.89/1.47 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ), Y ), alpha39( X, Y, Z ) }.
% 0.89/1.47 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.89/1.47 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), alpha10( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha11( X, Y, Z ), alpha40
% 0.89/1.47 ( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha11( X, Y, Z
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha40( X, Y, Z
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.47 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), alpha40( X, Y, Z ) }.
% 0.89/1.47 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.89/1.47 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ), alpha11( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 0.89/1.47 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, U, Z ) = c_Groups_Otimes__class_Otimes
% 0.89/1.47 ( X, T, Y ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), ! c_Groups_Otimes__class_Otimes( X, U,
% 0.89/1.47 Z ) = c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, T ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 X, Y, Z ) ) = c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, T, Y ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha41( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha12( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha41( X, Y, Z, T ), !
% 0.89/1.47 alpha12( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 0.89/1.47 { ! alpha41( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, Z ) }.
% 0.89/1.47 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha41( X, Y, Z, T ) }.
% 0.89/1.47 { ! T = c_Groups_Otimes__class_Otimes( X, Y, Z ), alpha41( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha12( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { Z = c_Groups_Ozero__class_Ozero( X ), alpha12( X, Y, Z ) }.
% 0.89/1.47 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha12( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha42( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha13( X, Y, T ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha42( X, Y, Z, T ), !
% 0.89/1.47 alpha13( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 0.89/1.47 { ! alpha42( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, T, Y ) = Z }.
% 0.89/1.47 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha42( X, Y, Z, T ) }.
% 0.89/1.47 { ! c_Groups_Otimes__class_Otimes( X, T, Y ) = Z, alpha42( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha13( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { Y = c_Groups_Ozero__class_Ozero( X ), alpha13( X, Y, Z ) }.
% 0.89/1.47 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha13( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.89/1.47 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs(
% 0.89/1.47 X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, T, Y ) ), Y ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 0.89/1.47 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ), Z ), Y ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), Y ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 0.89/1.47 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 0.89/1.47 ( X, T, c_Groups_Otimes__class_Otimes( X, Y, Z ) ), Y ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 X, T, Y ) ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.47 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, c_RealVector_Oof__real
% 0.89/1.47 ( tc_Complex_Ocomplex, Y ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 tc_Complex_Ocomplex, c_Complex_Oii, c_RealVector_Oof__real(
% 0.89/1.47 tc_Complex_Ocomplex, X ) ) ) ) = c_Groups_Ominus__class_Ominus(
% 0.89/1.47 tc_Complex_Ocomplex, c_RealVector_Oof__real( tc_Complex_Ocomplex,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.47 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ) ) ) ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 tc_Complex_Ocomplex, c_Complex_Oii, c_RealVector_Oof__real(
% 0.89/1.47 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.47 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ) ) ) ) ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 tc_RealDef_Oreal, Z, c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X
% 0.89/1.47 , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq(
% 0.89/1.47 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.47 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ) ) ), X ) }.
% 0.89/1.47 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, X ) =
% 0.89/1.47 c_Complex_Ocomplex_OComplex( c_Rings_Oinverse__class_Odivide(
% 0.89/1.47 tc_RealDef_Oreal, c_Complex_ORe( X ), c_Groups_Oplus__class_Oplus(
% 0.89/1.47 tc_RealDef_Oreal, c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.47 c_Complex_ORe( X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.89/1.47 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.89/1.47 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_Complex_OIm( X ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ) ) ), c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal
% 0.89/1.47 , c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_Complex_OIm( X ) )
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.47 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_Complex_ORe( X ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.47 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.47 c_Complex_OIm( X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.89/1.47 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, c_Rings_Oinverse__class_Oinverse( X
% 0.89/1.47 , Y ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Y, Z ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.89/1.47 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.89/1.47 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.89/1.47 ( X, Y ), Z ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.89/1.47 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.89/1.47 ( X, Z ), Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.89/1.47 , Y, Z ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 0.89/1.47 , Y, Z ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 0.89/1.47 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha14( X, Y, Z ), alpha43( X,
% 0.89/1.47 Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha14( X, Y, Z
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.89/1.47 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha43( X, Y, Z
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 0.89/1.47 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! alpha43( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), alpha43( X, Y, Z ) }.
% 0.89/1.47 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.89/1.47 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.47 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), alpha14( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha15( X, Y, Z ), alpha44
% 0.89/1.47 ( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha15( X, Y, Z
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha44( X, Y, Z
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.47 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! alpha44( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), alpha44( X, Y, Z ) }.
% 0.89/1.47 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.89/1.47 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.47 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), alpha15( X, Y, Z ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.89/1.47 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Z
% 0.89/1.47 , Y ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.89/1.47 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , Y ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.89/1.47 , Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.89/1.47 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.89/1.47 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.89/1.47 .
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.89/1.47 ) ) = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X
% 0.89/1.47 , Y ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.89/1.47 , Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.89/1.47 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.89/1.47 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.89/1.47 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.89/1.47 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.89/1.47 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y ) )
% 0.89/1.47 = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X, Y )
% 0.89/1.47 ) }.
% 0.89/1.47 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.89/1.47 .
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.89/1.47 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.89/1.47 .
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.89/1.47 , Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.89/1.47 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.89/1.47 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.89/1.47 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, U ) ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Z, Y ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.89/1.47 }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ), X =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.47 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.89/1.47 tc_RealDef_Oreal ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__div__algebra( X ), !
% 0.89/1.47 class_Rings_Odivision__ring__inverse__zero( X ), c_RealVector_Oof__real(
% 0.89/1.47 X, c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__div__algebra( X ), Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealVector_Oof__real(
% 0.89/1.47 X, c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, c_RealVector_Oof__real( X, Y ) ) }.
% 0.89/1.47 { c_Complex_Ocnj( c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, X
% 0.89/1.47 ) ) = c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex,
% 0.89/1.47 c_Complex_Ocnj( X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.89/1.47 c_NthRoot_Osqrt( X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.89/1.47 c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 Y, X ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.89/1.47 c_NthRoot_Osqrt( X ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ) ) =
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 0.89/1.47 class_Rings_Odivision__ring__inverse__zero( X ),
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.89/1.47 Y ) ) = c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.47 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.47 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.47 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.47 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.47 , ! Z = Y }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.47 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.47 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.47 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.89/1.47 ( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.47 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.47 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.47 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.47 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.89/1.47 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.47 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.47 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.47 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.47 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.47 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.47 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.89/1.47 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, Z, Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, Z, Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.89/1.47 , T ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.47 , T, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.47 , Y, T ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, Z, Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.47 , T, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, T, Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.47 , Y, Z ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.89/1.47 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.89/1.47 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.47 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.89/1.47 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.89/1.47 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.89/1.47 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.89/1.47 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.89/1.47 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.47 Y ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 Y ), ! Z = Y }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.47 Z ), ! Z = Y }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.47 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.47 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.47 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.47 , ! Z = Y }.
% 0.89/1.47 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.47 , ! Z = Y }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.47 , ! Y = Z }.
% 0.89/1.47 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.47 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.89/1.47 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.89/1.47 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.47 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.47 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.89/1.47 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.89/1.47 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.47 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.89/1.47 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.89/1.47 , Y ) ) = Y }.
% 0.89/1.47 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.89/1.47 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Y, Z ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.89/1.47 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.89/1.47 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.89/1.47 X, Y ) ) = Y }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.89/1.47 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.89/1.47 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.47 = Y }.
% 0.89/1.47 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.47 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.89/1.47 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.47 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.89/1.47 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, c_Power_Opower__class_Opower( X, Z,
% 0.89/1.47 Y ) ) = c_Power_Opower__class_Opower( X, c_Rings_Oinverse__class_Oinverse
% 0.89/1.47 ( X, Z ), Y ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.89/1.47 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y
% 0.89/1.47 , Z ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.89/1.47 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , Z, Y ) }.
% 0.89/1.47 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.89/1.47 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.47 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.89/1.47 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.47 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.89/1.47 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.47 , Y, T ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.89/1.47 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.89/1.47 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.89/1.47 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.47 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.89/1.47 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , c_Groups_Otimes__class_Otimes( X, Y, Y ), c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.89/1.47 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), alpha16( X, Y, Z, T ),
% 0.89/1.47 alpha45( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z, T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.89/1.47 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha45( X, Y, Z, T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.89/1.47 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.47 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha45( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.89/1.47 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.47 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha16( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.89/1.47 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), alpha17( X, Y, Z, T ),
% 0.89/1.47 alpha46( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z, T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.89/1.47 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha46( X, Y, Z, T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.89/1.47 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.47 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha46( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.89/1.47 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.89/1.47 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha17( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.89/1.47 T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.47 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.89/1.47 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z,
% 0.89/1.47 Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.89/1.47 .
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.89/1.47 .
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.89/1.47 T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.47 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.89/1.47 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, Z, T ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, T ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, T, Z ) ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , c_Rings_Oinverse__class_Oinverse( X, c_Power_Opower__class_Opower( X, Y
% 0.89/1.47 , Z ) ) = c_Power_Opower__class_Opower( X,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ), Z ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Power_Opower__class_Opower( X, Z, T )
% 0.89/1.47 , c_Power_Opower__class_Opower( X, Y, T ) ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, Y, Z ) ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Rings_Oinverse__class_Oinverse( X, Z
% 0.89/1.47 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.89/1.47 .
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 0.89/1.47 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.89/1.47 .
% 0.89/1.47 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, c_Complex_Oii ) =
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, c_Complex_Oii ) }.
% 0.89/1.47 { c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, Y, X ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex, Y,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, X ) ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oplus__class_Oplus( X
% 0.89/1.47 , Y, Z ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Rings_Oinverse__class_Oinverse
% 0.89/1.47 ( X, Y ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.89/1.47 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.89/1.47 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ominus__class_Ominus(
% 0.89/1.47 X, Z, Y ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.89/1.47 { ! class_Fields_Ofield( X ), ! class_Int_Onumber__ring( X ),
% 0.89/1.47 c_Rings_Oinverse__class_Oinverse( X, c_Int_Onumber__class_Onumber__of( X
% 0.89/1.47 , c_Int_OBit1( c_Int_OPls ) ) ) = c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.47 c_Int_OBit1( c_Int_OPls ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.89/1.47 , Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.89/1.47 , Z ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.89/1.47 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.89/1.47 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.89/1.47 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , U ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.47 , Z, U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.89/1.47 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.89/1.47 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.47 , Y, T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Y
% 0.89/1.47 , T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.47 , Y, T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Y
% 0.89/1.47 , T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.89/1.47 ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.89/1.47 ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.89/1.47 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.89/1.47 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.89/1.47 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) ), ! Z =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 X, Y, Y ) ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.89/1.47 X, Y, Y ) ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.89/1.47 ), c_Groups_Otimes__class_Otimes( X, Y, Y ) ),
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Power_Opower__class_Opower( X, Z, T ),
% 0.89/1.47 c_Power_Opower__class_Opower( X, Y, T ) ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.89/1.47 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 0.89/1.47 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.89/1.47 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.89/1.47 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.47 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.47 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.47 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U )
% 0.89/1.47 , T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 Z, U ), Y ) ), c_Orderings_Oord__class_Oless( X, T,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.89/1.47 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.89/1.47 , Y ) ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U )
% 0.89/1.47 , T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 Z, U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ) }.
% 0.89/1.47 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.89/1.47 , Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 Z, Y ) ), alpha47( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 Z, Y ) ), alpha59( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha47( X, Y, Z
% 0.89/1.47 , T ), ! alpha59( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.47 { ! alpha59( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ), alpha71( X, Y, Z, T ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.89/1.47 , alpha59( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha71( X, Y, Z, T ), alpha59( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha71( X, Y, Z, T ), alpha83( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha71( X, Y, Z, T ), alpha18( X, Y, T ) }.
% 0.89/1.47 { ! alpha83( X, Y, Z, T ), ! alpha18( X, Y, T ), alpha71( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha83( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 alpha83( X, Y, Z, T ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 T, Y ) ), alpha83( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha47( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, T, Y ), Z ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 alpha47( X, Y, Z, T ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.89/1.47 Y ), Z ), alpha47( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 , alpha18( X, Y, Z ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 , alpha18( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.89/1.47 Z ), Y ), alpha48( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.89/1.47 Z ), Y ), alpha60( X, Y, Z, T ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha48( X, Y, Z
% 0.89/1.47 , T ), ! alpha60( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.89/1.47 { ! alpha60( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ), alpha72( X, Y, Z, T ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.47 , alpha60( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha72( X, Y, Z, T ), alpha60( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha72( X, Y, Z, T ), alpha84( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha72( X, Y, Z, T ), alpha19( X, Y, Z ) }.
% 0.89/1.47 { ! alpha84( X, Y, Z, T ), ! alpha19( X, Y, Z ), alpha72( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha84( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( X, Y, Z ), T ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 alpha84( X, Y, Z, T ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.89/1.47 Z ), T ), alpha84( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha48( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 T, c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.47 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.89/1.47 alpha48( X, Y, Z, T ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.47 Y, Z ) ), alpha48( X, Y, Z, T ) }.
% 0.89/1.47 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.47 , alpha19( X, Y, Z ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.89/1.47 , alpha19( X, Y, Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Y
% 0.89/1.47 ), Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ), Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 Z, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.89/1.47 , Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.89/1.47 Y ), Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.89/1.47 Y ), Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ), Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 Z, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Otimes__class_Otimes( X, T
% 0.89/1.47 , Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, Z, c_Groups_Otimes__class_Otimes( X, T, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 0.89/1.47 Z, Y ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.89/1.47 ), T ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 0.89/1.47 ( X, c_Groups_Otimes__class_Otimes( X, Z, Y ), T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 0.89/1.47 Y ), Z ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.89/1.47 Z ) ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide
% 0.89/1.47 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.47 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.89/1.47 ) ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide(
% 0.89/1.47 X, T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.89/1.47 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.89/1.47 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 0.89/1.47 }.
% 0.89/1.47 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.47 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.89/1.47 ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.89/1.47 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 0.89/1.47 ( X, Z, Y ), T ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 0.89/1.47 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 0.89/1.47 ( X, Z, Y ) ) }.
% 0.89/1.47 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.47 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.89/1.47 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 0.89/1.47 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 0.89/1.47 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.47 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ), Y
% 0.89/1.47 ) = c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 0.89/1.47 , Y ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.89/1.47 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.89/1.47 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.89/1.47 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.89/1.47 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, c_Groups_Otimes__class_Otimes( X, Z,
% 0.89/1.47 U ) ), c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, T ) ) }.
% 0.89/1.47 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.89/1.47 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.89/1.47 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.89/1.47 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.47 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.47 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.48 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.89/1.48 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.48 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.89/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.48 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.48 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.89/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.89/1.48 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.89/1.48 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.48 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.89/1.48 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.89/1.48 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.89/1.48 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.48 c_Groups_Otimes__class_Otimes( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.89/1.48 ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ),
% 0.89/1.48 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.89/1.48 ( X, Z, Y ) ), alpha49( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.89/1.48 ( X, Z, Y ) ), alpha61( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha49( X, Y, Z
% 0.89/1.48 , T ), ! alpha61( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.48 { ! alpha61( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Y ), alpha73( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.89/1.48 , alpha61( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha73( X, Y, Z, T ), alpha61( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha73( X, Y, Z, T ), alpha85( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha73( X, Y, Z, T ), alpha20( X, Y, T ) }.
% 0.89/1.48 { ! alpha85( X, Y, Z, T ), ! alpha20( X, Y, T ), alpha73( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha85( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.48 , Z, c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.48 alpha85( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Otimes__class_Otimes
% 0.89/1.48 ( X, T, Y ) ), alpha85( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha49( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.89/1.48 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ), Z ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.48 alpha49( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.48 , T, Y ), Z ), alpha49( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.48 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.48 , alpha20( X, Y, Z ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ) ), alpha20( X, Y, Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.89/1.48 , T, Z ), Y ), alpha50( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.89/1.48 , T, Z ), Y ), alpha62( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha50( X, Y, Z
% 0.89/1.48 , T ), ! alpha62( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 0.89/1.48 { ! alpha62( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Z ), alpha74( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.48 , alpha62( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha74( X, Y, Z, T ), alpha62( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha74( X, Y, Z, T ), alpha86( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha74( X, Y, Z, T ), alpha21( X, Y, Z ) }.
% 0.89/1.48 { ! alpha86( X, Y, Z, T ), ! alpha21( X, Y, Z ), alpha74( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha86( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.48 , c_Groups_Otimes__class_Otimes( X, Y, Z ), T ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.48 alpha86( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.48 , Y, Z ), T ), alpha86( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha50( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.89/1.48 ( X, T, c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.89/1.48 alpha50( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes
% 0.89/1.48 ( X, Y, Z ) ), alpha50( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.48 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.48 , alpha21( X, Y, Z ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.48 , Y ), alpha21( X, Y, Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.48 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.89/1.48 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.48 c_Groups_Otimes__class_Otimes( X, T, Y ), Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.48 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.89/1.48 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.48 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.89/1.48 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.48 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.48 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes( X
% 0.89/1.48 , Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.48 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes( X
% 0.89/1.48 , Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.48 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.89/1.48 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.48 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 0.89/1.48 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.48 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.48 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Otimes__class_Otimes( X
% 0.89/1.48 , T, Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.48 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.89/1.48 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.48 c_Groups_Otimes__class_Otimes( X, Z, Y ), T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.48 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.89/1.48 , Y ), T ), c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field( X ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.89/1.48 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.48 , c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.89/1.48 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.48 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.48 , c_Groups_Otimes__class_Otimes( X, Z, Y ) ),
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 0.89/1.48 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 X, Z ) ), Y ), alpha51( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 X, Z ) ), Y ), alpha63( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! alpha51( X, Y, Z, T ), ! alpha63( X, Y, Z, T )
% 0.89/1.48 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 0.89/1.48 , c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 0.89/1.48 { ! alpha63( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.89/1.48 ) ), alpha75( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha63( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha75( X, Y, Z, T ), alpha63( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha75( X, Y, Z, T ), alpha87( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha75( X, Y, Z, T ), alpha22( X, Y, Z ) }.
% 0.89/1.48 { ! alpha87( X, Y, Z, T ), ! alpha22( X, Y, Z ), alpha75( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha87( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.48 , Y, c_Int_Onumber__class_Onumber__of( X, Z ) ), T ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.89/1.48 ), c_Groups_Ozero__class_Ozero( X ) ), alpha87( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Z ) ), T ), alpha87( X, Y, Z, T ) }
% 0.89/1.48 .
% 0.89/1.48 { ! alpha51( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.89/1.48 ) ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Otimes__class_Otimes
% 0.89/1.48 ( X, Y, c_Int_Onumber__class_Onumber__of( X, Z ) ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha51( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.48 Y, c_Int_Onumber__class_Onumber__of( X, Z ) ) ), alpha51( X, Y, Z, T ) }
% 0.89/1.48 .
% 0.89/1.48 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.48 , Y ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.48 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha22( X, Y, Z ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.89/1.48 , alpha22( X, Y, Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha52( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha64( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! alpha52( X, Y, Z, T ), ! alpha64( X, Y, Z, T )
% 0.89/1.48 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 0.89/1.48 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.89/1.48 { ! alpha64( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Z ), alpha76( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.48 , alpha64( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha76( X, Y, Z, T ), alpha64( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha76( X, Y, Z, T ), alpha88( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha76( X, Y, Z, T ), alpha23( X, Y, Z ) }.
% 0.89/1.48 { ! alpha88( X, Y, Z, T ), ! alpha23( X, Y, Z ), alpha76( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha88( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.48 ), Z ), T ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.48 alpha88( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ), Z ), T ), alpha88( X, Y, Z, T )
% 0.89/1.48 }.
% 0.89/1.48 { ! alpha52( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 T, c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X
% 0.89/1.48 , Y ), Z ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.89/1.48 alpha52( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ), Z ) ), alpha52( X, Y, Z, T ) }
% 0.89/1.48 .
% 0.89/1.48 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.48 ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.48 , alpha23( X, Y, Z ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha23( X, Y, Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.89/1.48 ( X, Z, Y ) ), alpha53( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.89/1.48 ( X, Z, Y ) ), alpha65( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! alpha53( X, Y, Z, T ), ! alpha65( X, Y, Z, T )
% 0.89/1.48 , c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.48 T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.48 { ! alpha65( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Y ), alpha77( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.89/1.48 , alpha65( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha77( X, Y, Z, T ), alpha65( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha77( X, Y, Z, T ), alpha89( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha77( X, Y, Z, T ), alpha24( X, Y, T ) }.
% 0.89/1.48 { ! alpha89( X, Y, Z, T ), ! alpha24( X, Y, T ), alpha77( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha89( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.48 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.89/1.48 ), Y ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.48 alpha89( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, T ), Y ) ), alpha89( X, Y, Z, T ) }
% 0.89/1.48 .
% 0.89/1.48 { ! alpha53( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.89/1.48 ), Y ), Z ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.48 alpha53( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, T ), Y ), Z ), alpha53( X, Y, Z, T )
% 0.89/1.48 }.
% 0.89/1.48 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.48 , alpha24( X, Y, Z ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.48 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha24( X, Y, Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 X, Y ) ) ), alpha54( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 X, Y ) ) ), alpha66( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! alpha54( X, Y, Z, T ), ! alpha66( X, Y, Z, T )
% 0.89/1.48 , c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X
% 0.89/1.48 , Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.89/1.48 { ! alpha66( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.48 ) ), alpha78( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha66( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha78( X, Y, Z, T ), alpha66( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha78( X, Y, Z, T ), alpha90( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha78( X, Y, Z, T ), alpha25( X, Y, T ) }.
% 0.89/1.48 { ! alpha90( X, Y, Z, T ), ! alpha25( X, Y, T ), alpha78( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha90( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ) ), c_Orderings_Oord__class_Oless( X, Z, c_Groups_Otimes__class_Otimes
% 0.89/1.48 ( X, T, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.48 ), c_Groups_Ozero__class_Ozero( X ) ), alpha90( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.48 T, c_Int_Onumber__class_Onumber__of( X, Y ) ) ), alpha90( X, Y, Z, T ) }
% 0.89/1.48 .
% 0.89/1.48 { ! alpha54( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.48 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.48 , T, c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha54( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), alpha54( X, Y, Z, T ) }
% 0.89/1.48 .
% 0.89/1.48 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ) ), c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.48 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha25( X, Y, Z ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.48 , alpha25( X, Y, Z ) }.
% 0.89/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.48 ), c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.89/1.48 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.48 Y ) ) }.
% 0.89/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ),
% 0.89/1.48 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.48 ), c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.89/1.48 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 0.89/1.48 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.89/1.48 c_Rings_Oinverse__class_Oinverse( X, Z ) ), T ) =
% 0.89/1.48 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.48 c_Groups_Otimes__class_Otimes( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.89/1.48 ), c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X
% 0.89/1.48 , Y, Z ), T ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 X, Z ) ), Y ), alpha55( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 X, Z ) ), Y ), alpha67( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! alpha55( X, Y, Z, T ), ! alpha67( X, Y, Z, T )
% 0.89/1.48 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 0.89/1.48 X, T, c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 0.89/1.48 { ! alpha67( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.89/1.48 ) ), alpha79( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha67( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha79( X, Y, Z, T ), alpha67( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha79( X, Y, Z, T ), alpha91( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha79( X, Y, Z, T ), alpha26( X, Y, Z ) }.
% 0.89/1.48 { ! alpha91( X, Y, Z, T ), ! alpha26( X, Y, Z ), alpha79( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha91( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes
% 0.89/1.48 ( X, Y, c_Int_Onumber__class_Onumber__of( X, Z ) ), T ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.89/1.48 ), c_Groups_Ozero__class_Ozero( X ) ), alpha91( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.48 , Y, c_Int_Onumber__class_Onumber__of( X, Z ) ), T ), alpha91( X, Y, Z, T
% 0.89/1.48 ) }.
% 0.89/1.48 { ! alpha55( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 0.89/1.48 ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.48 c_Groups_Otimes__class_Otimes( X, Y, c_Int_Onumber__class_Onumber__of( X
% 0.89/1.48 , Z ) ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha55( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes
% 0.89/1.48 ( X, Y, c_Int_Onumber__class_Onumber__of( X, Z ) ) ), alpha55( X, Y, Z, T
% 0.89/1.48 ) }.
% 0.89/1.48 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.89/1.48 X ), Y ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.48 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha26( X, Y, Z ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.48 , Y ), alpha26( X, Y, Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha56( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha68( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! alpha56( X, Y, Z, T ), ! alpha68( X, Y, Z, T )
% 0.89/1.48 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 0.89/1.48 X, T, Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.89/1.48 { ! alpha68( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Z ), alpha80( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.89/1.48 , alpha68( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha80( X, Y, Z, T ), alpha68( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha80( X, Y, Z, T ), alpha92( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha80( X, Y, Z, T ), alpha27( X, Y, Z ) }.
% 0.89/1.48 { ! alpha92( X, Y, Z, T ), ! alpha27( X, Y, Z ), alpha80( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha92( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.48 , c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.48 Y ), Z ), T ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.48 alpha92( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.48 , c_Int_Onumber__class_Onumber__of( X, Y ), Z ), T ), alpha92( X, Y, Z, T
% 0.89/1.48 ) }.
% 0.89/1.48 { ! alpha56( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 0.89/1.48 ( X, T, c_Groups_Otimes__class_Otimes( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ), Z ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.89/1.48 alpha56( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Otimes__class_Otimes
% 0.89/1.48 ( X, c_Int_Onumber__class_Onumber__of( X, Y ), Z ) ), alpha56( X, Y, Z, T
% 0.89/1.48 ) }.
% 0.89/1.48 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.48 , c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.48 Y ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.48 , alpha27( X, Y, Z ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.89/1.48 , c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha27( X, Y, Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.89/1.48 ( X, Z, Y ) ), alpha57( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 0.89/1.48 ( X, Z, Y ) ), alpha69( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! alpha57( X, Y, Z, T ), ! alpha69( X, Y, Z, T )
% 0.89/1.48 , c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 0.89/1.48 ( X, T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 0.89/1.48 { ! alpha69( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Y ), alpha81( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 0.89/1.48 , alpha69( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha81( X, Y, Z, T ), alpha69( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha81( X, Y, Z, T ), alpha93( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha81( X, Y, Z, T ), alpha28( X, Y, T ) }.
% 0.89/1.48 { ! alpha93( X, Y, Z, T ), ! alpha28( X, Y, T ), alpha81( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha93( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.48 , Z, c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 X, T ), Y ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.89/1.48 alpha93( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Otimes__class_Otimes
% 0.89/1.48 ( X, c_Int_Onumber__class_Onumber__of( X, T ), Y ) ), alpha93( X, Y, Z, T
% 0.89/1.48 ) }.
% 0.89/1.48 { ! alpha57( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.89/1.48 ( X, c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 X, T ), Y ), Z ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.89/1.48 alpha57( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.48 , c_Int_Onumber__class_Onumber__of( X, T ), Y ), Z ), alpha57( X, Y, Z, T
% 0.89/1.48 ) }.
% 0.89/1.48 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.89/1.48 , c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero(
% 0.89/1.48 X ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 0.89/1.48 , alpha28( X, Y, Z ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 0.89/1.48 ( X, Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha28( X, Y, Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 X, Y ) ) ), alpha58( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 X, Y ) ) ), alpha70( X, Y, Z, T ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber( X ), ! alpha58( X, Y, Z, T ), ! alpha70( X, Y, Z, T )
% 0.89/1.48 , c_Orderings_Oord__class_Oless__eq( X, T,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 X, Y ) ) ) }.
% 0.89/1.48 { ! alpha70( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.48 ) ), alpha82( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha70( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha82( X, Y, Z, T ), alpha70( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha82( X, Y, Z, T ), alpha94( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha82( X, Y, Z, T ), alpha29( X, Y, T ) }.
% 0.89/1.48 { ! alpha94( X, Y, Z, T ), ! alpha29( X, Y, T ), alpha82( X, Y, Z, T ) }.
% 0.89/1.48 { ! alpha94( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.48 c_Groups_Otimes__class_Otimes( X, T, c_Int_Onumber__class_Onumber__of( X
% 0.89/1.48 , Y ) ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.48 ), c_Groups_Ozero__class_Ozero( X ) ), alpha94( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Otimes__class_Otimes
% 0.89/1.48 ( X, T, c_Int_Onumber__class_Onumber__of( X, Y ) ) ), alpha94( X, Y, Z, T
% 0.89/1.48 ) }.
% 0.89/1.48 { ! alpha58( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.89/1.48 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes
% 0.89/1.48 ( X, T, c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha58( X, Y, Z, T ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.89/1.48 , T, c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), alpha58( X, Y, Z, T
% 0.89/1.48 ) }.
% 0.89/1.48 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 0.89/1.48 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha29( X, Y, Z ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ) ), alpha29( X, Y, Z ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.89/1.48 ) ) ) ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 0.89/1.48 ( X ), Y ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.89/1.48 ) ) ) ) ) }.
% 0.89/1.48 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.89/1.48 class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.89/1.48 ) ) ) ) ) }.
% 0.89/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.48 , c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.48 , c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ) ), ! Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.89/1.48 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.48 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.89/1.48 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.48 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.89/1.48 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.48 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) }.
% 0.89/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.89/1.48 ( X, c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.89/1.48 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.89/1.48 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.89/1.48 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.89/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.48 , c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.48 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.89/1.48 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.89/1.48 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.89/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), ! Z =
% 0.89/1.48 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.89/1.48 }.
% 0.89/1.48 { ! class_Rings_Olinordered__idom( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ) ) ) }.
% 0.89/1.48 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.89/1.48 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.89/1.48 c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ) ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.48 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.89/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.89/1.48 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt(
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.48 c_Int_OBit1( c_Int_OPls ) ) ) ) ), X ) }.
% 0.89/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.89/1.48 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.89/1.48 , c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc(
% 0.89/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ), Z ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.89/1.48 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex,
% 0.89/1.48 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex(
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y,
% 0.89/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ) ) ), c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal
% 0.89/1.48 , c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ),
% 0.89/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.89/1.48 { c_Complex_ORe( c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, X )
% 0.89/1.48 ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_Complex_ORe( X
% 0.89/1.48 ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_Complex_ORe( X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.48 c_Complex_OIm( X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.89/1.48 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.89/1.48 { c_Complex_OIm( c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, X )
% 0.89/1.48 ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_Complex_OIm( X ) ),
% 0.89/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_Complex_ORe( X ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.48 c_Complex_OIm( X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.89/1.48 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ),
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt(
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.48 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), ! c_Orderings_Oord__class_Oless(
% 0.89/1.48 tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ),
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt(
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.89/1.48 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), c_Orderings_Oord__class_Oless(
% 0.89/1.48 tc_RealDef_Oreal, c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 0.89/1.48 tc_RealDef_Oreal, c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ) ) ), X ) }.
% 0.89/1.48 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 0.89/1.48 c_RealVector_Onorm__class_Onorm( X, Y ) ), !
% 0.89/1.48 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.48 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.89/1.48 Y ) ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Z ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.89/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ) ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.89/1.48 ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.89/1.48 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.89/1.48 X ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.89/1.48 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.89/1.48 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.89/1.48 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.89/1.48 Y ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X )
% 0.89/1.48 , Y ) }.
% 0.89/1.48 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.89/1.48 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 0.89/1.48 .
% 0.89/1.48 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) =
% 0.89/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y,
% 0.89/1.48 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ) }.
% 0.89/1.48 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) =
% 0.89/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y,
% 0.89/1.48 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ) }.
% 0.89/1.48 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.89/1.48 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.89/1.48 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.89/1.48 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.89/1.48 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.89/1.48 = c_Groups_Oone__class_Oone( X ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.89/1.48 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.89/1.48 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.89/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.89/1.48 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.89/1.48 ) ) }.
% 0.89/1.48 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.89/1.48 .
% 0.89/1.48 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.89/1.48 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.89/1.48 tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.89/1.48 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.89/1.48 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.89/1.48 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.89/1.48 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.89/1.48 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.89/1.48 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.89/1.48 { class_Power_Opower( tc_Int_Oint ) }.
% 0.89/1.48 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.89/1.48 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.89/1.48 { class_Int_Onumber( tc_Int_Oint ) }.
% 0.89/1.48 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.89/1.48 tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Int_Onumber( tc_Nat_Onat ) }.
% 0.89/1.48 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.89/1.48 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.89/1.48 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.89/1.48 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.89/1.48 tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.89/1.48 .
% 0.89/1.48 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_RealVector_Oreal__div__algebra( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_RealVector_Oreal__algebra__1( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Int_Onumber__ring( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Oabs__if( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Int_Onumber( tc_RealDef_Oreal ) }.
% 0.89/1.48 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.89/1.48 tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_RealVector_Oreal__div__algebra( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_RealVector_Oreal__algebra__1( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 0.89/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.89/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.89/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_Complex_ORe(
% 0.89/1.48 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_x, v_y ) ),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.89/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.89/1.48 c_Complex_OIm( c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, v_x,
% 0.89/1.48 v_y ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.89/1.48 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), c_Groups_Oplus__class_Oplus(
% 0.89/1.48 tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_Complex_ORe( v_x ),
% 0.89/1.48 c_Complex_ORe( v_y ) ) ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.89/1.48 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, c_Complex_OIm( v_x ),
% 0.89/1.48 c_Complex_OIm( v_y ) ) ) ) ) }.
% 0.89/1.48
% 0.89/1.48 *** allocated 15000 integers for clauses
% 0.89/1.48 *** allocated 22500 integers for clauses
% 0.89/1.48 *** allocated 33750 integers for clauses
% 0.89/1.48 *** allocated 50625 integers for clauses
% 0.89/1.48 *** allocated 75937 integers for clauses
% 0.89/1.48 *** allocated 113905 integers for clauses
% 0.89/1.48 percentage equality = 0.269456, percentage horn = 0.906064
% 0.89/1.48 This is a problem with some equality
% 0.89/1.48
% 0.89/1.48
% 0.89/1.48
% 0.89/1.48 Options Used:
% 0.89/1.48
% 0.89/1.48 useres = 1
% 0.89/1.48 useparamod = 1
% 0.89/1.48 useeqrefl = 1
% 0.89/1.48 useeqfact = 1
% 0.89/1.48 usefactor = 1
% 0.89/1.48 usesimpsplitting = 0
% 0.89/1.48 usesimpdemod = 5
% 0.89/1.48 usesimpres = 3
% 0.89/1.48
% 0.89/1.48 resimpinuse = 1000
% 0.89/1.48 resimpclauses = 20000
% 0.89/1.48 substype = eqrewr
% 0.89/1.48 backwardsubs = 1
% 0.89/1.48 selectoldest = 5
% 0.89/1.48
% 0.89/1.48 litorderings [0] = split
% 0.89/1.48 litorderings [1] = extend the termordering, first sorting on arguments
% 0.89/1.48
% 0.89/1.48 termordering = kbo
% 0.89/1.48
% 0.89/1.48 litapriori = 0
% 0.89/1.48 termapriori = 1
% 0.89/1.48 litaposteriori = 0
% 0.89/1.48 termaposteriori = 0
% 0.89/1.48 demodaposteriori = 0
% 0.89/1.48 ordereqreflfact = 0
% 0.89/1.48
% 0.89/1.48 litselect = negord
% 0.89/1.48
% 0.89/1.48 maxweight = 15
% 0.89/1.48 maxdepth = 30000
% 0.89/1.48 maxlength = 115
% 0.89/1.48 maxnrvars = 195
% 0.89/1.48 excuselevel = 1
% 0.89/1.48 increasemaxweight = 1
% 0.89/1.48
% 0.89/1.48 maxselected = 10000000
% 0.89/1.48 maxnrclauses = 10000000
% 0.89/1.48
% 0.89/1.48 showgenerated = 0
% 0.89/1.48 showkept = 0
% 0.89/1.48 showselected = 0
% 0.89/1.48 showdeleted = 0
% 0.89/1.48 showresimp = 1
% 0.89/1.48 showstatus = 2000
% 0.89/1.48
% 0.89/1.48 prologoutput = 0
% 0.89/1.48 nrgoals = 5000000
% 0.89/1.48 totalproof = 1
% 0.89/1.48
% 0.89/1.48 Symbols occurring in the translation:
% 0.89/1.48
% 0.89/1.48 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.89/1.48 . [1, 2] (w:1, o:179, a:1, s:1, b:0),
% 0.89/1.48 ! [4, 1] (w:0, o:95, a:1, s:1, b:0),
% 0.89/1.48 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.89/1.48 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.89/1.48 tc_RealDef_Oreal [35, 0] (w:1, o:8, a:1, s:1, b:0),
% 0.89/1.48 v_x [36, 0] (w:1, o:9, a:1, s:1, b:0),
% 0.89/1.48 c_Complex_ORe [37, 1] (w:1, o:100, a:1, s:1, b:0),
% 0.89/1.48 v_y [38, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.89/1.48 c_Groups_Ominus__class_Ominus [39, 3] (w:1, o:222, a:1, s:1, b:0),
% 0.89/1.48 c_Groups_Ozero__class_Ozero [40, 1] (w:1, o:102, a:1, s:1, b:0),
% 0.89/1.48 c_Groups_Oplus__class_Oplus [41, 3] (w:1, o:223, a:1, s:1, b:0),
% 0.89/1.48 tc_Nat_Onat [42, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.89/1.48 c_Int_OPls [43, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.89/1.48 c_Int_OBit1 [44, 1] (w:1, o:104, a:1, s:1, b:0),
% 0.89/1.48 c_Int_OBit0 [45, 1] (w:1, o:103, a:1, s:1, b:0),
% 0.89/1.48 c_Int_Onumber__class_Onumber__of [46, 2] (w:1, o:203, a:1, s:1, b:0)
% 0.89/1.48 ,
% 0.89/1.48 c_Power_Opower__class_Opower [47, 3] (w:1, o:226, a:1, s:1, b:0),
% 0.89/1.48 c_Complex_OIm [48, 1] (w:1, o:105, a:1, s:1, b:0),
% 0.89/1.48 c_NthRoot_Osqrt [49, 1] (w:1, o:106, a:1, s:1, b:0),
% 0.89/1.48 c_Orderings_Oord__class_Oless__eq [50, 3] (w:1, o:224, a:1, s:1, b:0)
% 0.89/1.48 ,
% 0.89/1.48 c_Groups_Oabs__class_Oabs [53, 2] (w:1, o:204, a:1, s:1, b:0),
% 0.89/1.48 class_Rings_Olinordered__idom [59, 1] (w:1, o:107, a:1, s:1, b:0),
% 0.89/1.48 class_Groups_Oordered__ab__group__add__abs [60, 1] (w:1, o:112, a:1
% 0.89/1.48 , s:1, b:0),
% 0.89/1.48 tc_Complex_Ocomplex [61, 0] (w:1, o:33, a:1, s:1, b:0),
% 0.89/1.48 class_Groups_Ozero [63, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.89/1.48 class_Groups_Ocomm__monoid__add [64, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.89/1.48
% 0.89/1.48 class_Groups_Omonoid__add [65, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.89/1.48 class_Groups_Olinordered__ab__group__add [67, 1] (w:1, o:115, a:1, s:
% 0.89/1.48 1, b:0),
% 0.89/1.48 class_Groups_Ogroup__add [69, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.89/1.48 class_Groups_Oab__group__add [70, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.89/1.48 tc_Int_Oint [73, 0] (w:1, o:37, a:1, s:1, b:0),
% 0.89/1.48 class_Groups_Oordered__comm__monoid__add [74, 1] (w:1, o:119, a:1, s:
% 0.89/1.48 1, b:0),
% 0.89/1.48 class_Groups_Oordered__ab__group__add [76, 1] (w:1, o:120, a:1, s:1
% 0.89/1.48 , b:0),
% 0.89/1.48 class_Int_Onumber__ring [77, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.89/1.48 class_Groups_Ocancel__semigroup__add [78, 1] (w:1, o:122, a:1, s:1
% 0.89/1.48 , b:0),
% 0.89/1.48 class_Groups_Ocancel__ab__semigroup__add [79, 1] (w:1, o:123, a:1, s:
% 0.89/1.48 1, b:0),
% 0.89/1.48 class_Groups_Oab__semigroup__add [81, 1] (w:1, o:124, a:1, s:1, b:0)
% 0.89/1.48 ,
% 0.89/1.48 class_Rings_Oring__1__no__zero__divisors [83, 1] (w:1, o:125, a:1, s:
% 0.89/1.48 1, b:0),
% 0.89/1.48 class_Rings_Osemiring__1 [84, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.89/1.48 class_Rings_Olinordered__semidom [85, 1] (w:1, o:133, a:1, s:1, b:0)
% 0.89/1.48 ,
% 0.89/1.48 class_Groups_Oordered__ab__semigroup__add__imp__le [86, 1] (w:1, o:
% 0.89/1.48 134, a:1, s:1, b:0),
% 0.89/1.48 class_Groups_Oordered__ab__semigroup__add [87, 1] (w:1, o:135, a:1
% 0.89/1.48 , s:1, b:0),
% 0.89/1.48 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt [90, 1] (w:1, o:101
% 0.89/1.48 , a:1, s:1, b:0),
% 0.89/1.48 class_Power_Opower [94, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.89/1.48 class_Rings_Omult__zero [95, 1] (w:1, o:144, a:1, s:1, b:0),
% 0.89/1.48 class_Rings_Ono__zero__divisors [96, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.89/1.48
% 0.89/1.48 class_Rings_Ozero__neq__one [97, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.89/1.48 class_Int_Onumber [106, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.89/1.48 class_Int_Oring__char__0 [107, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.89/1.48 c_Groups_Otimes__class_Otimes [114, 3] (w:1, o:227, a:1, s:1, b:0),
% 0.89/1.48 c_RealVector_Onorm__class_Onorm [115, 2] (w:1, o:205, a:1, s:1, b:0)
% 0.89/1.48 ,
% 0.89/1.48 class_Orderings_Opreorder [116, 1] (w:1, o:138, a:1, s:1, b:0),
% 0.89/1.48 class_Groups_Oab__semigroup__mult [117, 1] (w:1, o:149, a:1, s:1, b:0
% 0.89/1.48 ),
% 0.89/1.48 class_Groups_Omonoid__mult [120, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.89/1.48 class_Groups_Ocomm__monoid__mult [121, 1] (w:1, o:151, a:1, s:1, b:0)
% 0.89/1.48 ,
% 0.89/1.48 class_Rings_Olinordered__ring__strict [122, 1] (w:1, o:131, a:1, s:1
% 0.89/1.48 , b:0),
% 0.89/1.48 class_Rings_Osemiring [124, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.89/1.48 class_Rings_Oring [125, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.89/1.48 class_Rings_Olinordered__ring [126, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.89/1.48 class_Orderings_Olinorder [127, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.89/1.48 class_Orderings_Oord [130, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.89/1.48 tc_fun [131, 2] (w:1, o:208, a:1, s:1, b:0),
% 0.89/1.48 hAPP [132, 2] (w:1, o:209, a:1, s:1, b:0),
% 0.89/1.48 class_Orderings_Oorder [133, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.89/1.48 class_Rings_Ocomm__semiring__1 [138, 1] (w:1, o:154, a:1, s:1, b:0),
% 0.89/1.48
% 0.89/1.48 class_RealVector_Oreal__normed__vector [139, 1] (w:1, o:155, a:1, s:1
% 0.89/1.48 , b:0),
% 0.89/1.48 class_RealVector_Oreal__normed__algebra__1 [140, 1] (w:1, o:156, a:1
% 0.89/1.48 , s:1, b:0),
% 0.89/1.48 class_RealVector_Oreal__normed__algebra [149, 1] (w:1, o:157, a:1, s:
% 0.89/1.48 1, b:0),
% 0.89/1.48 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.89/1.48 150, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.89/1.48 class_RealVector_Oreal__normed__div__algebra [154, 1] (w:1, o:158, a:
% 0.89/1.48 1, s:1, b:0),
% 0.89/1.48 class_Rings_Oordered__ring__abs [157, 1] (w:1, o:159, a:1, s:1, b:0)
% 0.89/1.48 ,
% 0.89/1.48 class_Rings_Oordered__ring [159, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.89/1.48 class_Rings_Oring__no__zero__divisors [160, 1] (w:1, o:127, a:1, s:1
% 0.89/1.48 , b:0),
% 0.89/1.48 class_Rings_Ocomm__semiring [161, 1] (w:1, o:161, a:1, s:1, b:0),
% 0.89/1.48 class_Rings_Oordered__cancel__semiring [163, 1] (w:1, o:162, a:1, s:1
% 0.89/1.48 , b:0),
% 0.89/1.48 class_Rings_Oordered__semiring [164, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.89/1.51
% 0.89/1.51 class_Rings_Oordered__comm__semiring [165, 1] (w:1, o:164, a:1, s:1
% 0.89/1.51 , b:0),
% 0.89/1.51 c_Complex_Ocomplex_OComplex [166, 2] (w:1, o:210, a:1, s:1, b:0),
% 0.89/1.51 c_Nat_OSuc [168, 1] (w:1, o:173, a:1, s:1, b:0),
% 0.89/1.51 c_Complex_Ocnj [169, 1] (w:1, o:174, a:1, s:1, b:0),
% 0.89/1.51 class_Rings_Osemiring__0 [178, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.89/1.51 class_Rings_Ocomm__ring__1 [179, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.89/1.51 c_Complex_Ocomplex_Ocomplex__size [182, 1] (w:1, o:175, a:1, s:1, b:0
% 0.89/1.51 ),
% 0.89/1.51 c_RealVector_Oof__real [183, 2] (w:1, o:211, a:1, s:1, b:0),
% 0.89/1.51 c_Nat_Osize__class_Osize [184, 2] (w:1, o:212, a:1, s:1, b:0),
% 0.89/1.51 class_RealVector_Oreal__algebra__1 [185, 1] (w:1, o:165, a:1, s:1, b:
% 0.89/1.51 0),
% 0.89/1.51 c_Complex_Oii [187, 0] (w:1, o:88, a:1, s:1, b:0),
% 0.89/1.51 c_Groups_Ouminus__class_Ouminus [188, 2] (w:1, o:213, a:1, s:1, b:0)
% 0.89/1.51 ,
% 0.89/1.51 c_Rings_Oinverse__class_Odivide [189, 3] (w:1, o:228, a:1, s:1, b:0)
% 0.89/1.51 ,
% 0.89/1.51 c_Complex_Ocomplex_Ocomplex__rec [191, 3] (w:1, o:229, a:1, s:1, b:0)
% 0.89/1.51 ,
% 0.89/1.51 c_Complex_Ocomplex_Ocomplex__case [192, 3] (w:1, o:230, a:1, s:1, b:0
% 0.89/1.51 ),
% 0.89/1.51 class_Fields_Ofield__inverse__zero [193, 1] (w:1, o:108, a:1, s:1, b:
% 0.89/1.51 0),
% 0.89/1.51 class_RealVector_Oreal__field [194, 1] (w:1, o:166, a:1, s:1, b:0),
% 0.89/1.51 class_Rings_Odivision__ring [195, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.89/1.51 class_Rings_Odivision__ring__inverse__zero [196, 1] (w:1, o:168, a:1
% 0.89/1.51 , s:1, b:0),
% 0.89/1.51 class_Rings_Oidom [197, 1] (w:1, o:169, a:1, s:1, b:0),
% 0.89/1.51 class_RealVector_Oreal__normed__field [198, 1] (w:1, o:170, a:1, s:1
% 0.89/1.51 , b:0),
% 0.89/1.51 class_Fields_Ofield [199, 1] (w:1, o:109, a:1, s:1, b:0),
% 0.89/1.51 class_Rings_Oring__1 [202, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.89/1.51 class_Fields_Olinordered__field__inverse__zero [204, 1] (w:1, o:110
% 0.89/1.51 , a:1, s:1, b:0),
% 0.89/1.51 class_Fields_Olinordered__field [205, 1] (w:1, o:111, a:1, s:1, b:0)
% 0.89/1.51 ,
% 0.89/1.51 c_Rings_Oinverse__class_Oinverse [206, 2] (w:1, o:214, a:1, s:1, b:0)
% 0.89/1.51 ,
% 0.89/1.51 c_Orderings_Oord__class_Oless [207, 3] (w:1, o:225, a:1, s:1, b:0),
% 0.89/1.51 class_RealVector_Oreal__div__algebra [208, 1] (w:1, o:171, a:1, s:1
% 0.89/1.51 , b:0),
% 0.89/1.51 class_Groups_Oordered__cancel__ab__semigroup__add [209, 1] (w:1, o:
% 0.89/1.51 176, a:1, s:1, b:0),
% 0.89/1.51 class_Rings_Olinordered__semiring__strict [210, 1] (w:1, o:141, a:1
% 0.89/1.51 , s:1, b:0),
% 0.89/1.51 class_Rings_Olinordered__comm__semiring__strict [211, 1] (w:1, o:142
% 0.89/1.51 , a:1, s:1, b:0),
% 0.89/1.51 class_Rings_Olinordered__semiring [212, 1] (w:1, o:143, a:1, s:1, b:0
% 0.89/1.51 ),
% 0.89/1.51 class_Groups_Oabs__if [213, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.89/1.51 c_Groups_Oone__class_Oone [214, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.89/1.51 tc_HOL_Obool [219, 0] (w:1, o:36, a:1, s:1, b:0),
% 0.89/1.51 alpha1 [220, 3] (w:1, o:231, a:1, s:1, b:1),
% 0.89/1.51 alpha2 [221, 3] (w:1, o:240, a:1, s:1, b:1),
% 0.89/1.51 alpha3 [222, 2] (w:1, o:215, a:1, s:1, b:1),
% 0.89/1.51 alpha4 [223, 2] (w:1, o:219, a:1, s:1, b:1),
% 0.89/1.51 alpha5 [224, 2] (w:1, o:220, a:1, s:1, b:1),
% 0.89/1.51 alpha6 [225, 3] (w:1, o:241, a:1, s:1, b:1),
% 0.89/1.51 alpha7 [226, 3] (w:1, o:242, a:1, s:1, b:1),
% 0.89/1.51 alpha8 [227, 3] (w:1, o:243, a:1, s:1, b:1),
% 0.89/1.51 alpha9 [228, 3] (w:1, o:244, a:1, s:1, b:1),
% 0.89/1.51 alpha10 [229, 3] (w:1, o:232, a:1, s:1, b:1),
% 0.89/1.51 alpha11 [230, 3] (w:1, o:233, a:1, s:1, b:1),
% 0.89/1.51 alpha12 [231, 3] (w:1, o:234, a:1, s:1, b:1),
% 0.89/1.51 alpha13 [232, 3] (w:1, o:235, a:1, s:1, b:1),
% 0.89/1.51 alpha14 [233, 3] (w:1, o:236, a:1, s:1, b:1),
% 0.89/1.51 alpha15 [234, 3] (w:1, o:237, a:1, s:1, b:1),
% 0.89/1.51 alpha16 [235, 4] (w:1, o:262, a:1, s:1, b:1),
% 0.89/1.51 alpha17 [236, 4] (w:1, o:263, a:1, s:1, b:1),
% 0.89/1.51 alpha18 [237, 3] (w:1, o:238, a:1, s:1, b:1),
% 0.89/1.51 alpha19 [238, 3] (w:1, o:239, a:1, s:1, b:1),
% 0.89/1.51 alpha20 [239, 3] (w:1, o:245, a:1, s:1, b:1),
% 0.89/1.51 alpha21 [240, 3] (w:1, o:246, a:1, s:1, b:1),
% 0.89/1.51 alpha22 [241, 3] (w:1, o:247, a:1, s:1, b:1),
% 0.89/1.51 alpha23 [242, 3] (w:1, o:248, a:1, s:1, b:1),
% 0.89/1.51 alpha24 [243, 3] (w:1, o:249, a:1, s:1, b:1),
% 0.89/1.51 alpha25 [244, 3] (w:1, o:250, a:1, s:1, b:1),
% 0.89/1.51 alpha26 [245, 3] (w:1, o:251, a:1, s:1, b:1),
% 0.89/1.51 alpha27 [246, 3] (w:1, o:252, a:1, s:1, b:1),
% 10.05/10.46 alpha28 [247, 3] (w:1, o:253, a:1, s:1, b:1),
% 10.05/10.46 alpha29 [248, 3] (w:1, o:254, a:1, s:1, b:1),
% 10.05/10.46 alpha30 [249, 3] (w:1, o:255, a:1, s:1, b:1),
% 10.05/10.46 alpha31 [250, 3] (w:1, o:256, a:1, s:1, b:1),
% 10.05/10.46 alpha32 [251, 2] (w:1, o:216, a:1, s:1, b:1),
% 10.05/10.46 alpha33 [252, 2] (w:1, o:217, a:1, s:1, b:1),
% 10.05/10.46 alpha34 [253, 2] (w:1, o:218, a:1, s:1, b:1),
% 10.05/10.46 alpha35 [254, 4] (w:1, o:264, a:1, s:1, b:1),
% 10.05/10.46 alpha36 [255, 4] (w:1, o:265, a:1, s:1, b:1),
% 10.05/10.46 alpha37 [256, 4] (w:1, o:266, a:1, s:1, b:1),
% 10.05/10.46 alpha38 [257, 4] (w:1, o:267, a:1, s:1, b:1),
% 10.05/10.46 alpha39 [258, 3] (w:1, o:257, a:1, s:1, b:1),
% 10.05/10.46 alpha40 [259, 3] (w:1, o:258, a:1, s:1, b:1),
% 10.05/10.46 alpha41 [260, 4] (w:1, o:268, a:1, s:1, b:1),
% 10.05/10.46 alpha42 [261, 4] (w:1, o:269, a:1, s:1, b:1),
% 10.05/10.46 alpha43 [262, 3] (w:1, o:259, a:1, s:1, b:1),
% 10.05/10.46 alpha44 [263, 3] (w:1, o:260, a:1, s:1, b:1),
% 10.05/10.46 alpha45 [264, 4] (w:1, o:270, a:1, s:1, b:1),
% 10.05/10.46 alpha46 [265, 4] (w:1, o:271, a:1, s:1, b:1),
% 10.05/10.46 alpha47 [266, 4] (w:1, o:272, a:1, s:1, b:1),
% 10.05/10.46 alpha48 [267, 4] (w:1, o:273, a:1, s:1, b:1),
% 10.05/10.46 alpha49 [268, 4] (w:1, o:274, a:1, s:1, b:1),
% 10.05/10.46 alpha50 [269, 4] (w:1, o:275, a:1, s:1, b:1),
% 10.05/10.46 alpha51 [270, 4] (w:1, o:276, a:1, s:1, b:1),
% 10.05/10.46 alpha52 [271, 4] (w:1, o:277, a:1, s:1, b:1),
% 10.05/10.46 alpha53 [272, 4] (w:1, o:278, a:1, s:1, b:1),
% 10.05/10.46 alpha54 [273, 4] (w:1, o:279, a:1, s:1, b:1),
% 10.05/10.46 alpha55 [274, 4] (w:1, o:280, a:1, s:1, b:1),
% 10.05/10.46 alpha56 [275, 4] (w:1, o:281, a:1, s:1, b:1),
% 10.05/10.46 alpha57 [276, 4] (w:1, o:282, a:1, s:1, b:1),
% 10.05/10.46 alpha58 [277, 4] (w:1, o:283, a:1, s:1, b:1),
% 10.05/10.46 alpha59 [278, 4] (w:1, o:284, a:1, s:1, b:1),
% 10.05/10.46 alpha60 [279, 4] (w:1, o:285, a:1, s:1, b:1),
% 10.05/10.46 alpha61 [280, 4] (w:1, o:286, a:1, s:1, b:1),
% 10.05/10.46 alpha62 [281, 4] (w:1, o:287, a:1, s:1, b:1),
% 10.05/10.46 alpha63 [282, 4] (w:1, o:288, a:1, s:1, b:1),
% 10.05/10.46 alpha64 [283, 4] (w:1, o:289, a:1, s:1, b:1),
% 10.05/10.46 alpha65 [284, 4] (w:1, o:290, a:1, s:1, b:1),
% 10.05/10.46 alpha66 [285, 4] (w:1, o:291, a:1, s:1, b:1),
% 10.05/10.46 alpha67 [286, 4] (w:1, o:292, a:1, s:1, b:1),
% 10.05/10.46 alpha68 [287, 4] (w:1, o:293, a:1, s:1, b:1),
% 10.05/10.46 alpha69 [288, 4] (w:1, o:294, a:1, s:1, b:1),
% 10.05/10.46 alpha70 [289, 4] (w:1, o:295, a:1, s:1, b:1),
% 10.05/10.46 alpha71 [290, 4] (w:1, o:296, a:1, s:1, b:1),
% 10.05/10.46 alpha72 [291, 4] (w:1, o:297, a:1, s:1, b:1),
% 10.05/10.46 alpha73 [292, 4] (w:1, o:298, a:1, s:1, b:1),
% 10.05/10.46 alpha74 [293, 4] (w:1, o:299, a:1, s:1, b:1),
% 10.05/10.46 alpha75 [294, 4] (w:1, o:300, a:1, s:1, b:1),
% 10.05/10.46 alpha76 [295, 4] (w:1, o:301, a:1, s:1, b:1),
% 10.05/10.46 alpha77 [296, 4] (w:1, o:302, a:1, s:1, b:1),
% 10.05/10.46 alpha78 [297, 4] (w:1, o:303, a:1, s:1, b:1),
% 10.05/10.46 alpha79 [298, 4] (w:1, o:304, a:1, s:1, b:1),
% 10.05/10.46 alpha80 [299, 4] (w:1, o:305, a:1, s:1, b:1),
% 10.05/10.46 alpha81 [300, 4] (w:1, o:306, a:1, s:1, b:1),
% 10.05/10.46 alpha82 [301, 4] (w:1, o:307, a:1, s:1, b:1),
% 10.05/10.46 alpha83 [302, 4] (w:1, o:308, a:1, s:1, b:1),
% 10.05/10.46 alpha84 [303, 4] (w:1, o:309, a:1, s:1, b:1),
% 10.05/10.46 alpha85 [304, 4] (w:1, o:310, a:1, s:1, b:1),
% 10.05/10.46 alpha86 [305, 4] (w:1, o:311, a:1, s:1, b:1),
% 10.05/10.46 alpha87 [306, 4] (w:1, o:312, a:1, s:1, b:1),
% 10.05/10.46 alpha88 [307, 4] (w:1, o:313, a:1, s:1, b:1),
% 10.05/10.46 alpha89 [308, 4] (w:1, o:314, a:1, s:1, b:1),
% 10.05/10.46 alpha90 [309, 4] (w:1, o:315, a:1, s:1, b:1),
% 10.05/10.46 alpha91 [310, 4] (w:1, o:316, a:1, s:1, b:1),
% 10.05/10.46 alpha92 [311, 4] (w:1, o:317, a:1, s:1, b:1),
% 10.05/10.46 alpha93 [312, 4] (w:1, o:318, a:1, s:1, b:1),
% 10.05/10.46 alpha94 [313, 4] (w:1, o:319, a:1, s:1, b:1),
% 10.05/10.46 alpha95 [314, 2] (w:1, o:221, a:1, s:1, b:1),
% 10.05/10.46 skol1 [315, 3] (w:1, o:261, a:1, s:1, b:1),
% 10.05/10.46 skol2 [316, 2] (w:1, o:206, a:1, s:1, b:1),
% 10.05/10.46 skol3 [317, 2] (w:1, o:207, a:1, s:1, b:1),
% 10.05/10.46 skol4 [318, 0] (w:1, o:6, a:1, s:1, b:1),
% 10.05/10.46 skol5 [319, 0] (w:1, o:7, a:1, s:1, b:1).
% 10.05/10.46
% 10.05/10.46
% 10.05/10.46 Starting Search:
% 10.05/10.46
% 10.05/10.46 *** allocated 170857 integers for clauses
% 10.05/10.46 Resimplifying inuse:
% 10.05/10.46 Done
% 10.05/10.46
% 10.05/10.46
% 10.05/10.46 Intermediate Status:
% 10.05/10.46 Generated: 2726
% 10.05/10.46 Kept: 2017
% 10.05/10.46 Inuse: 62
% 10.05/10.46 Deleted: 9
% 10.05/10.46 Deletedinuse: 0
% 10.05/10.46
% 10.05/10.46 *** allocated 256285 integers for clauses
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 *** allocated 170857 integers for termspace/termends
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 6288
% 46.25/46.64 Kept: 4084
% 46.25/46.64 Inuse: 188
% 46.25/46.64 Deleted: 13
% 46.25/46.64 Deletedinuse: 0
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 *** allocated 384427 integers for clauses
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 *** allocated 256285 integers for termspace/termends
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 10573
% 46.25/46.64 Kept: 6090
% 46.25/46.64 Inuse: 280
% 46.25/46.64 Deleted: 20
% 46.25/46.64 Deletedinuse: 0
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 *** allocated 576640 integers for clauses
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 16920
% 46.25/46.64 Kept: 8103
% 46.25/46.64 Inuse: 316
% 46.25/46.64 Deleted: 20
% 46.25/46.64 Deletedinuse: 0
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 25101
% 46.25/46.64 Kept: 10108
% 46.25/46.64 Inuse: 455
% 46.25/46.64 Deleted: 39
% 46.25/46.64 Deletedinuse: 0
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 *** allocated 384427 integers for termspace/termends
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 *** allocated 864960 integers for clauses
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 32407
% 46.25/46.64 Kept: 12146
% 46.25/46.64 Inuse: 507
% 46.25/46.64 Deleted: 39
% 46.25/46.64 Deletedinuse: 0
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 40493
% 46.25/46.64 Kept: 14149
% 46.25/46.64 Inuse: 600
% 46.25/46.64 Deleted: 256
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 48351
% 46.25/46.64 Kept: 16149
% 46.25/46.64 Inuse: 688
% 46.25/46.64 Deleted: 265
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 *** allocated 576640 integers for termspace/termends
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 56261
% 46.25/46.64 Kept: 18173
% 46.25/46.64 Inuse: 729
% 46.25/46.64 Deleted: 266
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 *** allocated 1297440 integers for clauses
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 Resimplifying clauses:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 64053
% 46.25/46.64 Kept: 20202
% 46.25/46.64 Inuse: 754
% 46.25/46.64 Deleted: 3681
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 70514
% 46.25/46.64 Kept: 22693
% 46.25/46.64 Inuse: 799
% 46.25/46.64 Deleted: 3681
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 77189
% 46.25/46.64 Kept: 24767
% 46.25/46.64 Inuse: 824
% 46.25/46.64 Deleted: 3681
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 *** allocated 864960 integers for termspace/termends
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 84413
% 46.25/46.64 Kept: 27323
% 46.25/46.64 Inuse: 864
% 46.25/46.64 Deleted: 3681
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 *** allocated 1946160 integers for clauses
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 91121
% 46.25/46.64 Kept: 29326
% 46.25/46.64 Inuse: 904
% 46.25/46.64 Deleted: 3681
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 97677
% 46.25/46.64 Kept: 31361
% 46.25/46.64 Inuse: 942
% 46.25/46.64 Deleted: 3681
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 110363
% 46.25/46.64 Kept: 33635
% 46.25/46.64 Inuse: 964
% 46.25/46.64 Deleted: 3681
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 123189
% 46.25/46.64 Kept: 35694
% 46.25/46.64 Inuse: 979
% 46.25/46.64 Deleted: 3681
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 132687
% 46.25/46.64 Kept: 37727
% 46.25/46.64 Inuse: 994
% 46.25/46.64 Deleted: 3681
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 141119
% 46.25/46.64 Kept: 39771
% 46.25/46.64 Inuse: 1034
% 46.25/46.64 Deleted: 3681
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying clauses:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 *** allocated 1297440 integers for termspace/termends
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 148625
% 46.25/46.64 Kept: 41784
% 46.25/46.64 Inuse: 1068
% 46.25/46.64 Deleted: 4044
% 46.25/46.64 Deletedinuse: 204
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 *** allocated 2919240 integers for clauses
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 158615
% 46.25/46.64 Kept: 44580
% 46.25/46.64 Inuse: 1089
% 46.25/46.64 Deleted: 4046
% 46.25/46.64 Deletedinuse: 206
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64 Resimplifying inuse:
% 46.25/46.64 Done
% 46.25/46.64
% 46.25/46.64
% 46.25/46.64 Intermediate Status:
% 46.25/46.64 Generated: 166763
% 46.25/46.64 Kept: 46630
% 118.90/119.38 Inuse: 1120
% 118.90/119.38 Deleted: 4046
% 118.90/119.38 Deletedinuse: 206
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38
% 118.90/119.38 Intermediate Status:
% 118.90/119.38 Generated: 175789
% 118.90/119.38 Kept: 49240
% 118.90/119.38 Inuse: 1139
% 118.90/119.38 Deleted: 4047
% 118.90/119.38 Deletedinuse: 207
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38
% 118.90/119.38 Intermediate Status:
% 118.90/119.38 Generated: 183156
% 118.90/119.38 Kept: 51256
% 118.90/119.38 Inuse: 1172
% 118.90/119.38 Deleted: 4050
% 118.90/119.38 Deletedinuse: 207
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38
% 118.90/119.38 Intermediate Status:
% 118.90/119.38 Generated: 194618
% 118.90/119.38 Kept: 53298
% 118.90/119.38 Inuse: 1197
% 118.90/119.38 Deleted: 4050
% 118.90/119.38 Deletedinuse: 207
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38
% 118.90/119.38 Intermediate Status:
% 118.90/119.38 Generated: 202049
% 118.90/119.38 Kept: 56099
% 118.90/119.38 Inuse: 1220
% 118.90/119.38 Deleted: 4052
% 118.90/119.38 Deletedinuse: 209
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38
% 118.90/119.38 Intermediate Status:
% 118.90/119.38 Generated: 210517
% 118.90/119.38 Kept: 59723
% 118.90/119.38 Inuse: 1246
% 118.90/119.38 Deleted: 4052
% 118.90/119.38 Deletedinuse: 209
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38 *** allocated 1946160 integers for termspace/termends
% 118.90/119.38 Resimplifying clauses:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38
% 118.90/119.38 Intermediate Status:
% 118.90/119.38 Generated: 221262
% 118.90/119.38 Kept: 62880
% 118.90/119.38 Inuse: 1256
% 118.90/119.38 Deleted: 4382
% 118.90/119.38 Deletedinuse: 209
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38
% 118.90/119.38 Intermediate Status:
% 118.90/119.38 Generated: 225204
% 118.90/119.38 Kept: 65073
% 118.90/119.38 Inuse: 1261
% 118.90/119.38 Deleted: 4382
% 118.90/119.38 Deletedinuse: 209
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38 *** allocated 4378860 integers for clauses
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38
% 118.90/119.38 Intermediate Status:
% 118.90/119.38 Generated: 246532
% 118.90/119.38 Kept: 67789
% 118.90/119.38 Inuse: 1297
% 118.90/119.38 Deleted: 4399
% 118.90/119.38 Deletedinuse: 212
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38
% 118.90/119.38 Intermediate Status:
% 118.90/119.38 Generated: 258815
% 118.90/119.38 Kept: 70752
% 118.90/119.38 Inuse: 1312
% 118.90/119.38 Deleted: 4399
% 118.90/119.38 Deletedinuse: 212
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38
% 118.90/119.38 Intermediate Status:
% 118.90/119.38 Generated: 272788
% 118.90/119.38 Kept: 73725
% 118.90/119.38 Inuse: 1337
% 118.90/119.38 Deleted: 4399
% 118.90/119.38 Deletedinuse: 212
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.38
% 118.90/119.38
% 118.90/119.38 Intermediate Status:
% 118.90/119.38 Generated: 281615
% 118.90/119.38 Kept: 75764
% 118.90/119.38 Inuse: 1372
% 118.90/119.38 Deleted: 4401
% 118.90/119.38 Deletedinuse: 214
% 118.90/119.38
% 118.90/119.38 Resimplifying inuse:
% 118.90/119.38 Done
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39
% 118.90/119.39 Intermediate Status:
% 118.90/119.39 Generated: 291012
% 118.90/119.39 Kept: 77883
% 118.90/119.39 Inuse: 1412
% 118.90/119.39 Deleted: 4401
% 118.90/119.39 Deletedinuse: 214
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39
% 118.90/119.39 Intermediate Status:
% 118.90/119.39 Generated: 301961
% 118.90/119.39 Kept: 81896
% 118.90/119.39 Inuse: 1442
% 118.90/119.39 Deleted: 4401
% 118.90/119.39 Deletedinuse: 214
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39 Resimplifying clauses:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39
% 118.90/119.39 Intermediate Status:
% 118.90/119.39 Generated: 308257
% 118.90/119.39 Kept: 83919
% 118.90/119.39 Inuse: 1463
% 118.90/119.39 Deleted: 5228
% 118.90/119.39 Deletedinuse: 214
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39
% 118.90/119.39 Intermediate Status:
% 118.90/119.39 Generated: 326053
% 118.90/119.39 Kept: 88479
% 118.90/119.39 Inuse: 1502
% 118.90/119.39 Deleted: 5236
% 118.90/119.39 Deletedinuse: 222
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39
% 118.90/119.39 Intermediate Status:
% 118.90/119.39 Generated: 330118
% 118.90/119.39 Kept: 91050
% 118.90/119.39 Inuse: 1505
% 118.90/119.39 Deleted: 5236
% 118.90/119.39 Deletedinuse: 222
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39 *** allocated 2919240 integers for termspace/termends
% 118.90/119.39
% 118.90/119.39 Intermediate Status:
% 118.90/119.39 Generated: 340774
% 118.90/119.39 Kept: 94181
% 118.90/119.39 Inuse: 1512
% 118.90/119.39 Deleted: 5236
% 118.90/119.39 Deletedinuse: 222
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39
% 118.90/119.39 Intermediate Status:
% 118.90/119.39 Generated: 350296
% 118.90/119.39 Kept: 96258
% 118.90/119.39 Inuse: 1552
% 118.90/119.39 Deleted: 5236
% 118.90/119.39 Deletedinuse: 222
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39
% 118.90/119.39 Intermediate Status:
% 118.90/119.39 Generated: 360165
% 118.90/119.39 Kept: 98367
% 118.90/119.39 Inuse: 1592
% 118.90/119.39 Deleted: 5236
% 118.90/119.39 Deletedinuse: 222
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39 *** allocated 6568290 integers for clauses
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39
% 118.90/119.39 Intermediate Status:
% 118.90/119.39 Generated: 369667
% 118.90/119.39 Kept: 100381
% 118.90/119.39 Inuse: 1635
% 118.90/119.39 Deleted: 5237
% 118.90/119.39 Deletedinuse: 223
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39
% 118.90/119.39 Intermediate Status:
% 118.90/119.39 Generated: 375347
% 118.90/119.39 Kept: 103140
% 118.90/119.39 Inuse: 1642
% 118.90/119.39 Deleted: 5237
% 118.90/119.39 Deletedinuse: 223
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39 Resimplifying clauses:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39
% 118.90/119.39 Intermediate Status:
% 118.90/119.39 Generated: 413425
% 118.90/119.39 Kept: 108002
% 118.90/119.39 Inuse: 1662
% 118.90/119.39 Deleted: 9136
% 118.90/119.39 Deletedinuse: 223
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39 Resimplifying inuse:
% 118.90/119.39 Done
% 118.90/119.39
% 118.90/119.39
% 118.90/119.39 Intermediate Status:
% 118.90/119.39 Generated: 422575
% 252.32/252.79 Kept: 110034
% 252.32/252.79 Inuse: 1690
% 252.32/252.79 Deleted: 9136
% 252.32/252.79 Deletedinuse: 223
% 252.32/252.79
% 252.32/252.79 Resimplifying inuse:
% 252.32/252.79 Done
% 252.32/252.79
% 252.32/252.79 Resimplifying inuse:
% 252.32/252.79 Done
% 252.32/252.79
% 252.32/252.79
% 252.32/252.79 Intermediate Status:
% 252.32/252.79 Generated: 455756
% 252.32/252.79 Kept: 113876
% 252.32/252.79 Inuse: 1717
% 252.32/252.79 Deleted: 9136
% 252.32/252.79 Deletedinuse: 223
% 252.32/252.79
% 252.32/252.79 Resimplifying inuse:
% 252.32/252.79 Done
% 252.32/252.79
% 252.32/252.79 Resimplifying inuse:
% 252.32/252.79 Done
% 252.32/252.79
% 252.32/252.79
% 252.32/252.79 Intermediate Status:
% 252.32/252.79 Generated: 463409
% 252.32/252.79 Kept: 115878
% 252.32/252.79 Inuse: 1742
% 252.32/252.79 Deleted: 9136
% 252.32/252.79 Deletedinuse: 223
% 252.32/252.79
% 252.32/252.79 Resimplifying inuse:
% 252.32/252.79 Done
% 252.32/252.79
% 252.32/252.79 Resimplifying inuse:
% 252.32/252.79 Done
% 252.32/252.79
% 252.32/252.79
% 252.32/252.79 Intermediate Status:
% 252.32/252.79 Generated: 470727
% 252.32/252.79 Kept: 118070
% 252.32/252.79 Inuse: 1767
% 252.32/252.79 Deleted: 9136
% 252.32/252.79 Deletedinuse: 223
% 252.32/252.79
% 252.32/252.79 Resimplifying inuse:
% 252.32/252.79 Done
% 252.32/252.79
% 252.32/252.79 Resimplifying inuse:
% 252.32/252.79 Done
% 252.32/252.79
% 252.32/252.79
% 252.32/252.79 Intermediate Status:
% 252.32/252.79 Generated: 476714
% 252.32/252.79 Kept: 120362
% 252.32/252.79 Inuse: 1793
% 252.32/252.79 Deleted: 9143
% 252.32/252.79 Deletedinuse: 226
% 252.32/252.79
% 252.32/252.79 Resimplifying inuse:
% 252.32/252.79 Done
% 252.32/252.79
% 252.32/252.79
% 252.32/252.79 Intermediate Status:
% 252.32/252.79 Generated: 488268
% 252.32/252.79 Kept: 123567
% 252.32/252.79 Inuse: 1806
% 252.32/252.79 Deleted: 9145
% 252.32/252.79 Deletedinuse: 226
% 252.32/252.79
% 252.32/252.79 Resimplifying inuse:
% 252.32/252.79 Done
% 252.32/252.79
% 252.32/252.79 Resimplifying clauses:
% 252.32/252.79 Done
% 252.32/252.79
% 252.32/252.79 *** allocated 4378860 integers for termspace/termends
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 496444
% 252.32/252.80 Kept: 127457
% 252.32/252.80 Inuse: 1814
% 252.32/252.80 Deleted: 9510
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 513712
% 252.32/252.80 Kept: 130078
% 252.32/252.80 Inuse: 1826
% 252.32/252.80 Deleted: 9510
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 533545
% 252.32/252.80 Kept: 133183
% 252.32/252.80 Inuse: 1841
% 252.32/252.80 Deleted: 9510
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 543333
% 252.32/252.80 Kept: 135425
% 252.32/252.80 Inuse: 1871
% 252.32/252.80 Deleted: 9510
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 557254
% 252.32/252.80 Kept: 137655
% 252.32/252.80 Inuse: 1891
% 252.32/252.80 Deleted: 9510
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 565772
% 252.32/252.80 Kept: 139907
% 252.32/252.80 Inuse: 1911
% 252.32/252.80 Deleted: 9510
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 573572
% 252.32/252.80 Kept: 142033
% 252.32/252.80 Inuse: 1936
% 252.32/252.80 Deleted: 9510
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 Resimplifying clauses:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 580274
% 252.32/252.80 Kept: 144034
% 252.32/252.80 Inuse: 1970
% 252.32/252.80 Deleted: 10086
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 586370
% 252.32/252.80 Kept: 146133
% 252.32/252.80 Inuse: 2001
% 252.32/252.80 Deleted: 10086
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 *** allocated 9852435 integers for clauses
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 606825
% 252.32/252.80 Kept: 151620
% 252.32/252.80 Inuse: 2031
% 252.32/252.80 Deleted: 10086
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 620958
% 252.32/252.80 Kept: 155783
% 252.32/252.80 Inuse: 2036
% 252.32/252.80 Deleted: 10086
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 637563
% 252.32/252.80 Kept: 160372
% 252.32/252.80 Inuse: 2046
% 252.32/252.80 Deleted: 10086
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 653478
% 252.32/252.80 Kept: 164904
% 252.32/252.80 Inuse: 2056
% 252.32/252.80 Deleted: 10086
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 Resimplifying clauses:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 670747
% 252.32/252.80 Kept: 168393
% 252.32/252.80 Inuse: 2076
% 252.32/252.80 Deleted: 10172
% 252.32/252.80 Deletedinuse: 226
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 683903
% 252.32/252.80 Kept: 170556
% 252.32/252.80 Inuse: 2088
% 252.32/252.80 Deleted: 10176
% 252.32/252.80 Deletedinuse: 227
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 692110
% 252.32/252.80 Kept: 172562
% 252.32/252.80 Inuse: 2115
% 252.32/252.80 Deleted: 10179
% 252.32/252.80 Deletedinuse: 228
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 712695
% 252.32/252.80 Kept: 175805
% 252.32/252.80 Inuse: 2126
% 252.32/252.80 Deleted: 10179
% 252.32/252.80 Deletedinuse: 228
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80 Resimplifying inuse:
% 252.32/252.80 Done
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 Generated: 721073
% 252.32/252.80 Kept: 177811
% 252.32/252.80 Inuse: 2151
% 252.32/252.80 Deleted: 10179
% 252.32/252.80 Deletedinuse: 228
% 252.32/252.80
% 252.32/252.80
% 252.32/252.80 Intermediate Status:
% 252.32/252.80 GenerCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------