TSTP Solution File: SWW172+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW172+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 23:21:01 EDT 2022
% Result : Timeout 300.02s 300.56s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW172+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sat Jun 4 18:39:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.91/1.48 *** allocated 10000 integers for termspace/termends
% 0.91/1.48 *** allocated 10000 integers for clauses
% 0.91/1.48 *** allocated 10000 integers for justifications
% 0.91/1.48 *** allocated 15000 integers for termspace/termends
% 0.91/1.48 *** allocated 22500 integers for termspace/termends
% 0.91/1.48 Bliksem 1.12
% 0.91/1.48
% 0.91/1.48
% 0.91/1.48 Automatic Strategy Selection
% 0.91/1.48
% 0.91/1.48 *** allocated 33750 integers for termspace/termends
% 0.91/1.48 *** allocated 50625 integers for termspace/termends
% 0.91/1.48 *** allocated 75937 integers for termspace/termends
% 0.91/1.48 *** allocated 113905 integers for termspace/termends
% 0.91/1.48
% 0.91/1.48 Clauses:
% 0.91/1.48
% 0.91/1.48 { v_y____ = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.48 { c_Int_OBit0( c_Int_OPls ) = c_Int_OPls }.
% 0.91/1.48 { ! c_Int_OPls = c_Int_OBit0( X ), c_Int_OPls = X }.
% 0.91/1.48 { ! c_Int_OPls = X, c_Int_OPls = c_Int_OBit0( X ) }.
% 0.91/1.48 { ! c_Int_OBit0( X ) = c_Int_OPls, X = c_Int_OPls }.
% 0.91/1.48 { ! X = c_Int_OPls, c_Int_OBit0( X ) = c_Int_OPls }.
% 0.91/1.48 { ! c_Int_OBit0( Y ) = c_Int_OBit1( X ) }.
% 0.91/1.48 { ! c_Int_OBit1( Y ) = c_Int_OBit0( X ) }.
% 0.91/1.48 { ! c_Int_OPls = c_Int_OBit1( X ) }.
% 0.91/1.48 { ! c_Int_OBit1( X ) = c_Int_OPls }.
% 0.91/1.48 { v_z = c_Complex_Ocomplex_OComplex( v_x____, v_y____ ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_x____ ),
% 0.91/1.48 c_Power_Opower__class_Opower( tc_Complex_Ocomplex,
% 0.91/1.48 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( v_z ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) = v_z }.
% 0.91/1.48 { ! class_Groups_Omonoid__mult( X ), ! class_Int_Onumber( X ),
% 0.91/1.48 c_Power_Opower__class_Opower( X, c_Int_Onumber__class_Onumber__of( X, Y )
% 0.91/1.48 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.91/1.48 ( c_Int_OPls ) ) ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Osemiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Rings_Oring__1__no__zero__divisors( X ), !
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.91/1.48 .
% 0.91/1.48 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_x____ ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_x____ ) ) }.
% 0.91/1.48 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ) ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.91/1.48 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Groups_Otimes__class_Otimes(
% 0.91/1.48 tc_Int_Oint, Z, Y ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.91/1.48 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.91/1.48 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.91/1.48 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.91/1.48 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Int_OPls, X ) = c_Int_OPls
% 0.91/1.48 }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Int_OBit0( Y ), X ) =
% 0.91/1.48 c_Int_OBit0( c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.48 { c_Int_OPls = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.91/1.48 X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Z,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ), Y ) ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.48 c_Int_OPls ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) }.
% 0.91/1.48 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Power_Opower__class_Opower(
% 0.91/1.48 X, Z, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.91/1.48 c_Int_OBit1( c_Int_OPls ) ) ) ) = c_Power_Opower__class_Opower( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), Z = Y }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Z
% 0.91/1.48 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.91/1.48 ( c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 0.91/1.48 ( X, Z, Y ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.91/1.48 X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ), Y ) = Y
% 0.91/1.48 }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }
% 0.91/1.48 .
% 0.91/1.48 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Y, Y ), Y ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 0.91/1.48 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.91/1.48 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 0.91/1.48 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 0.91/1.48 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 0.91/1.48 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 0.91/1.48 { ! c_Int_OBit1( Y ) = c_Int_OBit1( X ), Y = X }.
% 0.91/1.48 { ! Y = X, c_Int_OBit1( Y ) = c_Int_OBit1( X ) }.
% 0.91/1.48 { ! c_Int_OBit0( Y ) = c_Int_OBit0( X ), Y = X }.
% 0.91/1.48 { ! Y = X, c_Int_OBit0( Y ) = c_Int_OBit0( X ) }.
% 0.91/1.48 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) = c_Groups_Otimes__class_Otimes( X, Y, Y ) }.
% 0.91/1.48 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Z,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ), Y ) ) = c_Power_Opower__class_Opower( X,
% 0.91/1.48 c_Power_Opower__class_Opower( X, Z, Y ), c_Int_Onumber__class_Onumber__of
% 0.91/1.48 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.91/1.48 ( X, c_Power_Opower__class_Opower( X, Y, c_Groups_Otimes__class_Otimes(
% 0.91/1.48 tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.91/1.48 c_Int_OBit1( c_Int_OPls ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.48 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Z
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ), Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Power_Opower__class_Opower( X, Z, Y ), c_Power_Opower__class_Opower( X
% 0.91/1.48 , Z, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 Y, Y ) = c_Power_Opower__class_Opower( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) }.
% 0.91/1.48 { v_z = c_Complex_Ocomplex_OComplex( skol1, skol10 ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.91/1.48 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) = c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.91/1.48 c_Int_OBit1( c_Int_OPls ) ) ), X ), c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.91/1.48 { c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, v_x____ ) ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.91/1.48 v_x____ ) }.
% 0.91/1.48 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.91/1.48 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.91/1.48 , ! c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.91/1.48 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.91/1.48 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.91/1.48 , ! c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.91/1.48 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ), !
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.91/1.48 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.91/1.48 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.91/1.48 ( X, Z, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ), c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X
% 0.91/1.48 , Z, T ), c_Power_Opower__class_Opower( X, Y, T ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.91/1.48 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y
% 0.91/1.48 , Y ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), alpha1( X, Y, Z ), alpha11( X
% 0.91/1.48 , Y, Z ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.91/1.48 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ), alpha11( X, Y, Z ) }.
% 0.91/1.48 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.91/1.48 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y ), alpha1( X, Y, Z ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.91/1.48 , Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha2( X, Y, Z ), alpha12( X
% 0.91/1.48 , Y, Z ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.91/1.48 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.91/1.48 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.91/1.48 ( X ), Y ), alpha12( X, Y, Z ) }.
% 0.91/1.48 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.91/1.48 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ), alpha2( X, Y, Z ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.91/1.48 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 0.91/1.48 { c_NthRoot_Osqrt( c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y, X ) )
% 0.91/1.48 = c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.91/1.48 X ) }.
% 0.91/1.48 { c_NthRoot_Osqrt( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X )
% 0.91/1.48 ) = c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y
% 0.91/1.48 ), c_NthRoot_Osqrt( X ) ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.91/1.48 { c_Power_Opower__class_Opower( tc_Int_Oint, c_Power_Opower__class_Opower(
% 0.91/1.48 tc_Int_Oint, Z, Y ), X ) = c_Power_Opower__class_Opower( tc_Int_Oint, Z,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.91/1.48 ( tc_Int_Oint, Z, Y ), X ) = c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.91/1.48 Z, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.91/1.48 { ! c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ), Y = X }.
% 0.91/1.48 { ! Y = X, c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ) }.
% 0.91/1.48 { c_NthRoot_Osqrt( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) )
% 0.91/1.48 = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.91/1.48 ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) =
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.48 Y ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Groups_Ouminus__class_Ouminus(
% 0.91/1.48 tc_Int_Oint, Y ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.91/1.48 , c_NthRoot_Osqrt( X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y
% 0.91/1.48 ), c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.91/1.48 tc_RealDef_Oreal, Y, X ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 0.91/1.48 , c_NthRoot_Osqrt( X ) ) }.
% 0.91/1.48 { ! c_NthRoot_Osqrt( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.91/1.48 , X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.48 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X
% 0.91/1.48 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.48 { c_NthRoot_Osqrt( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.48 { ! class_Rings_Oidom( X ), ! c_Groups_Otimes__class_Otimes( X, Z, Z ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Y, Y ), Z = Y, Z =
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.91/1.48 { ! class_Rings_Oidom( X ), ! Z = Y, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.91/1.48 ) = c_Groups_Otimes__class_Otimes( X, Y, Y ) }.
% 0.91/1.48 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Z ) = c_Groups_Otimes__class_Otimes
% 0.91/1.48 ( X, Y, Y ) }.
% 0.91/1.48 { ! class_Rings_Oring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 0.91/1.48 ( X, Y ) ) = c_Groups_Otimes__class_Otimes( X, Z, Y ) }.
% 0.91/1.48 { ! class_Rings_Oring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.48 Y ) ) }.
% 0.91/1.48 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.91/1.48 , Y ) }.
% 0.91/1.48 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.48 Y ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.48 Z ) ), Y ) = c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Groups_Ouminus__class_Ouminus(
% 0.91/1.48 tc_Int_Oint, Z ) ), Y ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.91/1.48 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.91/1.48 ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.91/1.48 c_Int_OBit1( X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.91/1.48 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.91/1.48 ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.91/1.48 c_Int_OBit1( X ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OPls )
% 0.91/1.48 }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.91/1.48 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.91/1.48 ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.91/1.48 c_Int_OBit0( X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.91/1.48 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.91/1.48 ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.91/1.48 c_Int_OBit0( X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 0.91/1.48 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.91/1.48 .
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.91/1.48 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.91/1.48 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.91/1.48 .
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1
% 0.91/1.48 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.91/1.48 }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1(
% 0.91/1.48 X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.91/1.48 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.91/1.48 ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.91/1.48 c_Int_OBit1( X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.91/1.48 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.91/1.48 ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.91/1.48 c_Int_OBit1( X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0
% 0.91/1.48 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.91/1.48 }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0(
% 0.91/1.48 X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.91/1.48 c_Int_OPls ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.91/1.48 c_Int_OPls ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.91/1.48 c_Int_OPls ) }.
% 0.91/1.48 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.91/1.48 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, T, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, U, T
% 0.91/1.48 ), Y ) ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Z, Y ) ) = c_Groups_Otimes__class_Otimes( X, U,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.91/1.48 , Y ) ) ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, T, Y
% 0.91/1.48 ), Z ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.91/1.48 , Y ) ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.91/1.48 ), Y ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 T, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Otimes__class_Otimes( X, T
% 0.91/1.48 , Y ) ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 Z, Y ) = c_Groups_Otimes__class_Otimes( X, Y, Z ) }.
% 0.91/1.48 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, T,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) ) =
% 0.91/1.48 c_Power_Opower__class_Opower( X, c_Power_Opower__class_Opower( X, T, Z )
% 0.91/1.48 , Y ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.48 c_Power_Opower__class_Opower( X, T, Z ), Y ) =
% 0.91/1.48 c_Power_Opower__class_Opower( X, T, c_Groups_Otimes__class_Otimes(
% 0.91/1.48 tc_Nat_Onat, Z, Y ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.91/1.48 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.91/1.48 { ! c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) = X, c_Orderings_Oord__class_Oless__eq(
% 0.91/1.48 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }
% 0.91/1.48 .
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) = X }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) = X }.
% 0.91/1.48 { ! c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) = X, ! c_Orderings_Oord__class_Oless__eq(
% 0.91/1.48 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.91/1.48 c_NthRoot_Osqrt( X ) = Y }.
% 0.91/1.48 { ! class_Rings_Oring__1( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Int_Onumber__class_Onumber__of
% 0.91/1.48 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.91/1.48 { ! class_Rings_Oring__1( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.91/1.48 c_Int_OBit1( c_Int_OPls ) ) ), Y ) ) = c_Power_Opower__class_Opower( X, Z
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ), Y ) ) }.
% 0.91/1.48 { ! class_Rings_Ono__zero__divisors( X ), ! c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.91/1.48 .
% 0.91/1.48 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ), Z = c_Groups_Ozero__class_Ozero( X ), !
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Y, Z ) = c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Rings_Oring__no__zero__divisors( X ), !
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ), Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.91/1.48 ( X ) }.
% 0.91/1.48 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.91/1.48 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.91/1.48 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 Y, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 }.
% 0.91/1.48 { ! class_Rings_Omult__zero( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 }.
% 0.91/1.48 { ! class_Rings_Omult__zero( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 }.
% 0.91/1.48 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), ! c_Power_Opower__class_Opower( X, Y, Z
% 0.91/1.48 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.91/1.48 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.91/1.48 , ! c_Power_Opower__class_Opower( X, Z, Y ) = c_Groups_Ozero__class_Ozero
% 0.91/1.48 ( X ), Z = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.91/1.48 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.91/1.48 , ! c_Power_Opower__class_Opower( X, Z, Y ) = c_Groups_Ozero__class_Ozero
% 0.91/1.48 ( X ), ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.91/1.48 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.91/1.48 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.91/1.48 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( X, Z, Y ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Groups_Omonoid__mult( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Power_Opower__class_Opower( X, Z, Y ), Z ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, c_Power_Opower__class_Opower( X, Z,
% 0.91/1.48 Y ) ) }.
% 0.91/1.48 { ! class_Groups_Ocomm__monoid__mult( X ), c_Power_Opower__class_Opower( X
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T, Y )
% 0.91/1.48 , c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T, Y )
% 0.91/1.48 , c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.48 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.48 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__semiring( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ), U ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, U ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Y, T ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__semiring( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ), U ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, U ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Y, T ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.48 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( X, T, Y ), c_Groups_Otimes__class_Otimes
% 0.91/1.48 ( X, T, Z ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.48 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( X, Y, T ), c_Groups_Otimes__class_Otimes
% 0.91/1.48 ( X, Z, T ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__semiring( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__semiring( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Z, T ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.48 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( X, Z, Y ), c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), c_Groups_Otimes__class_Otimes( X, Y, Z
% 0.91/1.48 ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( X ) ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( X ) ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) ) }.
% 0.91/1.48 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 0.91/1.48 ( tc_Complex_Ocomplex, X ), Z = c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_RealDef_Oreal, X ) }.
% 0.91/1.48 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 0.91/1.48 ( tc_Complex_Ocomplex, X ), Y = c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_RealDef_Oreal ) }.
% 0.91/1.48 { ! Z = c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ), ! Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.48 c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Complex_Ocomplex, X ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ) ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Otimes__class_Otimes
% 0.91/1.48 ( tc_Int_Oint, X, Y ) ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.48 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.91/1.48 ( X, Y ), Y ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.48 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.91/1.48 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.91/1.48 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.48 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.91/1.48 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.48 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.48 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OPls ) = c_Int_OPls }
% 0.91/1.48 .
% 0.91/1.48 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit0( X ) ) =
% 0.91/1.48 c_Int_OBit0( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.91/1.48 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.48 { c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex,
% 0.91/1.48 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex(
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.91/1.48 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.91/1.48 { ! class_Groups_Oab__semigroup__mult( X ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, c_Groups_Otimes__class_Otimes( X, T, Z ), Y ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Otimes__class_Otimes( X, Z
% 0.91/1.48 , Y ) ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.48 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.48 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.91/1.48 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.91/1.48 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.91/1.48 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.91/1.48 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, Y ), X ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) }.
% 0.91/1.48 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.91/1.48 ), T = Y }.
% 0.91/1.48 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 0.91/1.48 ), Z = X }.
% 0.91/1.48 { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) =
% 0.91/1.48 c_Complex_Ocomplex_OComplex( Y, X ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 = Y }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.91/1.48 ( X ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.48 , Y ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.91/1.48 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.48 = Y }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.91/1.48 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.91/1.48 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.48 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.48 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.48 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.48 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.48 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Power_Opower__class_Opower
% 0.91/1.48 ( tc_Int_Oint, X, Y ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_Int_Oint ) ) }.
% 0.91/1.48 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ), Z = Y }.
% 0.91/1.48 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) }.
% 0.91/1.48 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ), Z = Y }.
% 0.91/1.48 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) }.
% 0.91/1.48 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) =
% 0.91/1.48 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.91/1.48 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.91/1.48 ) }.
% 0.91/1.48 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.91/1.48 ) }.
% 0.91/1.48 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.48 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_Complex_Ocomplex ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.91/1.48 { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) )
% 0.91/1.48 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, T,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.91/1.48 { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex,
% 0.91/1.48 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_Nat_Onat ) }.
% 0.91/1.48 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.91/1.48 , Y ) }.
% 0.91/1.48 { c_Complex_Ocomplex_Ocomplex__rec( T, Z, c_Complex_Ocomplex_OComplex( Y, X
% 0.91/1.48 ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.91/1.48 { c_Complex_Ocomplex_Ocomplex__case( T, Z, c_Complex_Ocomplex_OComplex( Y,
% 0.91/1.48 X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.91/1.48 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.91/1.48 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.91/1.48 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 T, Y ), Z = Y }.
% 0.91/1.48 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 T, Y ) }.
% 0.91/1.48 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 Y, Z ), T = Y }.
% 0.91/1.48 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 Y, Z ) }.
% 0.91/1.48 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 T, Y ), Z = Y }.
% 0.91/1.48 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 T, Y ), Z = Y }.
% 0.91/1.48 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 Y, T ), Z = Y }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 0.91/1.48 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.91/1.48 tc_Int_Oint, Z, Y ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.48 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.91/1.48 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.91/1.48 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.91/1.48 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.91/1.48 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.91/1.48 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.91/1.48 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.91/1.48 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.91/1.48 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.91/1.48 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.91/1.48 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.48 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.48 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.48 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.91/1.48 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.48 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.91/1.48 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.91/1.48 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.91/1.48 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.91/1.48 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.91/1.48 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.91/1.48 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.91/1.48 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.91/1.48 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.91/1.48 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.91/1.48 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.91/1.48 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.91/1.48 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.91/1.48 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.91/1.48 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.48 ( X ), ! c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.91/1.48 , U, T ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( X, Z, T ) ), U = Z, T = Y }.
% 0.91/1.48 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.48 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Z, T ) ) }.
% 0.91/1.48 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.48 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Z, T ) ) }.
% 0.91/1.48 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( X, Z, T ), Y ) ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, U, Z ), T ), Y ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, T, Z ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Y, Z ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.91/1.48 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.91/1.48 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.91/1.48 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.48 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, T, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, U, Y ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, T, Z ) ) }.
% 0.91/1.48 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.48 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 U, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( X, T, Z ) ), ! U = T }.
% 0.91/1.48 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.48 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 U, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Y )
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( X, T, Z ) ), ! Z = Y }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.91/1.48 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 Z, Y ) ) = Y }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.91/1.48 Y ) ) = Y }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.91/1.48 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.91/1.48 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.91/1.48 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ), X ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.48 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 Z, Y ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 Y, Z ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.91/1.48 .
% 0.91/1.48 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.91/1.48 .
% 0.91/1.48 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.91/1.48 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.91/1.48 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.91/1.48 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.48 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.91/1.48 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.91/1.48 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, W, c_Groups_Otimes__class_Otimes( X, Y, T
% 0.91/1.48 ) ) = c_Groups_Oplus__class_Oplus( X, U, c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Y, Z ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.91/1.48 .
% 0.91/1.48 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.91/1.48 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.91/1.48 .
% 0.91/1.48 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.91/1.48 ), c_Groups_Otimes__class_Otimes( X, Y, Y ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.91/1.48 , c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Groups_Otimes__class_Otimes
% 0.91/1.48 ( X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.91/1.48 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.91/1.48 ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, T ), Z ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.91/1.48 ), Y ) ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.48 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.91/1.48 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.91/1.48 ( X, Y ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.91/1.48 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.91/1.48 ( X, Z ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.48 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.91/1.48 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.48 Z ) = Y }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) = Y }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ), Y ) = Y }.
% 0.91/1.48 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.48 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.48 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.48 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.91/1.48 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.48 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.91/1.48 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ), Z =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.48 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Y, Y ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.91/1.48 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.91/1.48 X, Y, Y ) ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.48 c_Int_OBit0( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.48 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.91/1.48 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.91/1.48 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.91/1.48 hAPP( Y, U ) ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.48 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.48 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.91/1.48 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.48 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.48 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.48 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.91/1.48 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.91/1.48 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.91/1.48 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.91/1.48 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.48 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.48 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.91/1.48 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.91/1.48 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.91/1.48 hAPP( Y, U ) ) }.
% 0.91/1.48 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.91/1.48 ( X, Z, Y ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.91/1.48 ( X, Y, Z ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.48 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.48 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.91/1.48 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.91/1.48 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.91/1.48 hAPP( Y, U ) ) }.
% 0.91/1.48 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.91/1.48 ( Z, skol2( X, Y, Z ) ), hAPP( Y, skol2( X, Y, Z ) ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.91/1.48 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.91/1.48 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.48 Z, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, Y ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.91/1.48 ) ) ) ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.91/1.48 ) ) ), Y ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.91/1.48 .
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.91/1.48 .
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ), ! Y = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus
% 0.91/1.48 ( X, c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.91/1.48 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y
% 0.91/1.48 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.48 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X
% 0.91/1.48 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.48 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }
% 0.91/1.48 .
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.91/1.48 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.91/1.48 ( X, c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ), Z =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.91/1.48 ( X, c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.91/1.48 X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, Z, Y ), c_Int_Onumber__class_Onumber__of
% 0.91/1.48 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.48 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.91/1.48 ) ) ), Z ), Y ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ), Y = X, Z =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.91/1.48 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.91/1.48 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ), Z = X, Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! Z = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.91/1.48 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, X ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, X ) ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, T ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.91/1.48 { c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ), c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.91/1.48 c_Int_OBit1( c_Int_OPls ) ) ), Y ), X ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, T,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ), c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 0.91/1.48 tc_RealDef_Oreal, c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ) ) ) }.
% 0.91/1.48 { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ) = Y, X = c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_RealDef_Oreal ) }.
% 0.91/1.48 { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ) = Y, X = c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_RealDef_Oreal ) }.
% 0.91/1.48 { c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, T,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.91/1.48 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, T,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Z,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ) }.
% 0.91/1.48 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.91/1.48 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_NthRoot_Osqrt(
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.91/1.48 ( X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y
% 0.91/1.48 , c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ), Z ) ) ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), c_NthRoot_Osqrt(
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), c_NthRoot_Osqrt(
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( X, Z, Y ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) = c_Groups_Ominus__class_Ominus( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.48 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ), Z ), Y ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.48 c_Power_Opower__class_Opower( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ) ) ) }.
% 0.91/1.48 { ! class_Rings_Oring__1( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ), Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.48 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Z
% 0.91/1.48 , c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.48 c_Int_OPls ) ) ), Y ) ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, Z, Y )
% 0.91/1.48 , c_Power_Opower__class_Opower( X, Z, Y ) ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.91/1.48 ( tc_RealDef_Oreal ), c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) )
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.48 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.48 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.48 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.91/1.48 ( X ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.91/1.48 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.91/1.48 , Z, Y ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.48 tc_Nat_Onat, Z, Y ), X ) }.
% 0.91/1.48 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.91/1.48 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.91/1.48 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.91/1.48 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.48 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.48 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.48 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.48 tc_Nat_Onat, Z, X ), Y ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.91/1.48 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.91/1.48 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.48 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.91/1.48 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.48 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.48 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.48 X, Z, Y ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.48 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.48 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.48 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 0.91/1.48 }.
% 0.91/1.48 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.91/1.48 ( tc_RealDef_Oreal, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.91/1.48 , X ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.91/1.48 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.91/1.48 .
% 0.91/1.48 { c_Int_OBit1( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.91/1.48 tc_Int_Oint ), X ), X ) }.
% 0.91/1.48 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.48 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Power_Opower__class_Opower( X, Y,
% 0.91/1.48 c_Nat_OSuc( Z ) ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.48 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.48 c_Power_Opower__class_Opower( X, T, Y ), c_Power_Opower__class_Opower( X
% 0.91/1.48 , T, Z ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.91/1.48 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.48 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.91/1.48 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.48 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.91/1.48 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.91/1.48 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.91/1.48 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.91/1.48 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.91/1.48 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.91/1.48 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.48 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.91/1.48 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.48 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.91/1.48 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.48 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.91/1.48 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.91/1.48 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.48 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.91/1.48 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.91/1.48 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.91/1.48 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.91/1.48 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.91/1.48 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.91/1.48 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.91/1.48 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.48 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.48 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.91/1.48 , ! Y = Z }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.91/1.48 , ! Z = Y }.
% 0.91/1.48 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.48 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.48 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.48 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.48 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.91/1.48 , ! Z = Y }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.91/1.48 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.91/1.48 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.91/1.48 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.48 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.48 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.48 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.91/1.48 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.91/1.48 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.91/1.48 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.91/1.48 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.91/1.48 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.48 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.91/1.48 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.48 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.91/1.48 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.91/1.48 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.91/1.48 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.91/1.48 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.91/1.48 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.48 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.91/1.48 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.48 Y ), ! Z = Y }.
% 0.91/1.48 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.48 Z ), ! Z = Y }.
% 0.91/1.48 { ! c_Nat_OSuc( X ) = X }.
% 0.91/1.48 { ! X = c_Nat_OSuc( X ) }.
% 0.91/1.48 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.48 Y ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.91/1.48 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.91/1.48 ) }.
% 0.91/1.48 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha3( X, Y ), alpha13( X
% 0.91/1.48 , Y ) }.
% 0.91/1.48 { ! alpha3( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.91/1.48 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.48 { ! alpha13( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.91/1.48 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.48 { ! alpha13( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! alpha13( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_Nat_Onat ) ) }.
% 0.91/1.48 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha13( X, Y ) }.
% 0.91/1.48 { ! alpha3( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_Nat_Onat ) ) }.
% 0.91/1.48 { ! alpha3( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha3( X, Y ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.48 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha4( X, Y ), alpha14
% 0.91/1.48 ( X, Y ) }.
% 0.91/1.48 { ! alpha4( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.91/1.48 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.91/1.48 { ! alpha14( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.91/1.48 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.91/1.48 { ! alpha14( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! alpha14( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_Nat_Onat ) ) }.
% 0.91/1.48 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha14( X, Y ) }.
% 0.91/1.48 { ! alpha4( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.91/1.48 tc_Nat_Onat ) ) }.
% 0.91/1.48 { ! alpha4( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha4( X, Y ) }.
% 0.91/1.48 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.48 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.48 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.91/1.48 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.91/1.48 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.91/1.48 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.91/1.48 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.48 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, U ) ),
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.48 X, Y, Z ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.91/1.48 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.48 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.48 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.91/1.48 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.91/1.48 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.48 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Power_Opower__class_Opower
% 0.91/1.48 ( X, Y, T ) = c_Power_Opower__class_Opower( X, Y, Z ), T = Z }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z,
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, T ) = c_Power_Opower__class_Opower( X
% 0.91/1.48 , Y, Z ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.91/1.48 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.91/1.48 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.91/1.48 X, c_Groups_Oone__class_Oone( X ), c_Groups_Otimes__class_Otimes( X, Y, Z
% 0.91/1.48 ) ) }.
% 0.91/1.48 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex,
% 0.91/1.48 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.91/1.48 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.91/1.48 tc_RealDef_Oreal, T, Y ), c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 0.91/1.48 , Z, X ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.91/1.48 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.48 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.91/1.48 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.91/1.48 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.91/1.48 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.91/1.48 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.91/1.48 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.91/1.48 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.91/1.48 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.48 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.91/1.48 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.48 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.91/1.48 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.48 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.91/1.48 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 0.91/1.48 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.91/1.48 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.48 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.48 c_Power_Opower__class_Opower( X, T, Z ), c_Power_Opower__class_Opower( X
% 0.91/1.48 , T, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Power_Opower__class_Opower( X, Y, T ),
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.91/1.48 ( tc_Nat_Onat, T, Z ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Power_Opower__class_Opower( X, Y, T ),
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.91/1.48 ( tc_Nat_Onat, T, Z ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, T ), c_Power_Opower__class_Opower( X
% 0.91/1.48 , Y, Z ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.48 X, c_Groups_Oone__class_Oone( X ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.48 c_Nat_OSuc( Z ) ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.91/1.48 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.91/1.48 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 0.91/1.48 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 0.91/1.48 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.48 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( X, c_Groups_Oplus__class_Oplus( X, U, T )
% 0.91/1.48 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ), c_Groups_Oplus__class_Oplus
% 0.91/1.48 ( X, c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.91/1.48 ) ), c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.91/1.48 Y ) ) ) ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.48 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus(
% 0.91/1.48 X, c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.48 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.91/1.48 ) }.
% 0.91/1.48 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.91/1.48 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 0.91/1.48 }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.91/1.48 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.91/1.48 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls )
% 0.91/1.48 ), c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X
% 0.91/1.48 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.91/1.48 ( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.48 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y
% 0.91/1.48 ), c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U )
% 0.91/1.48 , T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 Z, U ), Y ) ), c_Orderings_Oord__class_Oless( X, T,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.91/1.48 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.91/1.48 , Y ) ) }.
% 0.91/1.48 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U )
% 0.91/1.48 , T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 Z, U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ) }.
% 0.91/1.48 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.48 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ),
% 0.91/1.48 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.91/1.48 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.91/1.48 , Y ) ) }.
% 0.91/1.48 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.48 c_Groups_Otimes__class_Otimes( X, Y, Y ), c_Groups_Oone__class_Oone( X )
% 0.91/1.48 ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.48 , c_Groups_Oone__class_Oone( X ) ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.91/1.48 c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.91/1.48 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.48 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.48 X, c_Groups_Oone__class_Oone( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.91/1.48 c_Power_Opower__class_Opower( X, Y, Z ) ) ) }.
% 0.91/1.48 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.48 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.48 X, c_Power_Opower__class_Opower( X, Y, Z ), c_Groups_Otimes__class_Otimes
% 0.91/1.48 ( X, Y, c_Power_Opower__class_Opower( X, Y, Z ) ) ) }.
% 0.91/1.48 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.91/1.48 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.91/1.48 tc_Int_Oint, Z, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }.
% 0.91/1.48 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.91/1.48 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.91/1.48 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.91/1.48 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.91/1.48 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) =
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) = X }.
% 0.91/1.49 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.49 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.91/1.49 c_Power_Opower__class_Opower( tc_Nat_Onat, X,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.91/1.49 ( tc_Nat_Onat ) ) ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 0.91/1.49 ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.49 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Y, Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 0.91/1.49 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.91/1.49 c_Power_Opower__class_Opower( X, Z, Y ) ) = c_Power_Opower__class_Opower
% 0.91/1.49 ( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.91/1.49 { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) =
% 0.91/1.49 c_Complex_Ocomplex_OComplex( c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 0.91/1.49 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.91/1.49 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Complex_Ocomplex ), Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 0.91/1.49 }.
% 0.91/1.49 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 0.91/1.49 ) }.
% 0.91/1.49 { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.49 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Complex_Ocomplex ) }.
% 0.91/1.49 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.91/1.49 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.91/1.49 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.91/1.49 ) }.
% 0.91/1.49 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.91/1.49 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.91/1.49 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.91/1.49 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.91/1.49 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.91/1.49 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.91/1.49 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.91/1.49 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.91/1.49 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.49 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.91/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.49 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.91/1.49 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.91/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.49 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.49 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.49 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.49 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.91/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.49 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.91/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.49 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.49 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.49 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.91/1.49 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.91/1.49 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.91/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.91/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.91/1.49 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.49 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.91/1.49 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.49 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.91/1.49 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.91/1.49 ( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.49 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.49 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.91/1.49 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.49 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.91/1.49 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.91/1.49 , ! Z = Y }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.49 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.49 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.91/1.49 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.49 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.49 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.91/1.49 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.91/1.49 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.49 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.49 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.91/1.49 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.91/1.49 ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, Z, Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, Z, Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.49 , T ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.49 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.49 , T, Y ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.49 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.49 , Y, T ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, Z, Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.49 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.49 , T, Y ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, T, Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.91/1.49 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.49 , Y, Z ) ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.91/1.49 { ! class_Groups_Omonoid__mult( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.91/1.49 { ! class_Groups_Ocomm__monoid__mult( X ), c_Groups_Otimes__class_Otimes( X
% 0.91/1.49 , c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.91/1.49 { ! class_Groups_Omonoid__mult( X ), c_Groups_Otimes__class_Otimes( X, Y,
% 0.91/1.49 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.91/1.49 { ! class_Groups_Ocomm__monoid__mult( X ), c_Groups_Otimes__class_Otimes( X
% 0.91/1.49 , Y, c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.91/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.91/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 Y, c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.91/1.49 { ! c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.91/1.49 c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { c_Power_Opower__class_Opower( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.91/1.49 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.91/1.49 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.91/1.49 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.49 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.49 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.91/1.49 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.91/1.49 ( X, Y ), Z ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.49 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.91/1.49 ( X, Z ), Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.91/1.49 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.91/1.49 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), X ) = X }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ) ) = X }.
% 0.91/1.49 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Int_Oint ) ) = X }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Int_Oint ), X ) = X }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OPls, X ) = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.91/1.49 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0(
% 0.91/1.49 X ) ) = c_Int_OBit0( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.91/1.49 .
% 0.91/1.49 { c_Int_OBit0( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, X ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Int_Oint, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( tc_Int_Oint, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X )
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.91/1.49 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.91/1.49 }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.91/1.49 c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.91/1.49 , c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.49 c_Groups_Oone__class_Oone( X ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X )
% 0.91/1.49 ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.91/1.49 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ), Y = X }
% 0.91/1.49 .
% 0.91/1.49 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y )
% 0.91/1.49 = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.91/1.49 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol3( X, Y ) ) }.
% 0.91/1.49 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Nat_Onat, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) )
% 0.91/1.49 }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Int_Oint, Z, Y ), c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ) )
% 0.91/1.49 }.
% 0.91/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Y
% 0.91/1.49 , c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = Y }.
% 0.91/1.49 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = Y }.
% 0.91/1.49 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.91/1.49 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.91/1.49 ( tc_Int_Oint ) }.
% 0.91/1.49 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) = X }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.91/1.49 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit1
% 0.91/1.49 ( c_Int_OPls ) ) ) ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.49 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 0.91/1.49 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), c_Groups_Ouminus__class_Ouminus(
% 0.91/1.49 tc_Int_Oint, Y ) ) ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Nat_Onat ), X ) = X }.
% 0.91/1.49 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), Y =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.49 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), X =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.49 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Nat_Onat ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, c_Groups_Oone__class_Oone
% 0.91/1.49 ( tc_Nat_Onat ) ) = X }.
% 0.91/1.49 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Nat_Onat ) }.
% 0.91/1.49 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Nat_Onat ) }.
% 0.91/1.49 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Nat_Onat, Y, X ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.91/1.49 ( tc_Int_Oint ) ) = X }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Int_Oint ), X ) = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.91/1.49 c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.91/1.49 c_NthRoot_Osqrt( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 0.91/1.49 c_NthRoot_Osqrt( X ) ) }.
% 0.91/1.49 { c_NthRoot_Osqrt( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.91/1.49 { ! c_NthRoot_Osqrt( X ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X
% 0.91/1.49 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.91/1.49 { ! X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X )
% 0.91/1.49 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.91/1.49 ), c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.49 Y ) ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.91/1.49 ), c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.91/1.49 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( Z ) ), Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, Z ) ), c_Power_Opower__class_Opower(
% 0.91/1.49 X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.91/1.49 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.91/1.49 tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.91/1.49 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Y
% 0.91/1.49 , T ), c_Power_Opower__class_Opower( X, Y, Z ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Y
% 0.91/1.49 , T ), c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Y
% 0.91/1.49 , T ), c_Power_Opower__class_Opower( X, Y, Z ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.91/1.49 { c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc( X ) ) ) = c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1
% 0.91/1.49 ( c_Int_OBit1( c_Int_OPls ) ) ), X ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.49 }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.49 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 0.91/1.49 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.49 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ),
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.91/1.49 ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.49 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 0.91/1.49 ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.91/1.49 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.91/1.49 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, U, Z ), c_Groups_Otimes__class_Otimes(
% 0.91/1.49 X, W, T ) ), Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.49 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.49 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.49 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 0.91/1.49 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.49 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.49 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.49 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Power_Opower__class_Opower( X, Z, T )
% 0.91/1.49 , c_Power_Opower__class_Opower( X, Y, T ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.91/1.49 c_Power_Opower__class_Opower( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.91/1.49 , Y ) ) = c_Groups_Oabs__class_Oabs( X, c_Power_Opower__class_Opower( X,
% 0.91/1.49 Z, Y ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.91/1.49 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.91/1.49 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ), X ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.91/1.49 , Y ), T = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( X, c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) }.
% 0.91/1.49 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, Z, W
% 0.91/1.49 ), U ), Y ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.91/1.49 , Y ) }.
% 0.91/1.49 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.91/1.49 , Y ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ) = Y }.
% 0.91/1.49 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, W, Z
% 0.91/1.49 ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, W, U ), T ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.91/1.49 , Y ) }.
% 0.91/1.49 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, U, T ), c_Groups_Otimes__class_Otimes(
% 0.91/1.49 X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, U, c_Groups_Ominus__class_Ominus( X, T
% 0.91/1.49 , Y ) ), c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( X, U, Z ), Y ) ) }.
% 0.91/1.49 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.91/1.49 ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, T ), Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Int_Onumber__class_Onumber__of( X, T
% 0.91/1.49 ), Y ) ) }.
% 0.91/1.49 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.91/1.49 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, T,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.91/1.49 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.91/1.49 X, Y ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.91/1.49 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) }.
% 0.91/1.49 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.91/1.49 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.91/1.49 X, Y ) ) }.
% 0.91/1.49 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.91/1.49 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.49 , Y ) ) }.
% 0.91/1.49 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.91/1.49 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.49 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.91/1.49 X, Z, Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , c_Groups_Otimes__class_Otimes( X, Y, Y ), c_Groups_Ozero__class_Ozero(
% 0.91/1.49 X ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.91/1.49 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), alpha5( X, Y, Z, T ),
% 0.91/1.49 alpha15( X, Y, Z, T ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.91/1.49 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z, T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.91/1.49 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.91/1.49 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.49 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha15( X, Y, Z, T ) }.
% 0.91/1.49 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.91/1.49 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.91/1.49 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha5( X, Y, Z, T ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.91/1.49 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), alpha6( X, Y, Z, T ),
% 0.91/1.49 alpha16( X, Y, Z, T ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z, T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.91/1.49 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z, T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.91/1.49 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.91/1.49 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.49 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha16( X, Y, Z, T ) }.
% 0.91/1.49 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.91/1.49 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.91/1.49 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.91/1.49 T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.91/1.49 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.49 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.91/1.49 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.49 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z,
% 0.91/1.49 Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.91/1.49 .
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Z, Y ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.91/1.49 .
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.91/1.49 T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.91/1.49 , c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Y,
% 0.91/1.49 Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.49 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Otimes__class_Otimes( X, Z, T ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Otimes__class_Otimes( X, Y, T ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Z, T ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Otimes__class_Otimes( X, T, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, T, Z ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.91/1.49 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.91/1.49 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.91/1.49 ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.91/1.49 ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.49 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.91/1.49 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.91/1.49 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.91/1.49 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.91/1.49 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.91/1.49 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.91/1.49 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.91/1.49 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.91/1.49 , Y, T ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.91/1.49 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.91/1.49 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.91/1.49 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.91/1.49 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.91/1.49 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.91/1.49 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.49 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.91/1.49 c_Power_Opower__class_Opower( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.91/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.49 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.49 , Y ) }.
% 0.91/1.49 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.49 , Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.49 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.91/1.49 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.91/1.49 .
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.91/1.49 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.91/1.49 ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.91/1.49 ( X ) ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.91/1.49 ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y
% 0.91/1.49 , Z ) ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.91/1.49 ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls
% 0.91/1.49 , X ) ) }.
% 0.91/1.49 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc
% 0.91/1.49 ( Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.91/1.49 c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Z
% 0.91/1.49 , c_Nat_OSuc( Y ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.91/1.49 c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Z,
% 0.91/1.49 c_Nat_OSuc( Y ) ) = c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Power_Opower__class_Opower( X, Z, Y ), Z ) }.
% 0.91/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 Z, c_Power_Opower__class_Opower( X, Z, Y ) ) =
% 0.91/1.49 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( Y ) ) }.
% 0.91/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Power_Opower__class_Opower( X, Z, Y ), Z ) =
% 0.91/1.49 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( Y ) ) }.
% 0.91/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.49 , Y ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X
% 0.91/1.49 , c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ), Y ) }
% 0.91/1.49 .
% 0.91/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.91/1.49 , c_Groups_Otimes__class_Otimes( X, Y, Z ) ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.91/1.49 c_Groups_Oone__class_Oone( X ) ), Z ) }.
% 0.91/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Z, Y ), Y ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.91/1.49 c_Groups_Oone__class_Oone( X ) ), Y ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.91/1.49 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, Z ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, T,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T, Z )
% 0.91/1.49 , c_Power_Opower__class_Opower( X, T, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Power_Opower__class_Opower( X, T, Z ), c_Power_Opower__class_Opower( X
% 0.91/1.49 , T, Y ) ) = c_Power_Opower__class_Opower( X, T,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ) }.
% 0.91/1.49 { c_NthRoot_Osqrt( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X )
% 0.91/1.49 ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.91/1.49 { ! class_Rings_Oring__1__no__zero__divisors( X ), !
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.91/1.49 , Y = c_Groups_Oone__class_Oone( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.91/1.49 ( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.49 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.91/1.49 c_Groups_Oone__class_Oone( X ), c_Groups_Otimes__class_Otimes( X, Y, Y )
% 0.91/1.49 = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.49 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.91/1.49 }.
% 0.91/1.49 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.91/1.49 ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.49 , c_Groups_Oone__class_Oone( X ) ), Y ) }.
% 0.91/1.49 { c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_RealDef_Oreal, Y, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.91/1.49 , X ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.91/1.49 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0(
% 0.91/1.49 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.91/1.49 .
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1(
% 0.91/1.49 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.91/1.49 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone
% 0.91/1.49 ( X ) }.
% 0.91/1.49 { ! class_Rings_Ocomm__semiring__1( X ), c_Power_Opower__class_Opower( X, Y
% 0.91/1.49 , c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, X, Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ), X =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.49 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, X ) ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.91/1.49 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.49 { ! Y = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ), X =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Int_Oint ) ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.91/1.49 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.91/1.49 ) = c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_RealDef_Oreal, T, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.49 Z, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 0.91/1.49 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 0.91/1.49 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 0.91/1.49 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 0.91/1.49 { c_Power_Opower__class_Opower( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Otimes__class_Otimes( tc_Int_Oint,
% 0.91/1.49 c_Power_Opower__class_Opower( tc_Int_Oint, Z, Y ),
% 0.91/1.49 c_Power_Opower__class_Opower( tc_Int_Oint, Z, X ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.91/1.49 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) = c_Groups_Oabs__class_Oabs(
% 0.91/1.49 X, c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Oordered__ring__abs( X ), alpha19( X, Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.49 ), c_Groups_Oabs__class_Oabs( X, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.91/1.49 ) ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.91/1.49 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Oordered__ring__abs( X ), alpha19( X, Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.49 ), c_Groups_Oabs__class_Oabs( X, c_Groups_Otimes__class_Otimes( X, Z, Y
% 0.91/1.49 ) ) = c_Groups_Otimes__class_Otimes( X, c_Groups_Oabs__class_Oabs( X, Z
% 0.91/1.49 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 0.91/1.49 { ! alpha19( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.91/1.49 { ! alpha19( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.49 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( X ) ), alpha19( X, Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.91/1.49 , c_Groups_Oabs__class_Oabs( X, Y ) ), c_Groups_Ozero__class_Ozero( X ) )
% 0.91/1.49 }.
% 0.91/1.49 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.49 ), c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.91/1.49 X, Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.91/1.49 X, c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, Z ), Y ) ) }.
% 0.91/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U
% 0.91/1.49 ), T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.91/1.49 , Z, U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ) }.
% 0.91/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.49 , T, c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, Z, W ), U ), Y ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.91/1.49 , Y ) ) }.
% 0.91/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, W, U
% 0.91/1.49 ), T ), c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.91/1.49 , Z, U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ) }.
% 0.91/1.49 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, W, Z ), U ), T ), Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, W, U ), T ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, U )
% 0.91/1.49 , Y ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.91/1.49 , Y, T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Y
% 0.91/1.49 , T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X
% 0.91/1.49 , Y, T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, Y
% 0.91/1.49 , T ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.91/1.49 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.91/1.49 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.49 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.49 , U ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X
% 0.91/1.49 , Z, U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, Z
% 0.91/1.49 , U ), c_Groups_Otimes__class_Otimes( X, Y, T ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.91/1.49 ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Groups_Otimes__class_Otimes( X, T, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Otimes__class_Otimes( X, T, Z
% 0.91/1.49 ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.91/1.49 , Z ), c_Groups_Otimes__class_Otimes( X, Y, Z ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Otimes__class_Otimes( X, T
% 0.91/1.49 , Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.49 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.49 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.49 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.91/1.49 ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.49 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.91/1.49 ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.91/1.49 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.91/1.49 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.49 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.91/1.49 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.91/1.49 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.91/1.49 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.91/1.49 X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ), Z ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z
% 0.91/1.49 ), c_Groups_Otimes__class_Otimes( X, Y, Y ) ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, Z, Z )
% 0.91/1.49 , c_Groups_Otimes__class_Otimes( X, Y, Y ) ) ), ! Z =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.49 }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.91/1.49 X, Y, Y ) ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Z, Z ), c_Groups_Otimes__class_Otimes(
% 0.91/1.49 X, Y, Y ) ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X, Z
% 0.91/1.49 , c_Nat_OSuc( T ) ), c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( T )
% 0.91/1.49 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( X ), Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Power_Opower__class_Opower(
% 0.91/1.49 X, Z, c_Nat_OSuc( T ) ) = c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc
% 0.91/1.49 ( T ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.49 ), Z = Y }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Power_Opower__class_Opower( X, Z, T ),
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, T ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.91/1.49 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Y, Z ), Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.91/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.91/1.49 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Z, Y ), Y ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z )
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) ) ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs
% 0.91/1.49 ( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) ),
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_RealDef_Oreal, Z, c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.91/1.49 , X ) ) ) ) ) }.
% 0.91/1.49 { ! class_Rings_Oidom( X ), ! c_Power_Opower__class_Opower( X, Z,
% 0.91/1.49 c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) )
% 0.91/1.49 = c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.91/1.49 { ! class_Rings_Oidom( X ), ! Z = Y, c_Power_Opower__class_Opower( X, Z,
% 0.91/1.49 c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) )
% 0.91/1.49 = c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.91/1.49 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.91/1.49 c_Power_Opower__class_Opower( X, Z, c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) =
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.91/1.49 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Oone__class_Oone( X
% 0.91/1.49 ) }.
% 0.91/1.49 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( X ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.49 c_Int_OBit1( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Oring__1( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ), Y )
% 0.91/1.49 , c_Power_Opower__class_Opower( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.91/1.49 , c_Orderings_Oord__class_Oless__eq( X, c_Power_Opower__class_Opower( X,
% 0.91/1.49 T, Z ), c_Power_Opower__class_Opower( X, T, Y ) ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.49 c_Int_OBit1( c_Int_OPls ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), c_Groups_Oone__class_Oone( X ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Int_OBit1( Y ), X ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0(
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X, Y ) ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex,
% 0.91/1.49 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 0.91/1.49 ) = c_Complex_Ocomplex_OComplex( c_Groups_Ominus__class_Ominus(
% 0.91/1.49 tc_RealDef_Oreal, c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, T, Y )
% 0.91/1.49 , c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, X ) ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, T, X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Z, Y ) ) ) }.
% 0.91/1.49 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.91/1.49 ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.91/1.49 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.91/1.49 ) }.
% 0.91/1.49 { c_Groups_Oone__class_Oone( tc_Int_Oint ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , c_Power_Opower__class_Opower( X, Y, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ), Z ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Rings_Oring__1( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.91/1.49 c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ), Y ) ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.49 c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.91/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X, U, Z )
% 0.91/1.49 , c_Groups_Otimes__class_Otimes( X, W, T ) ), Y ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.49 c_Groups_Oone__class_Oone( X ) ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.91/1.49 ) ) = c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.91/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.91/1.49 ( X ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Power_Opower__class_Opower( X, T, Y ), c_Power_Opower__class_Opower( X
% 0.91/1.49 , T, Z ) ) }.
% 0.91/1.49 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.91/1.49 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.91/1.49 ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.91/1.49 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 0.91/1.49 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) ) }.
% 0.91/1.49 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.49 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.91/1.49 ( X, c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( X, Y ), c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.91/1.49 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ) ) ) }.
% 0.91/1.49 { c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.91/1.49 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.91/1.49 ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.91/1.49 , Y ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.91/1.49 , Y ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X
% 0.91/1.49 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.91/1.49 ) ) ) }.
% 0.91/1.49 { ! class_Rings_Osemiring__1( X ), c_Power_Opower__class_Opower( X,
% 0.91/1.49 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X )
% 0.91/1.49 }.
% 0.91/1.49 { c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X ) }.
% 0.91/1.49 { c_NthRoot_Osqrt( c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , c_Groups_Ozero__class_Ozero( X ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ) ), ! Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Rings_Oring__1__no__zero__divisors( X ), !
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.91/1.49 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.91/1.49 c_Groups_Oone__class_Oone( X ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.49 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.91/1.49 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( X ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.91/1.49 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.91/1.49 c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.91/1.49 c_Int_OBit1( c_Int_OPls ) ) ), X ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.91/1.49 ( X, c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of
% 0.91/1.49 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Power_Opower__class_Opower( X, Z, c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ),
% 0.91/1.49 c_Power_Opower__class_Opower( X, Y, c_Int_Onumber__class_Onumber__of(
% 0.91/1.49 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), ! Z =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.91/1.49 }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ) ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ) ) ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( X, c_Power_Opower__class_Opower( X, Z,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ), c_Power_Opower__class_Opower( X, Y,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.91/1.49 { ! class_Groups_Omonoid__mult( X ), c_Power_Opower__class_Opower( X, Z,
% 0.91/1.49 c_Nat_OSuc( c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ), Y ) ) ) = c_Groups_Otimes__class_Otimes( X, Z,
% 0.91/1.49 c_Power_Opower__class_Opower( X, c_Power_Opower__class_Opower( X, Z, Y )
% 0.91/1.49 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.91/1.49 ( c_Int_OPls ) ) ) ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ),
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Power_Opower__class_Opower( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.91/1.49 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.91/1.49 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( X, T, Y ) ) ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Z ), c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_RealDef_Oreal, Y, c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_Int_Onumber__ring( X ), !
% 0.91/1.49 class_RealVector_Oreal__normed__algebra__1( X ),
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Int_Onumber__class_Onumber__of( X,
% 0.91/1.49 Y ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, X,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.91/1.49 ( X, Y ) ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.91/1.49 X ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.91/1.49 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.91/1.49 { alpha20( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.91/1.49 ( X, Y ), Z ) ) }.
% 0.91/1.49 { ! alpha20( X, Y, Z ), alpha21( X, Y, Z ), Z = Y }.
% 0.91/1.49 { ! alpha20( X, Y, Z ), alpha21( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.91/1.49 ) ) }.
% 0.91/1.49 { ! alpha21( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.91/1.49 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha20( X, Y, Z ) }.
% 0.91/1.49 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.91/1.49 }.
% 0.91/1.49 { ! alpha21( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.91/1.49 X, Y ), Z ) ), alpha21( X, Y, Z ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.91/1.49 , X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.91/1.49 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.91/1.49 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.91/1.49 .
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.91/1.49 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.91/1.49 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.91/1.49 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.91/1.49 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.91/1.49 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Z, X ), Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.91/1.49 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.91/1.49 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.91/1.49 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.91/1.49 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 0.91/1.49 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.91/1.49 { c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal, X ) =
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, X ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.91/1.49 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 0.91/1.49 tc_Int_Oint, X ) = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), alpha7( X, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.91/1.49 { ! alpha7( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.91/1.49 { ! alpha7( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha7( X, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ), alpha7( X
% 0.91/1.49 , Y ) }.
% 0.91/1.49 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.91/1.49 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.91/1.49 .
% 0.91/1.49 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.91/1.49 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.91/1.49 }.
% 0.91/1.49 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.91/1.49 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.91/1.49 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Int_Oint, X, Y ) ) = c_Groups_Oone__class_Oone( tc_Int_Oint ),
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) = c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Int_Oint ) }.
% 0.91/1.49 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.91/1.49 ( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) ), X =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), Y ) }.
% 0.91/1.49 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.91/1.49 ( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Z ),
% 0.91/1.49 c_Power_Opower__class_Opower( tc_Nat_Onat, X, Y ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.49 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.91/1.49 , ! alpha8( X, Y, Z ) }.
% 0.91/1.49 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.91/1.49 , ! alpha17( X, Y, Z ) }.
% 0.91/1.49 { alpha8( X, Y, Z ), alpha17( X, Y, Z ), hBOOL( hAPP( Z,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.91/1.49 { ! alpha17( X, Y, Z ), ! hBOOL( hAPP( Z, skol4( T, U, Z ) ) ) }.
% 0.91/1.49 { ! alpha17( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.91/1.49 skol4( X, Y, Z ) ) }.
% 0.91/1.49 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.91/1.49 ) ), alpha17( X, Y, Z ) }.
% 0.91/1.49 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! alpha8( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ) ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha8( X, Y, Z ) }.
% 0.91/1.49 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.91/1.49 , alpha9( X, Y, Z ) }.
% 0.91/1.49 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.91/1.49 , alpha18( X, Y, Z ) }.
% 0.91/1.49 { ! alpha9( X, Y, Z ), ! alpha18( X, Y, Z ), hBOOL( hAPP( Z,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.91/1.49 { ! alpha18( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.91/1.49 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.91/1.49 { ! hBOOL( hAPP( Z, skol5( T, U, Z ) ) ), alpha18( X, Y, Z ) }.
% 0.91/1.49 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol5( X, Y, Z ) ),
% 0.91/1.49 alpha18( X, Y, Z ) }.
% 0.91/1.49 { ! alpha9( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.91/1.49 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha9( X, Y, Z ) }.
% 0.91/1.49 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha9
% 0.91/1.49 ( X, Y, Z ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.91/1.49 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.91/1.49 ( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.91/1.49 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.91/1.49 ( X ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OPls ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.91/1.49 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.91/1.49 ( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.91/1.49 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.91/1.49 ( X ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol6( X, Y ) ) ) }.
% 0.91/1.49 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.91/1.49 }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.91/1.49 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.91/1.49 X ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.91/1.49 .
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.91/1.49 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.91/1.49 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.91/1.49 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.91/1.49 ( tc_Int_Oint ) ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.91/1.49 = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Int_Oint ) ) ) }.
% 0.91/1.49 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Int_Oint ) ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ), Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Int_Oint ), c_Power_Opower__class_Opower( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ), X ) ), ! Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Int_Oint ), c_Power_Opower__class_Opower( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ), X ) ) }.
% 0.91/1.49 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Int_Oint ), c_Power_Opower__class_Opower( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ), X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.91/1.49 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.91/1.49 }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), c_Int_OPls
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol7( X ) ) }.
% 0.91/1.49 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.91/1.49 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.91/1.49 c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { ! alpha10( X, Y ), Y = c_Nat_OSuc( skol8( Z, Y ) ) }.
% 0.91/1.49 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol8( X,
% 0.91/1.49 Y ), X ) }.
% 0.91/1.49 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.91/1.49 ), alpha10( X, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.91/1.49 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.91/1.49 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.91/1.49 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.91/1.49 ) ) = X }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.91/1.49 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.91/1.49 ( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.91/1.49 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.91/1.49 ( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X
% 0.91/1.49 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.91/1.49 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.91/1.49 }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), c_Int_OPls
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Int_Oint ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), c_Power_Opower__class_Opower( tc_Nat_Onat, Y,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.91/1.49 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.91/1.49 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Power_Opower__class_Opower( tc_Nat_Onat, Y,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Power_Opower__class_Opower
% 0.91/1.49 ( tc_Nat_Onat, Y, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) )
% 0.91/1.49 }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), Z ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Int_Oint ), X ), ! c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y
% 0.91/1.49 ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Int_Oint ), X ), ! c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y
% 0.91/1.49 ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.91/1.49 = c_Groups_Oone__class_Oone( tc_Int_Oint ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Nat_Onat, c_Nat_OSuc( Z ), X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Int_Oint ) ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.91/1.49 }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Int_Oint ) ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.91/1.49 }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.91/1.49 tc_Int_Oint ) ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Power_Opower__class_Opower
% 0.91/1.49 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ), X ) ) }.
% 0.91/1.49 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.91/1.49 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, Z,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.91/1.49 ( tc_Nat_Onat ) ) ), Z ) = c_Power_Opower__class_Opower( X, Z, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X
% 0.91/1.49 ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X )
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.91/1.49 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.91/1.49 }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.91/1.49 c_Int_OPls ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.91/1.49 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 0.91/1.49 ( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.91/1.49 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.91/1.49 ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 0.91/1.49 ( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.91/1.49 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.91/1.49 c_Int_OBit0( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.91/1.49 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.91/1.49 c_Int_OBit0( X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.91/1.49 ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.91/1.49 ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol9( X, Y ) ) }.
% 0.91/1.49 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.91/1.49 { ! class_Rings_Olinordered__semidom( X ), ! c_Power_Opower__class_Opower(
% 0.91/1.49 X, T, Z ) = c_Power_Opower__class_Opower( X, Y, Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.91/1.49 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ), X ),
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.91/1.49 ) ) ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0
% 0.91/1.49 ( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ), X ) ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ) ), X ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.91/1.49 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Y, X ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.91/1.49 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.91/1.49 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.49 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Y, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Ozero__class_Ozero( X ), Y ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.91/1.49 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.91/1.49 ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X,
% 0.91/1.49 T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.91/1.49 , Y ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.91/1.49 , T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.91/1.49 , Y ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Otimes__class_Otimes( X
% 0.91/1.49 , T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Ominus__class_Ominus( X, Z
% 0.91/1.49 , Y ) ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, T, c_Groups_Ominus__class_Ominus( X, Z
% 0.91/1.49 , Y ) ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( X, T, Z ), c_Groups_Otimes__class_Otimes( X, T, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.91/1.49 ), Y ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( X, T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, T, Z
% 0.91/1.49 ), Y ) = c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( X, T, Y ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.91/1.49 , Y ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.91/1.49 , Y ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.49 Y ) ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.91/1.49 Y ) ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( X, Z, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.91/1.49 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( X, Y, Z ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.91/1.49 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Oabs__class_Oabs
% 0.91/1.49 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ) ) =
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, c_Groups_Otimes__class_Otimes( X, U, T
% 0.91/1.49 ), c_Groups_Otimes__class_Otimes( X, Z, Y ) ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.91/1.49 ), c_Groups_Ominus__class_Ominus( X, T, Y ) ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Groups_Ominus__class_Ominus( X, U, Z
% 0.91/1.49 ), Y ) ), c_Groups_Otimes__class_Otimes( X, Z,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.91/1.49 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.91/1.49 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.91/1.49 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Groups_Otimes__class_Otimes( X, Z,
% 0.91/1.49 Y ) ) = c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.91/1.49 ( X, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_RealDef_Oreal ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Power_Opower__class_Opower( X, Z, Y
% 0.91/1.49 ) ) = c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Z ), Y ) }.
% 0.91/1.49 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.91/1.49 ), c_Power_Opower__class_Opower( X, Y, Z ) = c_Groups_Oone__class_Oone(
% 0.91/1.49 X ) }.
% 0.91/1.49 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.91/1.49 , c_Power_Opower__class_Opower( X, Y, Z ) = c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( X, Y, c_Power_Opower__class_Opower( X, Y, c_Groups_Ominus__class_Ominus
% 0.91/1.49 ( tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.91/1.49 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.91/1.49 tc_Nat_Onat, Z, Y ), c_Power_Opower__class_Opower( X, T,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( X, c_Power_Opower__class_Opower( X, T,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ) ), T ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.91/1.49 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.91/1.49 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Groups_Otimes__class_Otimes( X, Z,
% 0.91/1.49 Y ) ), c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.91/1.49 ( X, Y ) ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Groups_Otimes__class_Otimes( X, Z,
% 0.91/1.49 U ) ), c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal, Y, T ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.91/1.49 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.91/1.49 ( X, Y ) ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.91/1.49 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.91/1.49 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.91/1.49 ( X, Y ) ) ) }.
% 0.91/1.49 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, c_Power_Opower__class_Opower( X, Z, Y
% 0.91/1.49 ) ), c_Power_Opower__class_Opower( tc_RealDef_Oreal,
% 0.91/1.49 c_RealVector_Onorm__class_Onorm( X, Z ), Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.91/1.49 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, X, Y ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.91/1.49 ( tc_Int_Oint ), Y ) }.
% 0.91/1.49 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( tc_Int_Oint, W, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.91/1.49 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Int_Oint, U, T ), Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, U, Y ), X ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.91/1.49 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( tc_Int_Oint, W, U ), T ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.91/1.49 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Int_Oint, U, T ), Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Int_Oint, U, Y ), X ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.91/1.49 ( tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ),
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Int_Oint, c_Groups_Otimes__class_Otimes( tc_Int_Oint, Z, Y ), X ) ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.91/1.49 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, U ), T ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Nat_Onat, X, U ), Z ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, T
% 0.91/1.49 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes
% 0.91/1.49 ( tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z
% 0.91/1.49 ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), Z )
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Nat_Onat, Y, U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), Z ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Nat_Onat, Y, U ), Z ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T )
% 0.91/1.49 , Z ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), U ), T ), Z ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.91/1.49 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, U ), T ),
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Nat_Onat, Y, U ), Z ) ) }.
% 0.91/1.49 { ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ), Z =
% 0.91/1.49 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.91/1.49 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.91/1.49 { ! Y = X, c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, Y ) =
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Z, X ) }.
% 0.91/1.49 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Nat_Onat, T, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, Y, Z ), X ) ) =
% 0.91/1.49 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Otimes__class_Otimes(
% 0.91/1.49 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ), Z ), X ) }
% 0.91/1.49 .
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), ! c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z
% 0.91/1.49 ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ), Z = Y }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), ! Z = Y, c_Groups_Otimes__class_Otimes( tc_Nat_Onat
% 0.91/1.49 , X, Z ) = c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.91/1.49 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ),
% 0.91/1.49 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.91/1.49 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.91/1.49 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.91/1.49 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Z ),
% 0.91/1.49 c_Groups_Otimes__class_Otimes( tc_Nat_Onat, X, Y ) ) }.
% 0.91/1.49 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.91/1.49 ) ) }.
% 0.91/1.49 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.91/1.49 .
% 0.91/1.49 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.91/1.49 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.91/1.49 tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.91/1.49 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.91/1.49 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.91/1.49 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.91/1.50 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.91/1.50 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.91/1.50 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.91/1.50 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.91/1.50 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.91/1.50 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.91/1.50 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.91/1.50 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.91/1.50 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.91/1.50 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.91/1.50 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 0.91/1.50 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.91/1.50 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.91/1.50 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 0.91/1.50 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.91/1.50 { class_Power_Opower( tc_Int_Oint ) }.
% 0.91/1.50 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.91/1.50 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.91/1.50 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.91/1.50 { class_Int_Onumber( tc_Int_Oint ) }.
% 0.91/1.50 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.91/1.50 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.91/1.50 tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Int_Onumber( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.91/1.50 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.91/1.50 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.91/1.50 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.91/1.50 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.91/1.50 tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.91/1.50 .
% 0.91/1.50 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Int_Onumber__ring( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Oabs__if( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Int_Onumber( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.91/1.50 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.91/1.50 tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.91/1.50 { ! c_Power_Opower__class_Opower( tc_Complex_Ocomplex,
% 0.91/1.50 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( v_z ),
% 0.91/1.50 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.91/1.50 c_Int_OPls ) ) ) ) = v_z }.
% 0.91/1.50
% 0.91/1.50 *** allocated 15000 integers for clauses
% 0.91/1.50 *** allocated 22500 integers for clauses
% 0.91/1.50 *** allocated 33750 integers for clauses
% 0.91/1.50 *** allocated 50625 integers for clauses
% 0.91/1.50 *** allocated 75937 integers for clauses
% 0.91/1.50 percentage equality = 0.283825, percentage horn = 0.933380
% 0.91/1.50 This is a problem with some equality
% 0.91/1.50
% 0.91/1.50
% 0.91/1.50
% 0.91/1.50 Options Used:
% 0.91/1.50
% 0.91/1.50 useres = 1
% 0.91/1.50 useparamod = 1
% 0.91/1.50 useeqrefl = 1
% 0.91/1.50 useeqfact = 1
% 0.91/1.50 usefactor = 1
% 0.91/1.50 usesimpsplitting = 0
% 0.91/1.50 usesimpdemod = 5
% 0.91/1.50 usesimpres = 3
% 0.91/1.50
% 0.91/1.50 resimpinuse = 1000
% 0.91/1.50 resimpclauses = 20000
% 0.91/1.50 substype = eqrewr
% 0.91/1.50 backwardsubs = 1
% 0.91/1.50 selectoldest = 5
% 0.91/1.50
% 0.91/1.50 litorderings [0] = split
% 0.91/1.50 litorderings [1] = extend the termordering, first sorting on arguments
% 0.91/1.50
% 0.91/1.50 termordering = kbo
% 0.91/1.50
% 0.91/1.50 litapriori = 0
% 0.91/1.50 termapriori = 1
% 0.91/1.50 litaposteriori = 0
% 0.91/1.50 termaposteriori = 0
% 0.91/1.50 demodaposteriori = 0
% 0.91/1.50 ordereqreflfact = 0
% 0.91/1.50
% 0.91/1.50 litselect = negord
% 0.91/1.50
% 0.91/1.50 maxweight = 15
% 0.91/1.50 maxdepth = 30000
% 0.91/1.50 maxlength = 115
% 0.91/1.50 maxnrvars = 195
% 0.91/1.50 excuselevel = 1
% 0.91/1.50 increasemaxweight = 1
% 0.91/1.50
% 0.91/1.50 maxselected = 10000000
% 0.91/1.50 maxnrclauses = 10000000
% 0.91/1.50
% 0.91/1.50 showgenerated = 0
% 0.91/1.50 showkept = 0
% 0.91/1.50 showselected = 0
% 0.91/1.50 showdeleted = 0
% 0.91/1.50 showresimp = 1
% 0.91/1.50 showstatus = 2000
% 0.91/1.50
% 0.91/1.50 prologoutput = 0
% 0.91/1.50 nrgoals = 5000000
% 0.91/1.50 totalproof = 1
% 0.91/1.50
% 0.91/1.50 Symbols occurring in the translation:
% 0.91/1.50
% 0.91/1.50 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.91/1.50 . [1, 2] (w:1, o:178, a:1, s:1, b:0),
% 0.91/1.50 ! [4, 1] (w:0, o:102, a:1, s:1, b:0),
% 0.91/1.50 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.91/1.50 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.91/1.50 v_y____ [35, 0] (w:1, o:7, a:1, s:1, b:0),
% 0.91/1.50 tc_RealDef_Oreal [36, 0] (w:1, o:10, a:1, s:1, b:0),
% 0.91/1.50 c_Groups_Ozero__class_Ozero [37, 1] (w:1, o:108, a:1, s:1, b:0),
% 0.91/1.50 c_Int_OPls [38, 0] (w:1, o:11, a:1, s:1, b:0),
% 0.91/1.50 c_Int_OBit0 [39, 1] (w:1, o:109, a:1, s:1, b:0),
% 0.91/1.50 c_Int_OBit1 [44, 1] (w:1, o:110, a:1, s:1, b:0),
% 0.91/1.50 v_z [45, 0] (w:1, o:21, a:1, s:1, b:0),
% 0.91/1.50 v_x____ [46, 0] (w:1, o:6, a:1, s:1, b:0),
% 0.91/1.50 c_Complex_Ocomplex_OComplex [47, 2] (w:1, o:202, a:1, s:1, b:0),
% 0.91/1.50 c_Orderings_Oord__class_Oless__eq [48, 3] (w:1, o:221, a:1, s:1, b:0)
% 0.91/1.50 ,
% 0.91/1.50 tc_Complex_Ocomplex [49, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.91/1.50 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt [50, 1] (w:1, o:107
% 0.91/1.50 , a:1, s:1, b:0),
% 0.91/1.50 tc_Nat_Onat [51, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.91/1.50 c_Int_Onumber__class_Onumber__of [52, 2] (w:1, o:203, a:1, s:1, b:0)
% 0.91/1.50 ,
% 0.91/1.50 c_Power_Opower__class_Opower [53, 3] (w:1, o:223, a:1, s:1, b:0),
% 0.91/1.50 class_Groups_Omonoid__mult [56, 1] (w:1, o:112, a:1, s:1, b:0),
% 0.91/1.61 class_Int_Onumber [57, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.91/1.61 c_Groups_Otimes__class_Otimes [58, 3] (w:1, o:224, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Osemiring__1 [60, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Oring__1__no__zero__divisors [62, 1] (w:1, o:114, a:1, s:
% 0.91/1.61 1, b:0),
% 0.91/1.61 c_Groups_Ouminus__class_Ouminus [63, 2] (w:1, o:204, a:1, s:1, b:0),
% 0.91/1.61
% 0.91/1.61 tc_Int_Oint [64, 0] (w:1, o:36, a:1, s:1, b:0),
% 0.91/1.61 class_Int_Onumber__ring [66, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Olinordered__idom [69, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Olinordered__semidom [75, 1] (w:1, o:124, a:1, s:1, b:0)
% 0.91/1.61 ,
% 0.91/1.61 class_Int_Oring__char__0 [76, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Ocomm__semiring__1 [78, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.91/1.61 c_NthRoot_Osqrt [81, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.91/1.61 class_Power_Opower [82, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Omult__zero [83, 1] (w:1, o:139, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Ono__zero__divisors [84, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.91/1.61
% 0.91/1.61 class_Rings_Ozero__neq__one [85, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Olinordered__ring [87, 1] (w:1, o:122, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Olinordered__ring__strict [89, 1] (w:1, o:123, a:1, s:1
% 0.91/1.61 , b:0),
% 0.91/1.61 class_Rings_Oidom [95, 1] (w:1, o:142, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Oring [96, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Oring__1 [108, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Oring__no__zero__divisors [109, 1] (w:1, o:117, a:1, s:1
% 0.91/1.61 , b:0),
% 0.91/1.61 class_Groups_Ocomm__monoid__mult [111, 1] (w:1, o:143, a:1, s:1, b:0)
% 0.91/1.61 ,
% 0.91/1.61 class_Rings_Oordered__cancel__semiring [112, 1] (w:1, o:144, a:1, s:1
% 0.91/1.61 , b:0),
% 0.91/1.61 class_Rings_Oordered__ring [113, 1] (w:1, o:145, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Oordered__semiring [116, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.91/1.61
% 0.91/1.61 class_Rings_Oordered__comm__semiring [117, 1] (w:1, o:148, a:1, s:1
% 0.91/1.61 , b:0),
% 0.91/1.61 class_Groups_Olinordered__ab__group__add [119, 1] (w:1, o:111, a:1
% 0.91/1.61 , s:1, b:0),
% 0.91/1.61 class_Groups_Oordered__ab__group__add [120, 1] (w:1, o:149, a:1, s:1
% 0.91/1.61 , b:0),
% 0.91/1.61 class_Groups_Ozero [121, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.91/1.61 class_Groups_Oab__semigroup__mult [122, 1] (w:1, o:151, a:1, s:1, b:0
% 0.91/1.61 ),
% 0.91/1.61 class_Groups_Ogroup__add [123, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.91/1.61 c_Complex_Ocomplex_Ocomplex__size [131, 1] (w:1, o:153, a:1, s:1, b:0
% 0.91/1.61 ),
% 0.91/1.61 c_Groups_Oplus__class_Oplus [134, 3] (w:1, o:225, a:1, s:1, b:0),
% 0.91/1.61 c_Nat_Osize__class_Osize [135, 2] (w:1, o:205, a:1, s:1, b:0),
% 0.91/1.61 class_Orderings_Opreorder [136, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.91/1.61 c_Complex_Ocomplex_Ocomplex__rec [138, 3] (w:1, o:226, a:1, s:1, b:0)
% 0.91/1.61 ,
% 0.91/1.61 hAPP [139, 2] (w:1, o:206, a:1, s:1, b:0),
% 0.91/1.61 c_Complex_Ocomplex_Ocomplex__case [140, 3] (w:1, o:227, a:1, s:1, b:0
% 0.91/1.61 ),
% 0.91/1.61 class_Groups_Oab__semigroup__add [141, 1] (w:1, o:154, a:1, s:1, b:0)
% 0.91/1.61 ,
% 0.91/1.61 class_Groups_Ocancel__semigroup__add [142, 1] (w:1, o:155, a:1, s:1
% 0.91/1.61 , b:0),
% 0.91/1.61 class_Groups_Ocancel__ab__semigroup__add [143, 1] (w:1, o:156, a:1
% 0.91/1.61 , s:1, b:0),
% 0.91/1.61 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.91/1.61 144, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.91/1.61 class_Groups_Ocomm__monoid__add [145, 1] (w:1, o:164, a:1, s:1, b:0)
% 0.91/1.61 ,
% 0.91/1.61 class_Groups_Omonoid__add [146, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.91/1.61 class_Groups_Oordered__ab__semigroup__add__imp__le [147, 1] (w:1, o:
% 0.91/1.61 166, a:1, s:1, b:0),
% 0.91/1.61 class_Groups_Oordered__ab__semigroup__add [148, 1] (w:1, o:167, a:1
% 0.91/1.61 , s:1, b:0),
% 0.91/1.61 class_Rings_Osemiring [151, 1] (w:1, o:157, a:1, s:1, b:0),
% 0.91/1.61 class_Rings_Ocomm__semiring [152, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.91/1.61 class_Groups_Oab__group__add [154, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.91/1.61 class_Groups_Oordered__comm__monoid__add [155, 1] (w:1, o:169, a:1
% 0.91/1.61 , s:1, b:0),
% 0.91/1.61 class_Orderings_Olinorder [157, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.91/1.61 class_Orderings_Oord [160, 1] (w:1, o:129, a:1, s:1, b:0),
% 12.69/13.03 tc_fun [161, 2] (w:1, o:211, a:1, s:1, b:0),
% 12.69/13.03 class_Orderings_Oorder [162, 1] (w:1, o:130, a:1, s:1, b:0),
% 12.69/13.03 c_RealVector_Onorm__class_Onorm [164, 2] (w:1, o:212, a:1, s:1, b:0)
% 12.69/13.03 ,
% 12.69/13.03 c_Nat_OSuc [165, 1] (w:1, o:170, a:1, s:1, b:0),
% 12.69/13.03 c_Groups_Oabs__class_Oabs [166, 2] (w:1, o:213, a:1, s:1, b:0),
% 12.69/13.03 c_Groups_Ominus__class_Ominus [167, 3] (w:1, o:228, a:1, s:1, b:0),
% 12.69/13.03 c_Orderings_Oord__class_Oless [168, 3] (w:1, o:222, a:1, s:1, b:0),
% 12.69/13.03 c_Groups_Oone__class_Oone [169, 1] (w:1, o:171, a:1, s:1, b:0),
% 12.69/13.03 class_Groups_Oordered__ab__group__add__abs [170, 1] (w:1, o:172, a:1
% 12.69/13.03 , s:1, b:0),
% 12.69/13.03 class_Groups_Oone [176, 1] (w:1, o:173, a:1, s:1, b:0),
% 12.69/13.03 class_Groups_Oabs__if [177, 1] (w:1, o:174, a:1, s:1, b:0),
% 12.69/13.03 class_Groups_Oordered__cancel__ab__semigroup__add [179, 1] (w:1, o:
% 12.69/13.03 175, a:1, s:1, b:0),
% 12.69/13.03 class_Rings_Ocomm__ring__1 [183, 1] (w:1, o:126, a:1, s:1, b:0),
% 12.69/13.03 class_Rings_Olinordered__semiring__1__strict [184, 1] (w:1, o:134, a:
% 12.69/13.03 1, s:1, b:0),
% 12.69/13.03 class_Rings_Olinordered__semiring__strict [185, 1] (w:1, o:135, a:1
% 12.69/13.03 , s:1, b:0),
% 12.69/13.03 class_Rings_Olinordered__comm__semiring__strict [186, 1] (w:1, o:136
% 12.69/13.03 , a:1, s:1, b:0),
% 12.69/13.03 class_Rings_Osemiring__0 [187, 1] (w:1, o:118, a:1, s:1, b:0),
% 12.69/13.03 class_Rings_Oordered__ring__abs [190, 1] (w:1, o:146, a:1, s:1, b:0)
% 12.69/13.03 ,
% 12.69/13.03 class_Rings_Olinordered__semiring [191, 1] (w:1, o:137, a:1, s:1, b:0
% 12.69/13.03 ),
% 12.69/13.03 class_Rings_Olinordered__semiring__1 [192, 1] (w:1, o:138, a:1, s:1
% 12.69/13.03 , b:0),
% 12.69/13.03 class_RealVector_Oreal__normed__vector [193, 1] (w:1, o:159, a:1, s:1
% 12.69/13.03 , b:0),
% 12.69/13.03 class_RealVector_Oreal__normed__algebra__1 [194, 1] (w:1, o:160, a:1
% 12.69/13.03 , s:1, b:0),
% 12.69/13.03 hBOOL [196, 1] (w:1, o:176, a:1, s:1, b:0),
% 12.69/13.03 class_RealVector_Oreal__normed__algebra [205, 1] (w:1, o:161, a:1, s:
% 12.69/13.03 1, b:0),
% 12.69/13.03 class_RealVector_Oreal__normed__div__algebra [208, 1] (w:1, o:162, a:
% 12.69/13.03 1, s:1, b:0),
% 12.69/13.03 tc_HOL_Obool [214, 0] (w:1, o:35, a:1, s:1, b:0),
% 12.69/13.03 alpha1 [215, 3] (w:1, o:229, a:1, s:1, b:1),
% 12.69/13.03 alpha2 [216, 3] (w:1, o:234, a:1, s:1, b:1),
% 12.69/13.03 alpha3 [217, 2] (w:1, o:214, a:1, s:1, b:1),
% 12.69/13.03 alpha4 [218, 2] (w:1, o:215, a:1, s:1, b:1),
% 12.69/13.03 alpha5 [219, 4] (w:1, o:242, a:1, s:1, b:1),
% 12.69/13.03 alpha6 [220, 4] (w:1, o:243, a:1, s:1, b:1),
% 12.69/13.03 alpha7 [221, 2] (w:1, o:216, a:1, s:1, b:1),
% 12.69/13.03 alpha8 [222, 3] (w:1, o:235, a:1, s:1, b:1),
% 12.69/13.03 alpha9 [223, 3] (w:1, o:236, a:1, s:1, b:1),
% 12.69/13.03 alpha10 [224, 2] (w:1, o:217, a:1, s:1, b:1),
% 12.69/13.03 alpha11 [225, 3] (w:1, o:230, a:1, s:1, b:1),
% 12.69/13.03 alpha12 [226, 3] (w:1, o:231, a:1, s:1, b:1),
% 12.69/13.03 alpha13 [227, 2] (w:1, o:218, a:1, s:1, b:1),
% 12.69/13.03 alpha14 [228, 2] (w:1, o:219, a:1, s:1, b:1),
% 12.69/13.03 alpha15 [229, 4] (w:1, o:244, a:1, s:1, b:1),
% 12.69/13.03 alpha16 [230, 4] (w:1, o:245, a:1, s:1, b:1),
% 12.69/13.03 alpha17 [231, 3] (w:1, o:232, a:1, s:1, b:1),
% 12.69/13.03 alpha18 [232, 3] (w:1, o:233, a:1, s:1, b:1),
% 12.69/13.03 alpha19 [233, 2] (w:1, o:220, a:1, s:1, b:1),
% 12.69/13.03 alpha20 [234, 3] (w:1, o:237, a:1, s:1, b:1),
% 12.69/13.03 alpha21 [235, 3] (w:1, o:238, a:1, s:1, b:1),
% 12.69/13.03 skol1 [236, 0] (w:1, o:8, a:1, s:1, b:1),
% 12.69/13.03 skol2 [237, 3] (w:1, o:239, a:1, s:1, b:1),
% 12.69/13.03 skol3 [238, 2] (w:1, o:207, a:1, s:1, b:1),
% 12.69/13.03 skol4 [239, 3] (w:1, o:240, a:1, s:1, b:1),
% 12.69/13.03 skol5 [240, 3] (w:1, o:241, a:1, s:1, b:1),
% 12.69/13.03 skol6 [241, 2] (w:1, o:208, a:1, s:1, b:1),
% 12.69/13.03 skol7 [242, 1] (w:1, o:177, a:1, s:1, b:1),
% 12.69/13.03 skol8 [243, 2] (w:1, o:209, a:1, s:1, b:1),
% 12.69/13.03 skol9 [244, 2] (w:1, o:210, a:1, s:1, b:1),
% 12.69/13.03 skol10 [245, 0] (w:1, o:9, a:1, s:1, b:1).
% 12.69/13.03
% 12.69/13.03
% 12.69/13.03 Starting Search:
% 12.69/13.03
% 12.69/13.03 *** allocated 113905 integers for clauses
% 12.69/13.03 *** allocated 170857 integers for clauses
% 12.69/13.03 Resimplifying inuse:
% 12.69/13.03 Done
% 12.69/13.03
% 12.69/13.03
% 12.69/13.03 Intermediate Status:
% 12.69/13.03 Generated: 3373
% 12.69/13.03 Kept: 2010
% 12.69/13.03 Inuse: 173
% 12.69/13.03 Deleted: 13
% 12.69/13.03 Deletedinuse: 0
% 12.69/13.03
% 12.69/13.03 Resimplifying inuse:
% 12.69/13.03 Done
% 12.69/13.03
% 12.69/13.03 *** allocated 256285 integers for clauses
% 12.69/13.03 Resimplifying inuse:
% 12.69/13.03 Done
% 12.69/13.03
% 12.69/13.03
% 12.69/13.03 Intermediate Status:
% 12.69/13.03 Generated: 9643
% 12.69/13.03 Kept: 4050
% 12.69/13.03 Inuse: 345
% 12.69/13.03 Deleted: 27
% 12.69/13.03 Deletedinuse: 1
% 12.69/13.03
% 12.69/13.03 *** allocated 170857 integers for termspace/termends
% 63.55/63.96 *** allocated 384427 integers for clauses
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 16411
% 63.55/63.96 Kept: 6064
% 63.55/63.96 Inuse: 420
% 63.55/63.96 Deleted: 27
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 *** allocated 576640 integers for clauses
% 63.55/63.96 *** allocated 256285 integers for termspace/termends
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 24291
% 63.55/63.96 Kept: 8079
% 63.55/63.96 Inuse: 487
% 63.55/63.96 Deleted: 30
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 31794
% 63.55/63.96 Kept: 10095
% 63.55/63.96 Inuse: 592
% 63.55/63.96 Deleted: 34
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 *** allocated 864960 integers for clauses
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 39527
% 63.55/63.96 Kept: 12109
% 63.55/63.96 Inuse: 637
% 63.55/63.96 Deleted: 39
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 *** allocated 384427 integers for termspace/termends
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 48857
% 63.55/63.96 Kept: 14600
% 63.55/63.96 Inuse: 673
% 63.55/63.96 Deleted: 39
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 57796
% 63.55/63.96 Kept: 16705
% 63.55/63.96 Inuse: 711
% 63.55/63.96 Deleted: 41
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 *** allocated 576640 integers for termspace/termends
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 67136
% 63.55/63.96 Kept: 18719
% 63.55/63.96 Inuse: 751
% 63.55/63.96 Deleted: 41
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 *** allocated 1297440 integers for clauses
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 73168
% 63.55/63.96 Kept: 20816
% 63.55/63.96 Inuse: 780
% 63.55/63.96 Deleted: 42
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 Resimplifying clauses:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 79270
% 63.55/63.96 Kept: 22837
% 63.55/63.96 Inuse: 809
% 63.55/63.96 Deleted: 598
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 90337
% 63.55/63.96 Kept: 26198
% 63.55/63.96 Inuse: 865
% 63.55/63.96 Deleted: 598
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 97171
% 63.55/63.96 Kept: 28428
% 63.55/63.96 Inuse: 870
% 63.55/63.96 Deleted: 598
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 *** allocated 864960 integers for termspace/termends
% 63.55/63.96 *** allocated 1946160 integers for clauses
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 106853
% 63.55/63.96 Kept: 31196
% 63.55/63.96 Inuse: 890
% 63.55/63.96 Deleted: 598
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 115946
% 63.55/63.96 Kept: 34047
% 63.55/63.96 Inuse: 905
% 63.55/63.96 Deleted: 598
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 123306
% 63.55/63.96 Kept: 36501
% 63.55/63.96 Inuse: 910
% 63.55/63.96 Deleted: 598
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 129007
% 63.55/63.96 Kept: 38854
% 63.55/63.96 Inuse: 925
% 63.55/63.96 Deleted: 598
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 133409
% 63.55/63.96 Kept: 41188
% 63.55/63.96 Inuse: 935
% 63.55/63.96 Deleted: 598
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 Resimplifying clauses:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 138750
% 63.55/63.96 Kept: 43196
% 63.55/63.96 Inuse: 962
% 63.55/63.96 Deleted: 929
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 148243
% 63.55/63.96 Kept: 45216
% 63.55/63.96 Inuse: 972
% 63.55/63.96 Deleted: 929
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 *** allocated 2919240 integers for clauses
% 63.55/63.96 *** allocated 1297440 integers for termspace/termends
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 160494
% 63.55/63.96 Kept: 47323
% 63.55/63.96 Inuse: 980
% 63.55/63.96 Deleted: 929
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 167918
% 63.55/63.96 Kept: 49609
% 63.55/63.96 Inuse: 990
% 63.55/63.96 Deleted: 929
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 171948
% 63.55/63.96 Kept: 51633
% 63.55/63.96 Inuse: 998
% 63.55/63.96 Deleted: 929
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 178875
% 63.55/63.96 Kept: 53682
% 63.55/63.96 Inuse: 1037
% 63.55/63.96 Deleted: 929
% 63.55/63.96 Deletedinuse: 1
% 63.55/63.96
% 63.55/63.96 Resimplifying inuse:
% 63.55/63.96 Done
% 63.55/63.96
% 63.55/63.96
% 63.55/63.96 Intermediate Status:
% 63.55/63.96 Generated: 192854
% 63.55/63.96 Kept: 55705
% 63.55/63.96 Inuse: 1050
% 138.12/138.58 Deleted: 929
% 138.12/138.58 Deletedinuse: 1
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 203638
% 138.12/138.58 Kept: 57707
% 138.12/138.58 Inuse: 1072
% 138.12/138.58 Deleted: 929
% 138.12/138.58 Deletedinuse: 1
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 211821
% 138.12/138.58 Kept: 60715
% 138.12/138.58 Inuse: 1095
% 138.12/138.58 Deleted: 929
% 138.12/138.58 Deletedinuse: 1
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying clauses:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 219395
% 138.12/138.58 Kept: 62782
% 138.12/138.58 Inuse: 1115
% 138.12/138.58 Deleted: 1510
% 138.12/138.58 Deletedinuse: 2
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 227118
% 138.12/138.58 Kept: 64904
% 138.12/138.58 Inuse: 1152
% 138.12/138.58 Deleted: 1511
% 138.12/138.58 Deletedinuse: 2
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 *** allocated 4378860 integers for clauses
% 138.12/138.58 *** allocated 1946160 integers for termspace/termends
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 255033
% 138.12/138.58 Kept: 68679
% 138.12/138.58 Inuse: 1179
% 138.12/138.58 Deleted: 1511
% 138.12/138.58 Deletedinuse: 2
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 264647
% 138.12/138.58 Kept: 70729
% 138.12/138.58 Inuse: 1205
% 138.12/138.58 Deleted: 1513
% 138.12/138.58 Deletedinuse: 4
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 273388
% 138.12/138.58 Kept: 72773
% 138.12/138.58 Inuse: 1234
% 138.12/138.58 Deleted: 1515
% 138.12/138.58 Deletedinuse: 5
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 288463
% 138.12/138.58 Kept: 75651
% 138.12/138.58 Inuse: 1252
% 138.12/138.58 Deleted: 1516
% 138.12/138.58 Deletedinuse: 5
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 300063
% 138.12/138.58 Kept: 79608
% 138.12/138.58 Inuse: 1276
% 138.12/138.58 Deleted: 1516
% 138.12/138.58 Deletedinuse: 5
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying clauses:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 321759
% 138.12/138.58 Kept: 81641
% 138.12/138.58 Inuse: 1283
% 138.12/138.58 Deleted: 2162
% 138.12/138.58 Deletedinuse: 5
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 332036
% 138.12/138.58 Kept: 83925
% 138.12/138.58 Inuse: 1292
% 138.12/138.58 Deleted: 2163
% 138.12/138.58 Deletedinuse: 6
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 342555
% 138.12/138.58 Kept: 86274
% 138.12/138.58 Inuse: 1317
% 138.12/138.58 Deleted: 2163
% 138.12/138.58 Deletedinuse: 6
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 351681
% 138.12/138.58 Kept: 88276
% 138.12/138.58 Inuse: 1346
% 138.12/138.58 Deleted: 2163
% 138.12/138.58 Deletedinuse: 6
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 365497
% 138.12/138.58 Kept: 91387
% 138.12/138.58 Inuse: 1362
% 138.12/138.58 Deleted: 2163
% 138.12/138.58 Deletedinuse: 6
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 377843
% 138.12/138.58 Kept: 93924
% 138.12/138.58 Inuse: 1377
% 138.12/138.58 Deleted: 2163
% 138.12/138.58 Deletedinuse: 6
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 *** allocated 2919240 integers for termspace/termends
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 388055
% 138.12/138.58 Kept: 95942
% 138.12/138.58 Inuse: 1417
% 138.12/138.58 Deleted: 2163
% 138.12/138.58 Deletedinuse: 6
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 400791
% 138.12/138.58 Kept: 98039
% 138.12/138.58 Inuse: 1432
% 138.12/138.58 Deleted: 2163
% 138.12/138.58 Deletedinuse: 6
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 408568
% 138.12/138.58 Kept: 100218
% 138.12/138.58 Inuse: 1462
% 138.12/138.58 Deleted: 2166
% 138.12/138.58 Deletedinuse: 9
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 *** allocated 6568290 integers for clauses
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 422951
% 138.12/138.58 Kept: 104110
% 138.12/138.58 Inuse: 1472
% 138.12/138.58 Deleted: 2166
% 138.12/138.58 Deletedinuse: 9
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying clauses:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 433880
% 138.12/138.58 Kept: 106390
% 138.12/138.58 Inuse: 1507
% 138.12/138.58 Deleted: 2499
% 138.12/138.58 Deletedinuse: 9
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 439658
% 138.12/138.58 Kept: 109489
% 138.12/138.58 Inuse: 1512
% 138.12/138.58 Deleted: 2499
% 138.12/138.58 Deletedinuse: 9
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 456767
% 138.12/138.58 Kept: 111978
% 138.12/138.58 Inuse: 1527
% 138.12/138.58 Deleted: 2499
% 138.12/138.58 Deletedinuse: 9
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 138.12/138.58 Done
% 138.12/138.58
% 138.12/138.58
% 138.12/138.58 Intermediate Status:
% 138.12/138.58 Generated: 481345
% 138.12/138.58 Kept: 114696
% 138.12/138.58 Inuse: 1542
% 138.12/138.58 Deleted: 2499
% 138.12/138.58 Deletedinuse: 9
% 138.12/138.58
% 138.12/138.58 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 505885
% 282.23/282.77 Kept: 117340
% 282.23/282.77 Inuse: 1552
% 282.23/282.77 Deleted: 2499
% 282.23/282.77 Deletedinuse: 9
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 517590
% 282.23/282.77 Kept: 119450
% 282.23/282.77 Inuse: 1577
% 282.23/282.77 Deleted: 2499
% 282.23/282.77 Deletedinuse: 9
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 521883
% 282.23/282.77 Kept: 122276
% 282.23/282.77 Inuse: 1578
% 282.23/282.77 Deleted: 2499
% 282.23/282.77 Deletedinuse: 9
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying clauses:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 530134
% 282.23/282.77 Kept: 124281
% 282.23/282.77 Inuse: 1592
% 282.23/282.77 Deleted: 3222
% 282.23/282.77 Deletedinuse: 9
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 537700
% 282.23/282.77 Kept: 126405
% 282.23/282.77 Inuse: 1617
% 282.23/282.77 Deleted: 3227
% 282.23/282.77 Deletedinuse: 14
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 547152
% 282.23/282.77 Kept: 128406
% 282.23/282.77 Inuse: 1647
% 282.23/282.77 Deleted: 3227
% 282.23/282.77 Deletedinuse: 14
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 559587
% 282.23/282.77 Kept: 130643
% 282.23/282.77 Inuse: 1667
% 282.23/282.77 Deleted: 3228
% 282.23/282.77 Deletedinuse: 15
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 570146
% 282.23/282.77 Kept: 132692
% 282.23/282.77 Inuse: 1682
% 282.23/282.77 Deleted: 3229
% 282.23/282.77 Deletedinuse: 16
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 578334
% 282.23/282.77 Kept: 134694
% 282.23/282.77 Inuse: 1712
% 282.23/282.77 Deleted: 3229
% 282.23/282.77 Deletedinuse: 16
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 587657
% 282.23/282.77 Kept: 136702
% 282.23/282.77 Inuse: 1739
% 282.23/282.77 Deleted: 3229
% 282.23/282.77 Deletedinuse: 16
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 *** allocated 4378860 integers for termspace/termends
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 614859
% 282.23/282.77 Kept: 142704
% 282.23/282.77 Inuse: 1752
% 282.23/282.77 Deleted: 3229
% 282.23/282.77 Deletedinuse: 16
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying clauses:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 623387
% 282.23/282.77 Kept: 144735
% 282.23/282.77 Inuse: 1787
% 282.23/282.77 Deleted: 3821
% 282.23/282.77 Deletedinuse: 16
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 632252
% 282.23/282.77 Kept: 146780
% 282.23/282.77 Inuse: 1819
% 282.23/282.77 Deleted: 3821
% 282.23/282.77 Deletedinuse: 16
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 643082
% 282.23/282.77 Kept: 151526
% 282.23/282.77 Inuse: 1842
% 282.23/282.77 Deleted: 3822
% 282.23/282.77 Deletedinuse: 17
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 648959
% 282.23/282.77 Kept: 154991
% 282.23/282.77 Inuse: 1847
% 282.23/282.77 Deleted: 3822
% 282.23/282.77 Deletedinuse: 17
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 *** allocated 9852435 integers for clauses
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 656719
% 282.23/282.77 Kept: 158989
% 282.23/282.77 Inuse: 1857
% 282.23/282.77 Deleted: 3822
% 282.23/282.77 Deletedinuse: 17
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 662802
% 282.23/282.77 Kept: 162641
% 282.23/282.77 Inuse: 1862
% 282.23/282.77 Deleted: 3822
% 282.23/282.77 Deletedinuse: 17
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying clauses:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 673785
% 282.23/282.77 Kept: 164690
% 282.23/282.77 Inuse: 1877
% 282.23/282.77 Deleted: 4119
% 282.23/282.77 Deletedinuse: 17
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 687818
% 282.23/282.77 Kept: 166694
% 282.23/282.77 Inuse: 1890
% 282.23/282.77 Deleted: 4119
% 282.23/282.77 Deletedinuse: 17
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 696708
% 282.23/282.77 Kept: 168737
% 282.23/282.77 Inuse: 1915
% 282.23/282.77 Deleted: 4119
% 282.23/282.77 Deletedinuse: 17
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 712333
% 282.23/282.77 Kept: 170866
% 282.23/282.77 Inuse: 1927
% 282.23/282.77 Deleted: 4119
% 282.23/282.77 Deletedinuse: 17
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 720725
% 282.23/282.77 Kept: 172880
% 282.23/282.77 Inuse: 1952
% 282.23/282.77 Deleted: 4119
% 282.23/282.77 Deletedinuse: 17
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 729225
% 282.23/282.77 Kept: 174976
% 282.23/282.77 Inuse: 1977
% 282.23/282.77 Deleted: 4119
% 282.23/282.77 Deletedinuse: 17
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77 Resimplifying inuse:
% 282.23/282.77 Done
% 282.23/282.77
% 282.23/282.77
% 282.23/282.77 Intermediate Status:
% 282.23/282.77 Generated: 737339
% 282.23/282.77 Kept: 177598
% 282.23/282.77 Inuse: 1996
% 282.23/282.77 Deleted: 4120
% 282.23/282.77 DeCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------