TSTP Solution File: SWW171+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW171+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.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 23:21:00 EDT 2022
% Result : Timeout 300.07s 300.61s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWW171+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.14 % Command : bliksem %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jun 4 14:57:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.95/1.55 *** allocated 10000 integers for termspace/termends
% 0.95/1.55 *** allocated 10000 integers for clauses
% 0.95/1.55 *** allocated 10000 integers for justifications
% 0.95/1.55 *** allocated 15000 integers for termspace/termends
% 0.95/1.55 *** allocated 22500 integers for termspace/termends
% 0.95/1.55 *** allocated 33750 integers for termspace/termends
% 0.95/1.55 Bliksem 1.12
% 0.95/1.55
% 0.95/1.55
% 0.95/1.55 Automatic Strategy Selection
% 0.95/1.55
% 0.95/1.55 *** allocated 50625 integers for termspace/termends
% 0.95/1.55 *** allocated 75937 integers for termspace/termends
% 0.95/1.55 *** allocated 113905 integers for termspace/termends
% 0.95/1.55
% 0.95/1.55 Clauses:
% 0.95/1.55
% 0.95/1.55 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.95/1.55 { c_Int_OBit0( c_Int_OPls ) = c_Int_OPls }.
% 0.95/1.55 { ! c_Int_OPls = c_Int_OBit0( X ), c_Int_OPls = X }.
% 0.95/1.55 { ! c_Int_OPls = X, c_Int_OPls = c_Int_OBit0( X ) }.
% 0.95/1.55 { ! c_Int_OBit0( X ) = c_Int_OPls, X = c_Int_OPls }.
% 0.95/1.55 { ! X = c_Int_OPls, c_Int_OBit0( X ) = c_Int_OPls }.
% 0.95/1.55 { ! c_Int_OBit0( Y ) = c_Int_OBit1( X ) }.
% 0.95/1.55 { ! c_Int_OBit1( Y ) = c_Int_OBit0( X ) }.
% 0.95/1.55 { ! c_Int_OPls = c_Int_OBit1( X ) }.
% 0.95/1.55 { ! c_Int_OBit1( X ) = c_Int_OPls }.
% 0.95/1.55 { ! class_Groups_Omonoid__mult( X ), ! class_Int_Onumber( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 0.95/1.55 ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.95/1.55 c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.55 Y ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.55 { ! class_Rings_Osemiring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.55 ( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.95/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.55 .
% 0.95/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.95/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.55 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ) }.
% 0.95/1.55 { ! class_Rings_Osemiring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.55 ( X ), c_Groups_Oone__class_Oone( X ) ), c_Int_Onumber__class_Onumber__of
% 0.95/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.95/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.55 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, hAPP
% 0.95/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 0.95/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.55 ( X ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.55 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.55 Z ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), Z ) ) ), Y ) }.
% 0.95/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.95/1.55 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OPls ), X
% 0.95/1.55 ) = c_Int_OPls }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OBit0( Y
% 0.95/1.55 ) ), X ) = c_Int_OBit0( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.55 tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.55 { c_Int_OPls = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.55 { c_Groups_Oone__class_Oone( tc_Int_Oint ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.95/1.55 ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.55 c_Int_OPls ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) }.
% 0.95/1.55 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.55 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) )
% 0.95/1.55 , Y ) = Y }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.55 ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls
% 0.95/1.55 ) ) ) = Y }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.55 c_Int_OBit1( c_Int_OPls ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Oone__class_Oone( X ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.95/1.55 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.95/1.55 ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.55 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.95/1.55 ) }.
% 0.95/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.95/1.55 ( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ), Y ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 0.95/1.55 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.95/1.55 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 0.95/1.55 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 0.95/1.55 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 0.95/1.55 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 0.95/1.55 { ! c_Int_OBit1( Y ) = c_Int_OBit1( X ), Y = X }.
% 0.95/1.55 { ! Y = X, c_Int_OBit1( Y ) = c_Int_OBit1( X ) }.
% 0.95/1.55 { ! c_Int_OBit0( Y ) = c_Int_OBit0( X ), Y = X }.
% 0.95/1.55 { ! Y = X, c_Int_OBit0( Y ) = c_Int_OBit0( X ) }.
% 0.95/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.95/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP
% 0.95/1.55 ( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.95/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.95/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.55 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.55 tc_RealDef_Oreal ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 0.95/1.55 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ) }.
% 0.95/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.95/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.55 .
% 0.95/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), ! c_Int_Onumber__class_Onumber__of(
% 0.95/1.55 tc_Nat_Onat, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.55 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.95/1.55 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.55 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.55 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.55 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), Y ) ) ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.95/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.95/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), Y ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.55 X ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ) ) }.
% 0.95/1.55 { c_Groups_Oone__class_Oone( tc_Code__Numeral_Ocode__numeral ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Code__Numeral_Ocode__numeral,
% 0.95/1.55 c_Int_OBit1( c_Int_OPls ) ) }.
% 0.95/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.95/1.55 ( tc_Int_Oint ) }.
% 0.95/1.55 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OMin )
% 0.95/1.55 }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.95/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.95/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.95/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) =
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), alpha1( X, Y ), alpha14( X, Y )
% 0.95/1.55 }.
% 0.95/1.55 { ! alpha1( X, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 0.95/1.55 ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.55 { ! alpha14( X, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 0.95/1.55 ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.55 { ! alpha14( X, Y ), Y = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.95/1.55 c_Int_OMin ) }.
% 0.95/1.55 { ! alpha14( X, Y ), X = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.95/1.55 c_Int_OMin ) }.
% 0.95/1.55 { ! Y = c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), ! X =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), alpha14( X,
% 0.95/1.55 Y ) }.
% 0.95/1.55 { ! alpha1( X, Y ), Y = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.55 { ! alpha1( X, Y ), X = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! X =
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), alpha1( X, Y ) }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.95/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.55 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.95/1.55 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.95/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 0.95/1.55 tc_Int_Oint ), X = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.95/1.55 c_Int_OMin ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.95/1.55 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.95/1.55 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.95/1.55 c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.55 c_Int_OMin ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.95/1.55 c_Int_OMin ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit1
% 0.95/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, X )
% 0.95/1.55 }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit1(
% 0.95/1.55 X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OMin
% 0.95/1.55 ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OPls )
% 0.95/1.55 }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.95/1.55 c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.55 c_Int_OMin ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.95/1.55 c_Int_OMin ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.55 X ), Y ), Z = Y }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.95/1.55 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.95/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.95/1.55 { c_Int_OBit1( c_Int_OMin ) = c_Int_OMin }.
% 0.95/1.55 { ! c_Int_OMin = c_Int_OBit1( X ), c_Int_OMin = X }.
% 0.95/1.55 { ! c_Int_OMin = X, c_Int_OMin = c_Int_OBit1( X ) }.
% 0.95/1.55 { ! c_Int_OBit1( X ) = c_Int_OMin, X = c_Int_OMin }.
% 0.95/1.55 { ! X = c_Int_OMin, c_Int_OBit1( X ) = c_Int_OMin }.
% 0.95/1.55 { ! c_Int_OMin = c_Int_OPls }.
% 0.95/1.55 { ! c_Int_OPls = c_Int_OMin }.
% 0.95/1.55 { ! c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ) }.
% 0.95/1.55 { ! c_Int_OMin = c_Int_OBit0( X ) }.
% 0.95/1.55 { ! c_Int_OBit0( X ) = c_Int_OMin }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.95/1.55 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.95/1.55 ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.95/1.55 c_Int_OBit1( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.95/1.55 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.95/1.55 ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.95/1.55 c_Int_OBit1( X ) ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OPls )
% 0.95/1.55 }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.95/1.55 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.95/1.55 ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.95/1.55 c_Int_OBit0( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.95/1.55 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.95/1.55 ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.95/1.55 c_Int_OBit0( X ) ) }.
% 0.95/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.55 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.55 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.55 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.55 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.95/1.55 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.95/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.95/1.55 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.95/1.55 , Y ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 0.95/1.55 , Y ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X
% 0.95/1.55 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.95/1.55 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.95/1.55 ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1
% 0.95/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.95/1.55 }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1(
% 0.95/1.55 X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.95/1.55 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.95/1.55 ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.95/1.55 c_Int_OBit1( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.95/1.55 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.95/1.55 ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.95/1.55 c_Int_OBit1( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0
% 0.95/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 0.95/1.55 }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0(
% 0.95/1.55 X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.95/1.55 c_Int_OPls ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.55 c_Int_OPls ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 0.95/1.55 c_Int_OPls ) }.
% 0.95/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.95/1.55 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.95/1.55 ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.95/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.95/1.55 tc_Nat_Onat ) ) = Y }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.95/1.55 tc_Nat_Onat ) ) = Y }.
% 0.95/1.55 { c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Code__Numeral_Ocode__numeral,
% 0.95/1.55 c_Int_OPls ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.55 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), c_Nat_OSuc(
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), Y ) ) ) = c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.55 c_Int_OMin ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), Z ) ) ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.55 { c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) }.
% 0.95/1.55 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.55 tc_Nat_Onat ) ) ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), Y ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.55 X ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.55 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.95/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.95/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.95/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.95/1.55 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 0.95/1.55 ( c_Power_Opower__class_Opower( X ), Y ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.55 ), Z = Y }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.55 = Y }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.55 = Y }.
% 0.95/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( X ) }.
% 0.95/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.55 .
% 0.95/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.55 tc_Nat_Onat ) }.
% 0.95/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.95/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.95/1.55 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.95/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.55 = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.95/1.55 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.55 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.55 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.95/1.55 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.95/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( X ) ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( X ) ) ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.95/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.95/1.55 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.95/1.55 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.95/1.55 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) ) }.
% 0.95/1.55 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.55 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.95/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.95/1.55 tc_Int_Oint ) ) }.
% 0.95/1.55 { ! X = c_Nat_OSuc( X ) }.
% 0.95/1.55 { ! c_Nat_OSuc( X ) = X }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.95/1.55 .
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.95/1.55 ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.55 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.95/1.55 , c_Nat_OSuc( X ) ) }.
% 0.95/1.55 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.95/1.55 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.95/1.55 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.95/1.55 }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.95/1.55 c_Nat_OSuc( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.95/1.55 ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.95/1.55 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.95/1.55 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.95/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.95/1.55 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.95/1.55 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.95/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.95/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.95/1.55 }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.95/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.95/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.55 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.55 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.55 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.95/1.55 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.55 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.95/1.55 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.95/1.55 .
% 0.95/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.95/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.95/1.55 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.95/1.55 .
% 0.95/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.95/1.55 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.95/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.55 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.55 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.55 ), X ) ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.95/1.55 tc_Int_Oint ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.95/1.55 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.55 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.95/1.55 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.55 , Y ), X ) }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.95/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.95/1.55 tc_Nat_Onat ) }.
% 0.95/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.95/1.55 tc_Nat_Onat ) }.
% 0.95/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.55 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha2( X, Y
% 0.95/1.55 , Z ), alpha15( X, Y, Z ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.55 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.55 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.55 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ), alpha15( X, Y, Z ) }.
% 0.95/1.55 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.55 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.55 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Y ), alpha2( X, Y, Z ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( X ) ), alpha3( X, Y, Z ), alpha16( X, Y, Z ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( X ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( X ) ) }.
% 0.95/1.55 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.55 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.55 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( X ), Y ), alpha16( X, Y, Z ) }.
% 0.95/1.55 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.55 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.55 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ), alpha3( X, Y, Z ) }.
% 0.95/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.55 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.55 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( X ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.55 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.55 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.55 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__semiring( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.55 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.55 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.55 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.55 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.55 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.55 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( X ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.55 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.95/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.95/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.95/1.55 , Y ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.55 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( hAPP(
% 0.95/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), Z ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.55 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.95/1.55 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.95/1.55 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.55 ), c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.55 ), c_Nat_OSuc( hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.55 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 0.95/1.55 ( c_Int_OPls ) ) ) ), Y ) ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.55 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.55 { c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ) ) =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.95/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.95/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.95/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.95/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.95/1.55 .
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.55 c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.55 Z, Y ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.95/1.55 X ) ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.55 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.55 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.55 .
% 0.95/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.55 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.55 X, Y, Z ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, c_Groups_Ouminus__class_Ouminus(
% 0.95/1.55 tc_Int_Oint, Y ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) =
% 0.95/1.55 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.55 Y ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.95/1.55 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.95/1.55 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.55 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.55 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.55 , ! Z = Y }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.55 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.55 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.55 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.55 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.55 ( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.55 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.55 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.55 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.55 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.55 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.55 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.55 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.55 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.55 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.55 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.55 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.55 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.55 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.55 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.55 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.55 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.55 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.95/1.55 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.95/1.55 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.95/1.55 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.95/1.55 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.55 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.55 , ! Y = Z }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.55 , ! Z = Y }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.55 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.95/1.55 , ! Z = Y }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.95/1.55 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.55 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.55 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.55 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.95/1.55 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.55 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.95/1.55 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.55 Y ), ! Z = Y }.
% 0.95/1.55 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.55 Z ), ! Z = Y }.
% 0.95/1.55 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.55 Y ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.55 ( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Z ) ) ), Y ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Z ) ) ), Y ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.55 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.95/1.55 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.95/1.55 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), alpha4( X, Y ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.95/1.55 { ! alpha4( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.95/1.55 { ! alpha4( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha4( X, Y ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ), alpha4( X
% 0.95/1.55 , Y ) }.
% 0.95/1.55 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.95/1.55 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.95/1.55 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.55 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.95/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.95/1.55 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.55 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.95/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.95/1.55 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.95/1.55 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.55 ( X, Y ) ) }.
% 0.95/1.55 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.55 ) ), Y ) }.
% 0.95/1.55 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.95/1.55 ( X, Y ) ) }.
% 0.95/1.55 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.55 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OPls ) = c_Int_OPls }
% 0.95/1.55 .
% 0.95/1.55 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit0( X ) ) =
% 0.95/1.55 c_Int_OBit0( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.95/1.55 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.95/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.95/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.95/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.55 tc_Nat_Onat ), X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.95/1.55 .
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.55 tc_Nat_Onat ), X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.95/1.55 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.95/1.55 .
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.95/1.55 ( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.95/1.55 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.95/1.55 .
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.95/1.55 ( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OPls ) }
% 0.95/1.55 .
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.95/1.55 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.95/1.55 .
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.95/1.55 ( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.95/1.55 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.95/1.55 .
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.95/1.55 ( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.95/1.55 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.95/1.55 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.95/1.55 .
% 0.95/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.95/1.55 .
% 0.95/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.95/1.55 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.95/1.55 X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.55 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.95/1.55 }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.95/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.55 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OMin ) }
% 0.95/1.55 .
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.95/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.95/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.95/1.55 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.55 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.55 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.55 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.55 tc_Nat_Onat ), X ), Y ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.55 ( tc_Int_Oint, c_Int_OPls, Y ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, Y ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.95/1.55 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.55 tc_Int_Oint, Y, c_Int_OPls ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.95/1.55 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.55 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.95/1.55 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.55 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.95/1.55 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.55 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.55 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.55 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.95/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.55 ( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y
% 0.95/1.55 ), c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.55 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.95/1.55 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.55 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) }.
% 0.95/1.55 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls )
% 0.95/1.55 ), c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X
% 0.95/1.55 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.55 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.55 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.95/1.55 ) }.
% 0.95/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.95/1.55 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.95/1.55 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.55 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.55 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.55 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.95/1.55 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.95/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.95/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.55 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.56 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( X ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.95/1.56 .
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.95/1.56 .
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.56 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( X ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.56 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( X ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha5( X, Y, Z, T ),
% 0.95/1.56 alpha17( X, Y, Z, T ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z, T ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.56 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha17( X, Y, Z, T ) }.
% 0.95/1.56 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.95/1.56 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.95/1.56 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha5( X, Y, Z, T ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha6( X, Y, Z, T ),
% 0.95/1.56 alpha18( X, Y, Z, T ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z, T ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z, T ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.56 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha18( X, Y, Z, T ) }.
% 0.95/1.56 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.95/1.56 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.56 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha6( X, Y, Z, T ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.95/1.56 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.95/1.56 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.95/1.56 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.95/1.56 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.95/1.56 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.95/1.56 .
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.95/1.56 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.95/1.56 }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), c_Int_OPls
% 0.95/1.56 ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol2( X ) ) }.
% 0.95/1.56 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.95/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.56 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.56 c_Nat_OSuc( X ) ) }.
% 0.95/1.56 { ! alpha7( X, Y ), Y = c_Nat_OSuc( skol3( Z, Y ) ) }.
% 0.95/1.56 { ! alpha7( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol3( X, Y
% 0.95/1.56 ), X ) }.
% 0.95/1.56 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.95/1.56 ), alpha7( X, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.95/1.56 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.95/1.56 .
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.95/1.56 ( X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.95/1.56 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.95/1.56 .
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.95/1.56 ( X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X
% 0.95/1.56 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.95/1.56 ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.95/1.56 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.95/1.56 }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), c_Int_OPls
% 0.95/1.56 ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.95/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.56 { c_Int_OMin = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OMin ), X
% 0.95/1.56 ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.95/1.56 .
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.95/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.95/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), Z ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.95/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 Y ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.95/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.56 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.95/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.95/1.56 ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 0.95/1.56 c_Int_OMin ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OMin )
% 0.95/1.56 }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OMin ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), c_Int_OMin
% 0.95/1.56 ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( X
% 0.95/1.56 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( X )
% 0.95/1.56 ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OMin ) }
% 0.95/1.56 .
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OPls ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit0( X
% 0.95/1.56 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit0( X )
% 0.95/1.56 ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.95/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.95/1.56 ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.95/1.56 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), Y ) }.
% 0.95/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.95/1.56 ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.95/1.56 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.95/1.56 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.56 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.56 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.56 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.95/1.56 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.56 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.56 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.95/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.56 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.56 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.95/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.95/1.56 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), Y ) =
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ) =
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 c_Int_OMin ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.56 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.56 c_Groups_Oone__class_Oone( X ) ) = c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 c_Int_OMin ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.95/1.56 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.95/1.56 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OMin ) = c_Int_OBit1
% 0.95/1.56 ( c_Int_OPls ) }.
% 0.95/1.56 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.95/1.56 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.95/1.56 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.95/1.56 ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X
% 0.95/1.56 ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X )
% 0.95/1.56 ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.95/1.56 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 0.95/1.56 }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 0.95/1.56 c_Int_OPls ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.95/1.56 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.95/1.56 ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 0.95/1.56 ( X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 0.95/1.56 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 0.95/1.56 ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 0.95/1.56 ( X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.95/1.56 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.95/1.56 .
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.95/1.56 c_Int_OBit0( X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.95/1.56 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.95/1.56 .
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 0.95/1.56 c_Int_OBit0( X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Int_Oint ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.95/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.56 hAPP( Y, U ) ) }.
% 0.95/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.95/1.56 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.95/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.56 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.95/1.56 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.95/1.56 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.56 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.95/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.95/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.56 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.56 hAPP( Y, U ) ) }.
% 0.95/1.56 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.56 ( X, Z, Y ) }.
% 0.95/1.56 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.95/1.56 ( X, Y, Z ) }.
% 0.95/1.56 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.56 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.95/1.56 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.95/1.56 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.95/1.56 hAPP( Y, U ) ) }.
% 0.95/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.95/1.56 ( Z, skol4( X, Y, Z ) ), hAPP( Y, skol4( X, Y, Z ) ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.95/1.56 ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.95/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.95/1.56 ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.95/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.56 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.56 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.95/1.56 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit0
% 0.95/1.56 ( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit0(
% 0.95/1.56 X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 0.95/1.56 c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.56 c_Int_OMin ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), c_Int_OMin
% 0.95/1.56 ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.95/1.56 , Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.95/1.56 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.95/1.56 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.95/1.56 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.95/1.56 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.95/1.56 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.56 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0
% 0.95/1.56 ( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ), hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ) ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ), X ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ) ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ), X ) ) = hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.95/1.56 c_Groups_Oone__class_Oone( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.56 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.56 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.95/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.56 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.95/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.56 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.56 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.95/1.56 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), Y ) ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.56 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.95/1.56 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.95/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.56 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.95/1.56 ), c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.56 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.56 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.56 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 , Y ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.56 , Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( X, Y ), Y ) }.
% 0.95/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.95/1.56 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.95/1.56 .
% 0.95/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.95/1.56 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.95/1.56 }.
% 0.95/1.56 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.95/1.56 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.95/1.56 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.95/1.56 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.95/1.56 { alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.95/1.56 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.95/1.56 { alpha35( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.95/1.56 ( X, Y ), Z ) ) }.
% 0.95/1.56 { ! alpha35( X, Y, Z ), alpha37( X, Y, Z ), Z = Y }.
% 0.95/1.56 { ! alpha35( X, Y, Z ), alpha37( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.95/1.56 ) ) }.
% 0.95/1.56 { ! alpha37( X, Y, Z ), alpha35( X, Y, Z ) }.
% 0.95/1.56 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha35( X, Y, Z ) }.
% 0.95/1.56 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.95/1.56 }.
% 0.95/1.56 { ! alpha37( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.95/1.56 X, Y ), Z ) ), alpha37( X, Y, Z ) }.
% 0.95/1.56 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.95/1.56 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.95/1.56 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.95/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.56 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.95/1.56 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.56 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.56 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.95/1.56 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.56 = Y }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( X ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Y ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 = Y }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.56 = Y }.
% 0.95/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.95/1.56 = Y }.
% 0.95/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.56 = Y }.
% 0.95/1.56 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.95/1.56 = Y }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.56 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.56 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.95/1.56 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( X, Y ), Z ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.95/1.56 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( X, Z ), Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.95/1.56 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.56 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.95/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.56 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.95/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) ), Y ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.56 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.95/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.56 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.95/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.56 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.95/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.56 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.95/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.95/1.56 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.95/1.56 .
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.95/1.56 .
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.95/1.56 .
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.95/1.56 , X ) }.
% 0.95/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.95/1.56 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.56 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.56 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, Z, Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, Z, Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.56 , T ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.56 , T, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.56 , Y, T ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, Z, Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.56 , T, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, T, Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.56 , Y, Z ) ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 Z, Y ) ) = Y }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.56 Y ) ) = Y }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.95/1.56 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.95/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.95/1.56 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 T, Y ), Z = Y }.
% 0.95/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 T, Y ) }.
% 0.95/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 Y, Z ), T = Y }.
% 0.95/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 Y, Z ) }.
% 0.95/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 T, Y ), Z = Y }.
% 0.95/1.56 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 T, Y ), Z = Y }.
% 0.95/1.56 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 Y, T ), Z = Y }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.56 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.56 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.56 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.56 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.56 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.95/1.56 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.56 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.56 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.56 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.56 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.95/1.56 ) ), T ), Y ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.95/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.56 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.56 ), ! U = T }.
% 0.95/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.95/1.56 ), ! Z = Y }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.56 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.95/1.56 ) ), Z ) }.
% 0.95/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.56 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.56 ), U = Z, T = Y }.
% 0.95/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.56 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.56 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.95/1.56 ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ) ) = X }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), X ) = X }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ) ) = X }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Int_Oint ), X ) = X }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OPls, X ) = X }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0(
% 0.95/1.56 X ) ) = c_Int_OBit0( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.95/1.56 .
% 0.95/1.56 { c_Int_OBit0( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, X ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.95/1.56 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.56 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.95/1.56 .
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) }.
% 0.95/1.56 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 0.95/1.56 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, Z, Y ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.56 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.56 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.56 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.95/1.56 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 0.95/1.56 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.95/1.56 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.56 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.95/1.56 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.56 .
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.95/1.56 .
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.95/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 Y, Z ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 Z, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ) ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.56 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.95/1.56 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.95/1.56 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.95/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.95/1.56 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.56 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.56 , Y, T ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.95/1.56 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.95/1.56 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.95/1.56 ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), T ), c_Int_Onumber__class_Onumber__of( X, Y ) ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( X, Y ) ) ) }.
% 0.95/1.56 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 T ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 T ) ), Y ) ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.56 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( X, Z ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.95/1.56 X ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.56 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( X, Y ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.95/1.56 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.56 Z ) = Y }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.95/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.95/1.56 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.95/1.56 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.95/1.56 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.56 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.56 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.56 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) = Y }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ), Y ) = Y }.
% 0.95/1.56 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1(
% 0.95/1.56 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.95/1.56 .
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0(
% 0.95/1.56 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 0.95/1.56 .
% 0.95/1.56 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha8( X, Y ), alpha19
% 0.95/1.56 ( X, Y ) }.
% 0.95/1.56 { ! alpha8( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.56 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! alpha19( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.95/1.56 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { ! alpha19( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { ! alpha19( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ) ) }.
% 0.95/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha19( X, Y ) }.
% 0.95/1.56 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ) ) }.
% 0.95/1.56 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha9( X, Y ), alpha20( X
% 0.95/1.56 , Y ) }.
% 0.95/1.56 { ! alpha9( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.56 { ! alpha20( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.56 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.95/1.56 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { ! alpha20( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ) ) }.
% 0.95/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 0.95/1.56 { ! alpha9( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ) ) }.
% 0.95/1.56 { ! alpha9( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol6( X, Y ) ) ) }.
% 0.95/1.56 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.95/1.56 { c_Int_OBit1( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 0.95/1.56 tc_Int_Oint ), X ), X ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.95/1.56 .
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.95/1.56 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.95/1.56 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.56 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.95/1.56 = X }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.56 tc_Int_Oint ) ) ) }.
% 0.95/1.56 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.56 tc_Int_Oint ) ) ) }.
% 0.95/1.56 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.95/1.56 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.95/1.56 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.95/1.56 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.56 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.95/1.56 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.56 ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.95/1.56 ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.95/1.56 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.95/1.56 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 c_Int_OBit0( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 c_Int_OBit1( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OBit1( Y
% 0.95/1.56 ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( hAPP(
% 0.95/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.56 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.95/1.56 }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.95/1.56 tc_Int_Oint ) ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.56 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.95/1.56 }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.56 tc_Int_Oint ) ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.56 tc_Int_Oint ) ), X ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.95/1.56 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.95/1.56 ), Y ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.95/1.56 c_Groups_Oone__class_Oone( X ) ) ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 Y ) ) = c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) ) }.
% 0.95/1.56 { c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc( X ) ) ) = c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1
% 0.95/1.56 ( c_Int_OBit1( c_Int_OPls ) ) ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.95/1.56 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.95/1.56 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.95/1.56 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1
% 0.95/1.56 ( c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), Y ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 0.95/1.56 ) ) ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ), X ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X
% 0.95/1.56 ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.95/1.56 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.56 X ), ! Y = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.56 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.95/1.56 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.56 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.95/1.56 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.56 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.95/1.56 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 0.95/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) ) ) }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.56 ( X, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.95/1.56 ( X, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 }.
% 0.95/1.56 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.95/1.56 X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.95/1.56 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.95/1.56 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 0.95/1.56 c_Int_OBit1( c_Int_OPls ) ) ) ), Y ) ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.95/1.56 ( tc_Int_Oint ), Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.56 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.95/1.56 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.95/1.56 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.56 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.95/1.56 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.95/1.56 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.56 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.95/1.56 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.95/1.56 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.56 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! c_Int_Onumber__class_Onumber__of( X, Y
% 0.95/1.56 ) = c_Groups_Oone__class_Oone( X ), c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit1
% 0.95/1.56 ( c_Int_OPls ) ) ) ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit1
% 0.95/1.56 ( c_Int_OPls ) ) ) ) ), c_Int_Onumber__class_Onumber__of( X, Y ) =
% 0.95/1.56 c_Groups_Oone__class_Oone( X ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Y ), c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.56 tc_Int_Oint, Y ) ) ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.56 tc_Int_Oint, Y ) ) ) ), c_Groups_Oone__class_Oone( X ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.95/1.56 { ! class_Rings_Osemiring__1( X ), c_Int_Oiszero( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Rings_Osemiring__1( X ), ! c_Int_Oiszero( X, Y ), Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Rings_Osemiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.95/1.56 c_Int_Oiszero( X, Y ) }.
% 0.95/1.56 { ! class_Rings_Osemiring__1( X ), ! c_Int_Oiszero( X,
% 0.95/1.56 c_Groups_Oone__class_Oone( X ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.95/1.56 c_Int_Oiszero( X, c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( Y ) )
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.95/1.56 c_Int_Oiszero( X, c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) )
% 0.95/1.56 ), c_Int_Oiszero( X, c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.95/1.56 c_Int_Oiszero( X, c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.95/1.56 c_Int_Oiszero( X, c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) )
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! c_Int_Onumber__class_Onumber__of( X, Z
% 0.95/1.56 ) = c_Int_Onumber__class_Onumber__of( X, Y ), c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, Z, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) ) }
% 0.95/1.56 .
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, Z, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! c_Int_Onumber__class_Onumber__of( X, Y
% 0.95/1.56 ) = c_Groups_Ozero__class_Ozero( X ), c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OPls
% 0.95/1.56 ) ) ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OPls
% 0.95/1.56 ) ) ) ), c_Int_Onumber__class_Onumber__of( X, Y ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Y ), c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, c_Int_OPls, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y
% 0.95/1.56 ) ) ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, c_Int_OPls, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y
% 0.95/1.56 ) ) ) ), c_Groups_Ozero__class_Ozero( X ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.95/1.56 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.95/1.56 c_Complex_Oii ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 0.95/1.56 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex, c_Int_OMin ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.56 tc_Int_Oint ), c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0
% 0.95/1.56 ( c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }
% 0.95/1.56 .
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.95/1.56 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 0.95/1.56 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 0.95/1.56 .
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 0.95/1.56 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.56 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.95/1.56 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.95/1.56 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( tc_Int_Oint, Y ), X ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.95/1.56 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.95/1.56 ( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.56 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.95/1.56 , Y ) ), Y ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 0.95/1.56 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 0.95/1.56 .
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.95/1.56 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.56 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.95/1.56 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.56 tc_Int_Oint, X, Y ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 0.95/1.56 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol7( X, Y ) ) }.
% 0.95/1.56 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 0.95/1.56 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.56 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.95/1.56 , Y ) ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.95/1.56 ), Z ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.95/1.56 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.95/1.56 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.95/1.56 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.95/1.56 X, Z, Y ) }.
% 0.95/1.56 { ! c_Complex_Oii = c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex,
% 0.95/1.56 X ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.95/1.56 c_Complex_Oii ), c_Complex_Oii ) = c_Int_Onumber__class_Onumber__of(
% 0.95/1.56 tc_Complex_Ocomplex, c_Int_OMin ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.56 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 0.95/1.56 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 0.95/1.56 }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.95/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.95/1.56 }.
% 0.95/1.56 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.56 ( X, Z, Y ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.95/1.56 ( X, Y, Z ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.95/1.56 , Y ) ), Y ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.56 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.95/1.56 ), Z ), Y ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.95/1.56 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.95/1.56 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.95/1.56 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 T, Z ), Y ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.95/1.56 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 T, Y ), Z ) }.
% 0.95/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.95/1.56 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.95/1.56 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.95/1.56 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.95/1.56 ), Z ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.95/1.56 ( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.56 tc_Int_Oint, Y, X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.95/1.56 ( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 0.95/1.56 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 0.95/1.56 }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( tc_Int_Oint, c_Int_OBit0( Y ) ), c_Int_Onumber__class_Onumber__of(
% 0.95/1.56 tc_Int_Oint, c_Int_OBit0( X ) ) ) = hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) ) }.
% 0.95/1.56 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha36( X,
% 0.95/1.56 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.56 tc_Int_Oint, Z, Y ) = X }.
% 0.95/1.56 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha36( X,
% 0.95/1.56 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.56 tc_Int_Oint, Z, Y ) = X }.
% 0.95/1.56 { ! alpha36( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.95/1.56 { ! alpha36( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha36( X, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.95/1.56 , alpha36( X, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 0.95/1.56 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.56 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.95/1.56 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 0.95/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.95/1.56 alpha10( X, Y, Z ) }.
% 0.95/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 0.95/1.56 alpha21( X, Y, Z ) }.
% 0.95/1.56 { ! alpha10( X, Y, Z ), ! alpha21( X, Y, Z ), hBOOL( hAPP( Z,
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 0.95/1.56 { ! alpha21( X, Y, Z ), alpha25( X, Y, Z ) }.
% 0.95/1.56 { ! alpha21( X, Y, Z ), alpha27( X, Y, Z ) }.
% 0.95/1.56 { ! alpha25( X, Y, Z ), ! alpha27( X, Y, Z ), alpha21( X, Y, Z ) }.
% 0.95/1.56 { ! alpha27( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha30( X, Y, Z ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha27( X, Y, Z ) }.
% 0.95/1.56 { ! alpha30( X, Y, Z ), alpha27( X, Y, Z ) }.
% 0.95/1.56 { ! alpha30( X, Y, Z ), ! alpha32( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.95/1.56 { ! hBOOL( hAPP( Z, skol8( T, U, Z ) ) ), alpha30( X, Y, Z ) }.
% 0.95/1.56 { alpha32( X, Y, skol8( X, Y, Z ) ), alpha30( X, Y, Z ) }.
% 0.95/1.56 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 0.95/1.56 }.
% 0.95/1.56 { ! alpha32( X, Y, Z ), alpha34( X, Y, Z ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha34( X, Y, Z
% 0.95/1.56 ), alpha32( X, Y, Z ) }.
% 0.95/1.56 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! alpha34( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol9( X, Y, Z
% 0.95/1.56 ) ), Z ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha34( X,
% 0.95/1.56 Y, Z ) }.
% 0.95/1.56 { ! alpha25( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha28( X, Y, Z ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.95/1.56 tc_Int_Oint ), X ), alpha25( X, Y, Z ) }.
% 0.95/1.56 { ! alpha28( X, Y, Z ), alpha25( X, Y, Z ) }.
% 0.95/1.56 { ! alpha28( X, Y, Z ), ! alpha31( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.95/1.56 { ! hBOOL( hAPP( Z, skol10( T, U, Z ) ) ), alpha28( X, Y, Z ) }.
% 0.95/1.56 { alpha31( X, Y, skol10( X, Y, Z ) ), alpha28( X, Y, Z ) }.
% 0.95/1.56 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 0.95/1.56 { ! alpha31( X, Y, Z ), alpha33( X, Y, Z ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha33( X, Y, Z ),
% 0.95/1.56 alpha31( X, Y, Z ) }.
% 0.95/1.56 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 0.95/1.56 }.
% 0.95/1.56 { ! alpha33( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 0.95/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol11( X, Y,
% 0.95/1.56 Z ) ), Z ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! Y =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha33( X,
% 0.95/1.56 Y, Z ) }.
% 0.95/1.56 { ! alpha10( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.56 hBOOL( hAPP( Z, Y ) ) }.
% 0.95/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha10( X, Y, Z ) }.
% 0.95/1.56 { ! hBOOL( hAPP( Z, Y ) ), alpha10( X, Y, Z ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.95/1.56 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), !
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( tc_Int_Oint, c_Int_OBit1( X ) ), c_Int_Onumber__class_Onumber__of(
% 0.95/1.56 tc_Int_Oint, c_Int_OBit0( Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ) ),
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( tc_Int_Oint, c_Int_OBit1( X ) ), c_Int_Onumber__class_Onumber__of(
% 0.95/1.56 tc_Int_Oint, c_Int_OBit0( Y ) ) ) = c_Groups_Ominus__class_Ominus(
% 0.95/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ),
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ) ),
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 0.95/1.56 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.95/1.56 tc_Int_Oint ), c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0
% 0.95/1.56 ( c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ) = c_Groups_Ominus__class_Ominus
% 0.95/1.56 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.56 c_Int_OPls ) ) ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.95/1.56 tc_Int_Oint ) ), X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.95/1.56 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.95/1.56 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.95/1.56 Z ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.95/1.56 ( X, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.95/1.56 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 T ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.56 T ) ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.56 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.95/1.56 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.56 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.56 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol12( X, Y ) ) }.
% 0.95/1.56 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 0.95/1.56 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.56 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.95/1.56 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 0.95/1.56 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 0.95/1.56 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 0.95/1.56 , U ), Z ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.95/1.56 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.95/1.56 tc_Int_Oint, Z, X ), Y ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.95/1.56 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 0.95/1.56 tc_Int_Oint, Z, Y ), X ) }.
% 0.95/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 0.95/1.56 Y ) ), Y ) }.
% 0.95/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 0.95/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 0.95/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.95/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.56 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 0.95/1.56 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.56 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.95/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.95/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.95/1.56 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.95/1.56 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.95/1.56 ( X ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.95/1.56 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.95/1.56 , Z, Y ) }.
% 0.95/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.95/1.56 Z ) ), U ), T ) = Y }.
% 0.95/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.95/1.56 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), Z ), U ), Y ) }.
% 0.95/1.56 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.56 W ) ), U ), Y ) }.
% 0.95/1.56 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.56 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), Z ), U ), Y ) }.
% 0.95/1.56 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.95/1.56 Z ) ), Y ) ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.95/1.56 X, Y ) }.
% 0.95/1.56 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.95/1.56 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.95/1.56 X, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.95/1.56 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.95/1.56 , Y ) ) }.
% 0.95/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.95/1.56 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.95/1.56 X, Z, Y ) }.
% 0.95/1.56 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 0.95/1.56 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.95/1.56 ) }.
% 0.95/1.56 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 0.95/1.56 ( X ) ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.95/1.56 ) }.
% 0.95/1.56 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 0.95/1.56 ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls
% 0.95/1.56 , X ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.95/1.56 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.95/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.95/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.95/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.95/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.95/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.95/1.56 ) }.
% 0.95/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.95/1.56 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.95/1.56 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.95/1.56 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.95/1.56 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.56 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.95/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.95/1.56 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.95/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.95/1.56 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.95/1.56 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 0.95/1.56 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 0.95/1.56 ( X ) ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X )
% 0.95/1.56 ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.95/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.95/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.95/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.95/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.95/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.95/1.56 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.95/1.56 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.95/1.56 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.95/1.56 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.95/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.56 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.57 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.95/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.57 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.95/1.57 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.95/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.57 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.57 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.57 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.95/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.95/1.57 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.57 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.95/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.57 X, W, Z ) ), U ), T ), Y ) }.
% 0.95/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.57 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.57 ( X ), Z ), U ), Y ) ) }.
% 0.95/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.95/1.57 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( X, Z, W ) ), U ), Y ) ) }.
% 0.95/1.57 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.95/1.57 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.57 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.95/1.57 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.95/1.57 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.95/1.57 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.95/1.57 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.95/1.57 .
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.57 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.95/1.57 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.95/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.95/1.57 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Int_Oint, Z, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X )
% 0.95/1.57 ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin
% 0.95/1.57 , X ) ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin, c_Int_OBit0( X )
% 0.95/1.57 ) = c_Int_OBit1( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin
% 0.95/1.57 , X ) ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( X )
% 0.95/1.57 ) = c_Int_OBit0( c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Int_OMin
% 0.95/1.57 , X ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.95/1.57 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.95/1.57 .
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.95/1.57 ( tc_Int_Oint ) ) ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.95/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.95/1.57 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.57 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.57 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 0.95/1.57 ( tc_Int_Oint, Y, X ) ) }.
% 0.95/1.57 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.57 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.95/1.57 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 0.95/1.57 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 0.95/1.57 tc_Int_Oint, Y, X ), X ) }.
% 0.95/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.95/1.57 alpha11( X, Y, Z ) }.
% 0.95/1.57 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 0.95/1.57 alpha22( X, Y, Z ) }.
% 0.95/1.57 { ! alpha11( X, Y, Z ), ! alpha22( X, Y, Z ), hBOOL( hAPP( Z,
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 0.95/1.57 { ! alpha22( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.57 alpha26( X, Y, Z ) }.
% 0.95/1.57 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha22( X, Y, Z ) }.
% 0.95/1.57 { ! alpha26( X, Y, Z ), alpha22( X, Y, Z ) }.
% 0.95/1.57 { ! alpha26( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.95/1.57 ), alpha29( X, Y, Z, T ) }.
% 0.95/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol13( X, T, U ), X ),
% 0.95/1.57 alpha26( X, Y, Z ) }.
% 0.95/1.57 { ! alpha29( X, Y, Z, skol13( X, Y, Z ) ), alpha26( X, Y, Z ) }.
% 0.95/1.57 { ! alpha29( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.95/1.57 hBOOL( hAPP( Z, T ) ) }.
% 0.95/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol14( X, Y, T ) ), T
% 0.95/1.57 ), alpha29( X, Y, Z, T ) }.
% 0.95/1.57 { ! hBOOL( hAPP( Z, T ) ), alpha29( X, Y, Z, T ) }.
% 0.95/1.57 { ! alpha11( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.57 hBOOL( hAPP( Z, Y ) ) }.
% 0.95/1.57 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y, Z ) }.
% 0.95/1.57 { ! hBOOL( hAPP( Z, Y ) ), alpha11( X, Y, Z ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.95/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.95/1.57 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.57 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X )
% 0.95/1.57 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.57 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.95/1.57 X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T,
% 0.95/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ), Z ) }.
% 0.95/1.57 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.95/1.57 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.95/1.57 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.95/1.57 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.95/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( c_Nat_OSuc( X ) ),
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.57 c_Int_OPls ) ) ) ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.57 c_Int_OPls ) ) ) ) }.
% 0.95/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.57 c_Nat_OSuc( Y ) ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) )
% 0.95/1.57 = c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1(
% 0.95/1.57 c_Int_OBit1( c_Int_OPls ) ) ), Y ), c_Int_Onumber__class_Onumber__of(
% 0.95/1.57 tc_Nat_Onat, X ) ) }.
% 0.95/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.57 c_Nat_OSuc( Y ) ) ), X ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.95/1.57 c_Int_OPls ) ) ), Y ), X ) }.
% 0.95/1.57 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, c_Nat_OSuc( c_Nat_OSuc(
% 0.95/1.57 c_Nat_OSuc( X ) ) ) ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 0.95/1.57 c_Int_OPls ) ) ), X ) ) }.
% 0.95/1.57 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.57 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 0.95/1.57 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), c_Groups_Ouminus__class_Ouminus(
% 0.95/1.57 tc_Int_Oint, Y ) ) ) }.
% 0.95/1.57 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.95/1.57 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit1
% 0.95/1.57 ( c_Int_OPls ) ) ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.95/1.57 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), X ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.95/1.57 ( tc_Int_Oint ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.57 ( tc_Nat_Onat ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, X,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.57 c_Int_OPls ) ) ) ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, X,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.57 c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.57 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, X,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.57 c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.57 tc_Nat_Onat ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, X,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.57 c_Int_OPls ) ) ) ) ) }.
% 0.95/1.57 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.57 ( X ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ),
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.57 c_Int_OPls ) ) ) ) = c_Groups_Ominus__class_Ominus( X,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.57 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.95/1.57 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.95/1.57 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 0.95/1.57 c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.95/1.57 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) ), Y ) ) }.
% 0.95/1.57 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.95/1.57 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.95/1.57 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.95/1.57 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3mod( X, Y ) =
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 0.95/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), c_SMT_Oz3mod( X, Y ) =
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Int_Oint, X,
% 0.95/1.57 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.57 tc_Nat_Onat, X, Y ), Y ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 0.95/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.57 tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 0.95/1.57 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.57 tc_Nat_Onat, Y, X ), X ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.95/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.95/1.57 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, Z, X ), Y ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.95/1.57 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.95/1.57 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 0.95/1.57 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, Z, Y ), X ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, Z, X ), Y ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.57 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.57 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.95/1.57 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.57 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.57 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.57 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.95/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.57 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.95/1.57 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.95/1.57 ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.57 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.57 ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.95/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.95/1.57 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.95/1.57 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.95/1.57 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.57 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.95/1.57 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.95/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.95/1.57 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.95/1.57 ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.95/1.57 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.95/1.57 { c_Groups_Ominus__class_Ominus( tc_Code__Numeral_Ocode__numeral,
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ),
% 0.95/1.57 c_Groups_Oone__class_Oone( tc_Code__Numeral_Ocode__numeral ) ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.57 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.57 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.95/1.57 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.95/1.57 ) ) = X }.
% 0.95/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.95/1.57 , alpha12( X, Y, Z ) }.
% 0.95/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.95/1.57 , alpha23( X, Y, Z ) }.
% 0.95/1.57 { ! alpha12( X, Y, Z ), ! alpha23( X, Y, Z ), hBOOL( hAPP( Z,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.95/1.57 { ! alpha23( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.57 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.95/1.57 { ! hBOOL( hAPP( Z, skol15( T, U, Z ) ) ), alpha23( X, Y, Z ) }.
% 0.95/1.57 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol15( X, Y, Z ) ),
% 0.95/1.57 alpha23( X, Y, Z ) }.
% 0.95/1.57 { ! alpha12( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.95/1.57 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.95/1.57 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha12( X, Y, Z ) }
% 0.95/1.57 .
% 0.95/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12
% 0.95/1.57 ( X, Y, Z ) }.
% 0.95/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.95/1.57 , ! alpha13( X, Y, Z ) }.
% 0.95/1.57 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.95/1.57 , ! alpha24( X, Y, Z ) }.
% 0.95/1.57 { alpha13( X, Y, Z ), alpha24( X, Y, Z ), hBOOL( hAPP( Z,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.95/1.57 { ! alpha24( X, Y, Z ), ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ) }.
% 0.95/1.57 { ! alpha24( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.95/1.57 skol16( X, Y, Z ) ) }.
% 0.95/1.57 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.95/1.57 ) ), alpha24( X, Y, Z ) }.
% 0.95/1.57 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.95/1.57 }.
% 0.95/1.57 { ! alpha13( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.95/1.57 tc_Nat_Onat ) ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13( X, Y, Z ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.95/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.95/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.57 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.95/1.57 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.57 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.95/1.57 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.95/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.95/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.95/1.57 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.95/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.95/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.95/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.95/1.57 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.95/1.57 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.95/1.57 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.95/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.57 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.95/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.95/1.57 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.95/1.57 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.95/1.57 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.95/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.95/1.57 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.95/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.95/1.57 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.95/1.57 ( tc_Nat_Onat ) ) ) ) }.
% 0.95/1.57 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.95/1.57 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.95/1.57 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.95/1.57 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.95/1.57 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.95/1.57 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ), X ),
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 0.95/1.57 ) ) ) }.
% 0.95/1.57 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.95/1.57 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = c_Nat_OSuc(
% 0.95/1.57 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.95/1.57 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.95/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.57 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.95/1.57 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.95/1.57 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.95/1.57 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.95/1.57 ) ) }.
% 0.95/1.57 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.95/1.57 .
% 0.95/1.57 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.95/1.57 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.57 tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.95/1.57 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.95/1.57 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.95/1.57 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.95/1.57 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.95/1.57 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.95/1.57 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.95/1.57 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.95/1.57 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.95/1.57 { class_Power_Opower( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.95/1.57 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.95/1.57 { class_Int_Onumber( tc_Int_Oint ) }.
% 0.95/1.57 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.95/1.57 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.57 tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Int_Onumber( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.95/1.57 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.95/1.57 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.95/1.57 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.95/1.57 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.57 tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.95/1.57 .
% 0.95/1.57 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Int_Onumber__ring( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Int_Onumber( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.95/1.57 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.95/1.57 tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.95/1.57 { class_Groups_Oordered__cancel__ab__semigroup__add(
% 0.95/1.57 tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Groups_Oordered__ab__semigroup__add__imp__le(
% 0.95/1.57 tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Rings_Olinordered__comm__semiring__strict(
% 0.95/1.57 tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Rings_Olinordered__semiring__strict(
% 0.95/1.57 tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Groups_Oordered__ab__semigroup__add(
% 0.95/1.57 tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Groups_Oordered__comm__monoid__add( tc_Code__Numeral_Ocode__numeral
% 0.95/1.57 ) }.
% 0.95/1.57 { class_Groups_Ocancel__ab__semigroup__add( tc_Code__Numeral_Ocode__numeral
% 0.95/1.57 ) }.
% 0.95/1.57 { class_Rings_Oordered__cancel__semiring( tc_Code__Numeral_Ocode__numeral )
% 0.95/1.57 }.
% 0.95/1.57 { class_Rings_Oordered__comm__semiring( tc_Code__Numeral_Ocode__numeral ) }
% 0.95/1.57 .
% 0.95/1.57 { class_Groups_Ocancel__semigroup__add( tc_Code__Numeral_Ocode__numeral ) }
% 0.95/1.57 .
% 0.95/1.57 { class_Rings_Olinordered__semiring( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Rings_Olinordered__semidom( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Groups_Oab__semigroup__mult( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Groups_Ocomm__monoid__mult( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Groups_Oab__semigroup__add( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Rings_Oordered__semiring( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Rings_Ono__zero__divisors( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Groups_Ocomm__monoid__add( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Rings_Ocomm__semiring__1( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Divides_Osemiring__div( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Rings_Ocomm__semiring( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Rings_Ozero__neq__one( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Orderings_Opreorder( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Orderings_Olinorder( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Groups_Omonoid__mult( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Groups_Omonoid__add( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Rings_Osemiring__1( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Rings_Osemiring__0( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Rings_Omult__zero( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Orderings_Oorder( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Rings_Osemiring( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Orderings_Oord( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Power_Opower( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Groups_Ozero( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Int_Onumber( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { class_Groups_Oone( tc_Code__Numeral_Ocode__numeral ) }.
% 0.95/1.57 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.95/1.57 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( v_z ) ),
% 0.95/1.57 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 0.95/1.57 c_Int_OPls ) ) ) ) = v_z }.
% 0.95/1.57
% 0.95/1.57 *** allocated 15000 integers for clauses
% 0.95/1.57 *** allocated 22500 integers for clauses
% 0.95/1.57 *** allocated 33750 integers for clauses
% 0.95/1.57 *** allocated 50625 integers for clauses
% 0.95/1.57 *** allocated 75937 integers for clauses
% 0.95/1.57 percentage equality = 0.286302, percentage horn = 0.928431
% 0.95/1.57 This is a problem with some equality
% 0.95/1.57
% 0.95/1.57
% 0.95/1.57
% 0.95/1.57 Options Used:
% 0.95/1.57
% 0.95/1.57 useres = 1
% 0.95/1.57 useparamod = 1
% 0.95/1.57 useeqrefl = 1
% 0.95/1.57 useeqfact = 1
% 0.95/1.57 usefactor = 1
% 0.95/1.57 usesimpsplitting = 0
% 0.95/1.57 usesimpdemod = 5
% 0.95/1.57 usesimpres = 3
% 0.95/1.57
% 0.95/1.57 resimpinuse = 1000
% 0.95/1.57 resimpclauses = 20000
% 0.95/1.57 substype = eqrewr
% 0.95/1.57 backwardsubs = 1
% 0.95/1.57 selectoldest = 5
% 0.95/1.57
% 0.95/1.57 litorderings [0] = split
% 0.95/1.57 litorderings [1] = extend the termordering, first sorting on arguments
% 0.95/1.57
% 0.95/1.57 termordering = kbo
% 0.95/1.57
% 0.95/1.57 litapriori = 0
% 0.95/1.57 termapriori = 1
% 0.95/1.57 litaposteriori = 0
% 0.95/1.57 termaposteriori = 0
% 0.95/1.57 demodaposteriori = 0
% 0.95/1.57 ordereqreflfact = 0
% 0.95/1.57
% 0.95/1.57 litselect = negord
% 0.95/1.57
% 0.95/1.57 maxweight = 15
% 0.95/1.57 maxdepth = 30000
% 0.95/1.57 maxlength = 115
% 0.95/1.57 maxnrvars = 195
% 0.95/1.57 excuselevel = 1
% 0.95/1.57 increasemaxweight = 1
% 0.95/1.57
% 0.95/1.57 maxselected = 10000000
% 0.95/1.57 maxnrclauses = 10000000
% 0.95/1.57
% 0.95/1.57 showgenerated = 0
% 0.95/1.57 showkept = 0
% 0.95/1.57 showselected = 0
% 0.95/1.57 showdeleted = 0
% 0.95/1.57 showresimp = 1
% 0.95/1.57 showstatus = 2000
% 0.95/1.57
% 0.95/1.57 prologoutput = 0
% 0.95/1.57 nrgoals = 5000000
% 0.95/1.57 totalproof = 1
% 0.95/1.57
% 0.95/1.57 Symbols occurring in the translation:
% 0.95/1.57
% 0.95/1.57 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.95/1.57 . [1, 2] (w:1, o:169, a:1, s:1, b:0),
% 0.95/1.57 ! [4, 1] (w:0, o:96, a:1, s:1, b:0),
% 0.95/1.57 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.95/1.57 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.95/1.57 hAPP [38, 2] (w:1, o:193, a:1, s:1, b:0),
% 0.95/1.57 c_Int_OPls [39, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.95/1.57 c_Int_OBit0 [40, 1] (w:1, o:101, a:1, s:1, b:0),
% 0.95/1.57 c_Int_OBit1 [45, 1] (w:1, o:102, a:1, s:1, b:0),
% 0.95/1.57 class_Groups_Omonoid__mult [48, 1] (w:1, o:104, a:1, s:1, b:0),
% 0.95/1.57 class_Int_Onumber [49, 1] (w:1, o:105, a:1, s:1, b:0),
% 0.95/1.57 c_Power_Opower__class_Opower [50, 1] (w:1, o:106, a:1, s:1, b:0),
% 0.95/1.57 c_Int_Onumber__class_Onumber__of [51, 2] (w:1, o:194, a:1, s:1, b:0)
% 0.95/1.57 ,
% 0.95/1.57 tc_Nat_Onat [52, 0] (w:1, o:36, a:1, s:1, b:0),
% 0.95/1.57 c_Groups_Otimes__class_Otimes [53, 1] (w:1, o:108, a:1, s:1, b:0),
% 0.95/1.57 class_Rings_Osemiring__1 [55, 1] (w:1, o:114, a:1, s:1, b:0),
% 0.95/1.57 c_Groups_Ozero__class_Ozero [56, 1] (w:1, o:115, a:1, s:1, b:0),
% 0.95/1.57 class_Rings_Oring__1__no__zero__divisors [58, 1] (w:1, o:109, a:1, s:
% 0.95/1.57 1, b:0),
% 0.95/1.57 c_Groups_Oone__class_Oone [61, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.95/1.57 tc_Int_Oint [62, 0] (w:1, o:46, a:1, s:1, b:0),
% 0.95/1.57 class_Int_Onumber__ring [64, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.95/1.57 class_Int_Oring__char__0 [70, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.95/1.57 class_Rings_Ocomm__semiring__1 [72, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.95/1.57 tc_RealDef_Oreal [73, 0] (w:1, o:54, a:1, s:1, b:0),
% 0.95/1.57 class_Power_Opower [74, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.95/1.57 class_Rings_Osemiring__0 [75, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.95/1.57 class_Rings_Omult__zero [76, 1] (w:1, o:135, a:1, s:1, b:0),
% 0.95/1.57 class_Rings_Ono__zero__divisors [77, 1] (w:1, o:136, a:1, s:1, b:0),
% 0.95/1.57
% 0.95/1.57 class_Rings_Ozero__neq__one [78, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.95/1.57 c_Int_OMin [79, 0] (w:1, o:55, a:1, s:1, b:0),
% 0.95/1.57 class_Rings_Olinordered__idom [80, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq [81, 3] (w:1, o:214, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 c_Nat_OSuc [85, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.28/1.67 tc_Code__Numeral_Ocode__numeral [86, 0] (w:1, o:59, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Olinordered__semidom [94, 1] (w:1, o:129, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 class_Groups_Ocomm__monoid__mult [104, 1] (w:1, o:139, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 class_Rings_Oring__no__zero__divisors [111, 1] (w:1, o:110, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Rings_Olinordered__ring [114, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Olinordered__ring__strict [115, 1] (w:1, o:128, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Rings_Oordered__cancel__semiring [116, 1] (w:1, o:140, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Rings_Oordered__ring [117, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Oordered__semiring [119, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.28/1.67
% 1.28/1.67 class_Rings_Oordered__comm__semiring [120, 1] (w:1, o:143, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Orderings_Opreorder [122, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.28/1.67 c_Orderings_Oord__class_Oless [123, 3] (w:1, o:215, a:1, s:1, b:0),
% 1.28/1.67 c_Power_Opower_Opower [124, 3] (w:1, o:216, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Oring__1 [125, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.28/1.67 c_Groups_Ouminus__class_Ouminus [126, 2] (w:1, o:195, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 c_Code__Numeral_Ocode__numeral_Ocode__numeral__size [127, 1] (w:1, o:
% 1.28/1.67 144, a:1, s:1, b:0),
% 1.28/1.67 class_Orderings_Olinorder [128, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.28/1.67 class_Orderings_Oorder [129, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.28/1.67 class_Orderings_Oord [130, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Oidom [131, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Oring [132, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Ocomm__ring__1 [134, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Olinordered__comm__semiring__strict [135, 1] (w:1, o:130
% 1.28/1.67 , a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Olinordered__semiring__strict [136, 1] (w:1, o:131, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 class_Rings_Olinordered__semiring [140, 1] (w:1, o:132, a:1, s:1, b:0
% 1.28/1.67 ),
% 1.28/1.67 tc_fun [143, 2] (w:1, o:202, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Oordered__ab__group__add [145, 1] (w:1, o:146, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Groups_Olinordered__ab__group__add [146, 1] (w:1, o:103, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 hBOOL [150, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Ozero [151, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Oab__semigroup__mult [152, 1] (w:1, o:149, a:1, s:1, b:0
% 1.28/1.67 ),
% 1.28/1.67 class_Groups_Oone [153, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Ogroup__add [154, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.28/1.67 c_Groups_Oplus__class_Oplus [155, 3] (w:1, o:217, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Omonoid__add [156, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Ocomm__monoid__add [157, 1] (w:1, o:153, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 class_Groups_Oordered__ab__semigroup__add__imp__le [158, 1] (w:1, o:
% 1.28/1.67 154, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Oordered__cancel__ab__semigroup__add [159, 1] (w:1, o:
% 1.28/1.67 155, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Oab__group__add [160, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Oab__semigroup__add [161, 1] (w:1, o:157, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 class_Groups_Ocancel__semigroup__add [162, 1] (w:1, o:158, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Groups_Ocancel__ab__semigroup__add [163, 1] (w:1, o:159, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 class_Groups_Oordered__ab__semigroup__add [164, 1] (w:1, o:160, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.28/1.67 165, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Ocomm__semiring [166, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Osemiring [168, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Oordered__comm__monoid__add [171, 1] (w:1, o:165, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 class_Rings_Olinordered__semiring__1 [174, 1] (w:1, o:133, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Rings_Olinordered__semiring__1__strict [175, 1] (w:1, o:134, a:
% 1.28/1.67 1, s:1, b:0),
% 1.28/1.67 c_Int_Oiszero [179, 2] (w:1, o:203, a:1, s:1, b:0),
% 1.28/1.67 tc_Complex_Ocomplex [180, 0] (w:1, o:89, a:1, s:1, b:0),
% 24.39/24.76 c_Complex_Oii [181, 0] (w:1, o:90, a:1, s:1, b:0),
% 24.39/24.76 c_Divides_Odiv__class_Omod [182, 3] (w:1, o:218, a:1, s:1, b:0),
% 24.39/24.76 class_Divides_Oring__div [184, 1] (w:1, o:166, a:1, s:1, b:0),
% 24.39/24.76 class_Divides_Osemiring__div [185, 1] (w:1, o:167, a:1, s:1, b:0),
% 24.39/24.76 c_Groups_Ominus__class_Ominus [191, 3] (w:1, o:219, a:1, s:1, b:0),
% 24.39/24.76 class_RealVector_Oreal__normed__algebra [193, 1] (w:1, o:163, a:1, s:
% 24.39/24.76 1, b:0),
% 24.39/24.76 c_SMT_Oz3mod [194, 2] (w:1, o:204, a:1, s:1, b:0),
% 24.39/24.76 tc_HOL_Obool [201, 0] (w:1, o:45, a:1, s:1, b:0),
% 24.39/24.76 v_z [202, 0] (w:1, o:95, a:1, s:1, b:0),
% 24.39/24.76 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt [203, 1] (w:1, o:
% 24.39/24.76 107, a:1, s:1, b:0),
% 24.39/24.76 alpha1 [204, 2] (w:1, o:205, a:1, s:1, b:1),
% 24.39/24.76 alpha2 [205, 3] (w:1, o:226, a:1, s:1, b:1),
% 24.39/24.76 alpha3 [206, 3] (w:1, o:235, a:1, s:1, b:1),
% 24.39/24.76 alpha4 [207, 2] (w:1, o:207, a:1, s:1, b:1),
% 24.39/24.76 alpha5 [208, 4] (w:1, o:252, a:1, s:1, b:1),
% 24.39/24.76 alpha6 [209, 4] (w:1, o:253, a:1, s:1, b:1),
% 24.39/24.76 alpha7 [210, 2] (w:1, o:208, a:1, s:1, b:1),
% 24.39/24.76 alpha8 [211, 2] (w:1, o:209, a:1, s:1, b:1),
% 24.39/24.76 alpha9 [212, 2] (w:1, o:210, a:1, s:1, b:1),
% 24.39/24.76 alpha10 [213, 3] (w:1, o:220, a:1, s:1, b:1),
% 24.39/24.76 alpha11 [214, 3] (w:1, o:221, a:1, s:1, b:1),
% 24.39/24.76 alpha12 [215, 3] (w:1, o:222, a:1, s:1, b:1),
% 24.39/24.76 alpha13 [216, 3] (w:1, o:223, a:1, s:1, b:1),
% 24.39/24.76 alpha14 [217, 2] (w:1, o:211, a:1, s:1, b:1),
% 24.39/24.76 alpha15 [218, 3] (w:1, o:224, a:1, s:1, b:1),
% 24.39/24.76 alpha16 [219, 3] (w:1, o:225, a:1, s:1, b:1),
% 24.39/24.76 alpha17 [220, 4] (w:1, o:254, a:1, s:1, b:1),
% 24.39/24.76 alpha18 [221, 4] (w:1, o:255, a:1, s:1, b:1),
% 24.39/24.76 alpha19 [222, 2] (w:1, o:212, a:1, s:1, b:1),
% 24.39/24.76 alpha20 [223, 2] (w:1, o:213, a:1, s:1, b:1),
% 24.39/24.76 alpha21 [224, 3] (w:1, o:227, a:1, s:1, b:1),
% 24.39/24.76 alpha22 [225, 3] (w:1, o:228, a:1, s:1, b:1),
% 24.39/24.76 alpha23 [226, 3] (w:1, o:229, a:1, s:1, b:1),
% 24.39/24.76 alpha24 [227, 3] (w:1, o:230, a:1, s:1, b:1),
% 24.39/24.76 alpha25 [228, 3] (w:1, o:231, a:1, s:1, b:1),
% 24.39/24.76 alpha26 [229, 3] (w:1, o:232, a:1, s:1, b:1),
% 24.39/24.76 alpha27 [230, 3] (w:1, o:233, a:1, s:1, b:1),
% 24.39/24.76 alpha28 [231, 3] (w:1, o:234, a:1, s:1, b:1),
% 24.39/24.76 alpha29 [232, 4] (w:1, o:256, a:1, s:1, b:1),
% 24.39/24.76 alpha30 [233, 3] (w:1, o:236, a:1, s:1, b:1),
% 24.39/24.76 alpha31 [234, 3] (w:1, o:237, a:1, s:1, b:1),
% 24.39/24.76 alpha32 [235, 3] (w:1, o:238, a:1, s:1, b:1),
% 24.39/24.76 alpha33 [236, 3] (w:1, o:239, a:1, s:1, b:1),
% 24.39/24.76 alpha34 [237, 3] (w:1, o:240, a:1, s:1, b:1),
% 24.39/24.76 alpha35 [238, 3] (w:1, o:241, a:1, s:1, b:1),
% 24.39/24.76 alpha36 [239, 2] (w:1, o:206, a:1, s:1, b:1),
% 24.39/24.76 alpha37 [240, 3] (w:1, o:242, a:1, s:1, b:1),
% 24.39/24.76 skol1 [241, 2] (w:1, o:196, a:1, s:1, b:1),
% 24.39/24.76 skol2 [242, 1] (w:1, o:168, a:1, s:1, b:1),
% 24.39/24.76 skol3 [243, 2] (w:1, o:197, a:1, s:1, b:1),
% 24.39/24.76 skol4 [244, 3] (w:1, o:243, a:1, s:1, b:1),
% 24.39/24.76 skol5 [245, 2] (w:1, o:198, a:1, s:1, b:1),
% 24.39/24.76 skol6 [246, 2] (w:1, o:199, a:1, s:1, b:1),
% 24.39/24.76 skol7 [247, 2] (w:1, o:200, a:1, s:1, b:1),
% 24.39/24.76 skol8 [248, 3] (w:1, o:244, a:1, s:1, b:1),
% 24.39/24.76 skol9 [249, 3] (w:1, o:245, a:1, s:1, b:1),
% 24.39/24.76 skol10 [250, 3] (w:1, o:246, a:1, s:1, b:1),
% 24.39/24.76 skol11 [251, 3] (w:1, o:247, a:1, s:1, b:1),
% 24.39/24.76 skol12 [252, 2] (w:1, o:201, a:1, s:1, b:1),
% 24.39/24.76 skol13 [253, 3] (w:1, o:248, a:1, s:1, b:1),
% 24.39/24.76 skol14 [254, 3] (w:1, o:249, a:1, s:1, b:1),
% 24.39/24.76 skol15 [255, 3] (w:1, o:250, a:1, s:1, b:1),
% 24.39/24.76 skol16 [256, 3] (w:1, o:251, a:1, s:1, b:1).
% 24.39/24.76
% 24.39/24.76
% 24.39/24.76 Starting Search:
% 24.39/24.76
% 24.39/24.76 *** allocated 113905 integers for clauses
% 24.39/24.76 *** allocated 170857 integers for clauses
% 24.39/24.76 Resimplifying inuse:
% 24.39/24.76 Done
% 24.39/24.76
% 24.39/24.76
% 24.39/24.76 Intermediate Status:
% 24.39/24.76 Generated: 3121
% 24.39/24.76 Kept: 2002
% 24.39/24.76 Inuse: 109
% 24.39/24.76 Deleted: 9
% 24.39/24.76 Deletedinuse: 0
% 24.39/24.76
% 24.39/24.76 *** allocated 256285 integers for clauses
% 24.39/24.76 Resimplifying inuse:
% 24.39/24.76 Done
% 24.39/24.76
% 24.39/24.76 Resimplifying inuse:
% 24.39/24.76 Done
% 24.39/24.76
% 24.39/24.76 *** allocated 170857 integers for termspace/termends
% 24.39/24.76
% 24.39/24.76 Intermediate Status:
% 24.39/24.76 Generated: 8076
% 24.39/24.76 Kept: 4005
% 24.39/24.76 Inuse: 233
% 24.39/24.76 Deleted: 24
% 24.39/24.76 Deletedinuse: 1
% 24.39/24.76
% 24.39/24.76 *** allocated 384427 integers for clauses
% 24.39/24.76 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 13941
% 85.43/85.84 Kept: 6054
% 85.43/85.84 Inuse: 369
% 85.43/85.84 Deleted: 43
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 *** allocated 256285 integers for termspace/termends
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 *** allocated 576640 integers for clauses
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 19959
% 85.43/85.84 Kept: 8109
% 85.43/85.84 Inuse: 493
% 85.43/85.84 Deleted: 44
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 27004
% 85.43/85.84 Kept: 10443
% 85.43/85.84 Inuse: 658
% 85.43/85.84 Deleted: 49
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 *** allocated 384427 integers for termspace/termends
% 85.43/85.84 *** allocated 864960 integers for clauses
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 32913
% 85.43/85.84 Kept: 12444
% 85.43/85.84 Inuse: 703
% 85.43/85.84 Deleted: 49
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 40917
% 85.43/85.84 Kept: 14482
% 85.43/85.84 Inuse: 758
% 85.43/85.84 Deleted: 49
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 *** allocated 576640 integers for termspace/termends
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 48434
% 85.43/85.84 Kept: 16489
% 85.43/85.84 Inuse: 774
% 85.43/85.84 Deleted: 49
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 *** allocated 1297440 integers for clauses
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 55022
% 85.43/85.84 Kept: 18744
% 85.43/85.84 Inuse: 808
% 85.43/85.84 Deleted: 49
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 60988
% 85.43/85.84 Kept: 20945
% 85.43/85.84 Inuse: 833
% 85.43/85.84 Deleted: 49
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying clauses:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 72707
% 85.43/85.84 Kept: 22952
% 85.43/85.84 Inuse: 859
% 85.43/85.84 Deleted: 801
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 *** allocated 864960 integers for termspace/termends
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 87581
% 85.43/85.84 Kept: 25386
% 85.43/85.84 Inuse: 868
% 85.43/85.84 Deleted: 801
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 96828
% 85.43/85.84 Kept: 27434
% 85.43/85.84 Inuse: 913
% 85.43/85.84 Deleted: 801
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 *** allocated 1946160 integers for clauses
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 108858
% 85.43/85.84 Kept: 29854
% 85.43/85.84 Inuse: 938
% 85.43/85.84 Deleted: 801
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 120214
% 85.43/85.84 Kept: 31932
% 85.43/85.84 Inuse: 953
% 85.43/85.84 Deleted: 801
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 *** allocated 1297440 integers for termspace/termends
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 131058
% 85.43/85.84 Kept: 33950
% 85.43/85.84 Inuse: 973
% 85.43/85.84 Deleted: 801
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 147485
% 85.43/85.84 Kept: 36037
% 85.43/85.84 Inuse: 988
% 85.43/85.84 Deleted: 801
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 164360
% 85.43/85.84 Kept: 38045
% 85.43/85.84 Inuse: 999
% 85.43/85.84 Deleted: 801
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 177615
% 85.43/85.84 Kept: 41111
% 85.43/85.84 Inuse: 1028
% 85.43/85.84 Deleted: 801
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying clauses:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 183541
% 85.43/85.84 Kept: 43122
% 85.43/85.84 Inuse: 1053
% 85.43/85.84 Deleted: 1093
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 *** allocated 2919240 integers for clauses
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 188721
% 85.43/85.84 Kept: 45182
% 85.43/85.84 Inuse: 1113
% 85.43/85.84 Deleted: 1093
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 196464
% 85.43/85.84 Kept: 47366
% 85.43/85.84 Inuse: 1163
% 85.43/85.84 Deleted: 1093
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 *** allocated 1946160 integers for termspace/termends
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 209800
% 85.43/85.84 Kept: 49790
% 85.43/85.84 Inuse: 1193
% 85.43/85.84 Deleted: 1093
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 85.43/85.84 Generated: 220501
% 85.43/85.84 Kept: 52689
% 85.43/85.84 Inuse: 1248
% 85.43/85.84 Deleted: 1093
% 85.43/85.84 Deletedinuse: 1
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84 Resimplifying inuse:
% 85.43/85.84 Done
% 85.43/85.84
% 85.43/85.84
% 85.43/85.84 Intermediate Status:
% 233.77/234.32 Generated: 229578
% 233.77/234.32 Kept: 56835
% 233.77/234.32 Inuse: 1288
% 233.77/234.32 Deleted: 1093
% 233.77/234.32 Deletedinuse: 1
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 237087
% 233.77/234.32 Kept: 60233
% 233.77/234.32 Inuse: 1313
% 233.77/234.32 Deleted: 1093
% 233.77/234.32 Deletedinuse: 1
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 244867
% 233.77/234.32 Kept: 62278
% 233.77/234.32 Inuse: 1338
% 233.77/234.32 Deleted: 1093
% 233.77/234.32 Deletedinuse: 1
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying clauses:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 252651
% 233.77/234.32 Kept: 64345
% 233.77/234.32 Inuse: 1368
% 233.77/234.32 Deleted: 1294
% 233.77/234.32 Deletedinuse: 1
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 261130
% 233.77/234.32 Kept: 66360
% 233.77/234.32 Inuse: 1411
% 233.77/234.32 Deleted: 1294
% 233.77/234.32 Deletedinuse: 1
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 268551
% 233.77/234.32 Kept: 68360
% 233.77/234.32 Inuse: 1446
% 233.77/234.32 Deleted: 1294
% 233.77/234.32 Deletedinuse: 1
% 233.77/234.32
% 233.77/234.32 *** allocated 4378860 integers for clauses
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 288503
% 233.77/234.32 Kept: 71762
% 233.77/234.32 Inuse: 1448
% 233.77/234.32 Deleted: 1294
% 233.77/234.32 Deletedinuse: 1
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 *** allocated 2919240 integers for termspace/termends
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 298968
% 233.77/234.32 Kept: 73810
% 233.77/234.32 Inuse: 1478
% 233.77/234.32 Deleted: 1295
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 304733
% 233.77/234.32 Kept: 75892
% 233.77/234.32 Inuse: 1488
% 233.77/234.32 Deleted: 1295
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 320177
% 233.77/234.32 Kept: 81071
% 233.77/234.32 Inuse: 1528
% 233.77/234.32 Deleted: 1295
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying clauses:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 326203
% 233.77/234.32 Kept: 83083
% 233.77/234.32 Inuse: 1540
% 233.77/234.32 Deleted: 1433
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 340384
% 233.77/234.32 Kept: 87927
% 233.77/234.32 Inuse: 1573
% 233.77/234.32 Deleted: 1433
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 351973
% 233.77/234.32 Kept: 92251
% 233.77/234.32 Inuse: 1593
% 233.77/234.32 Deleted: 1433
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 362495
% 233.77/234.32 Kept: 96326
% 233.77/234.32 Inuse: 1608
% 233.77/234.32 Deleted: 1433
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 370355
% 233.77/234.32 Kept: 98461
% 233.77/234.32 Inuse: 1618
% 233.77/234.32 Deleted: 1433
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 380667
% 233.77/234.32 Kept: 100527
% 233.77/234.32 Inuse: 1638
% 233.77/234.32 Deleted: 1433
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 389382
% 233.77/234.32 Kept: 102745
% 233.77/234.32 Inuse: 1663
% 233.77/234.32 Deleted: 1433
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying clauses:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 395424
% 233.77/234.32 Kept: 104790
% 233.77/234.32 Inuse: 1683
% 233.77/234.32 Deleted: 1574
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 401268
% 233.77/234.32 Kept: 106837
% 233.77/234.32 Inuse: 1700
% 233.77/234.32 Deleted: 1574
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 *** allocated 6568290 integers for clauses
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 416549
% 233.77/234.32 Kept: 110256
% 233.77/234.32 Inuse: 1708
% 233.77/234.32 Deleted: 1574
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 *** allocated 4378860 integers for termspace/termends
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 424139
% 233.77/234.32 Kept: 112276
% 233.77/234.32 Inuse: 1730
% 233.77/234.32 Deleted: 1574
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 438548
% 233.77/234.32 Kept: 114443
% 233.77/234.32 Inuse: 1744
% 233.77/234.32 Deleted: 1574
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 444796
% 233.77/234.32 Kept: 116520
% 233.77/234.32 Inuse: 1768
% 233.77/234.32 Deleted: 1574
% 233.77/234.32 Deletedinuse: 2
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 Intermediate Status:
% 233.77/234.32 Generated: 455209
% 233.77/234.32 Kept: 118695
% 233.77/234.32 Inuse: 1778
% 233.77/234.32 Deleted: 1795
% 233.77/234.32 Deletedinuse: 223
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32 Resimplifying inuse:
% 233.77/234.32 Done
% 233.77/234.32
% 233.77/234.32
% 233.77/234.32 IntermeCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------