TSTP Solution File: SWW256+1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW256+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n032.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 23:21:37 EDT 2022
% Result : Timeout 300.01s 300.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : SWW256+1 : TPTP v8.1.0. Released v5.2.0.
% 0.08/0.10 % Command : bliksem %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % DateTime : Sat Jun 4 08:49:17 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.74/1.33 *** allocated 10000 integers for termspace/termends
% 0.74/1.33 *** allocated 10000 integers for clauses
% 0.74/1.33 *** allocated 10000 integers for justifications
% 0.74/1.33 *** allocated 15000 integers for termspace/termends
% 0.74/1.33 *** allocated 22500 integers for termspace/termends
% 0.74/1.33 *** allocated 33750 integers for termspace/termends
% 0.74/1.33 Bliksem 1.12
% 0.74/1.33
% 0.74/1.33
% 0.74/1.33 Automatic Strategy Selection
% 0.74/1.33
% 0.74/1.33 *** allocated 50625 integers for termspace/termends
% 0.74/1.33 *** allocated 75937 integers for termspace/termends
% 0.74/1.33 *** allocated 113905 integers for termspace/termends
% 0.74/1.33
% 0.74/1.33 Clauses:
% 0.74/1.33
% 0.74/1.33 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.74/1.33 { ! v_k____ = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { ! v_a____ = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.74/1.33 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.74/1.33 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.74/1.33 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.74/1.33 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.74/1.33 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.33 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.74/1.33 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.74/1.33 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.74/1.33 .
% 0.74/1.33 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.74/1.33 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.74/1.33 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.74/1.33 tc_Nat_Onat ) }.
% 0.74/1.33 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.74/1.33 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.74/1.33 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.74/1.33 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.74/1.33 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.74/1.33 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.33 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.33 ( tc_Nat_Onat, Z, Y ), X ) }.
% 0.74/1.33 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.33 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 0.74/1.33 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.74/1.33 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.74/1.33 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.74/1.33 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.74/1.33 .
% 0.74/1.33 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.74/1.33 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.74/1.33 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.74/1.33 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.74/1.33 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.74/1.33 .
% 0.74/1.33 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.74/1.33 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.74/1.33 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.74/1.33 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.74/1.33 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.74/1.33 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.74/1.33 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.74/1.33 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.74/1.33 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.74/1.33 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.74/1.33 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.33 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.33 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.74/1.33 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.74/1.33 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.33 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.33 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.74/1.33 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.74/1.33 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.33 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.74/1.33 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.74/1.33 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.33 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.74/1.33 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.74/1.33 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.74/1.33 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.74/1.33 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.74/1.33 { ! c_Nat_OSuc( X ) = X }.
% 0.74/1.33 { ! X = c_Nat_OSuc( X ) }.
% 0.74/1.33 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.33 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.74/1.33 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.74/1.33 ( X ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.74/1.33 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.74/1.33 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.74/1.33 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.74/1.33 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.74/1.33 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.74/1.33 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.74/1.33 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.33 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.74/1.33 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.33 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.74/1.33 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.33 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.74/1.33 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.33 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 0.74/1.33 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.33 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.74/1.33 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.74/1.33 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 0.74/1.33 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.74/1.33 ) }.
% 0.74/1.33 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.74/1.33 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 0.74/1.33 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 0.74/1.33 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.74/1.33 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.33 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.74/1.33 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.33 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.74/1.33 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.74/1.33 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.74/1.33 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.74/1.33 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.74/1.33 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.33 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.74/1.33 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 0.74/1.33 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 0.74/1.33 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 0.74/1.33 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.33 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.74/1.33 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.74/1.33 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.33 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.74/1.33 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.74/1.33 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.74/1.33 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.74/1.33 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.74/1.33 .
% 0.74/1.33 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 0.74/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.74/1.33 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.74/1.33 ( tc_Nat_Onat ) ) ) ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 0.74/1.33 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.74/1.33 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.74/1.33 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.74/1.33 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.74/1.33 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 0.74/1.33 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 0.74/1.33 hAPP( Z, Y ) ) }.
% 0.74/1.33 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.74/1.33 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.74/1.33 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.33 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.74/1.33 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 0.74/1.33 ) ) = X }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.74/1.33 X ) ) }.
% 0.74/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.74/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.74/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.33 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.74/1.33 .
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.74/1.33 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.33 c_Groups_Oone__class_Oone( X ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.74/1.33 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.74/1.33 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.74/1.33 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.74/1.33 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.74/1.33 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.33 ) }.
% 0.74/1.33 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.33 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.74/1.33 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.74/1.33 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.74/1.33 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.74/1.33 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.74/1.33 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.33 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.74/1.33 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.33 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.74/1.33 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 ) }.
% 0.74/1.33 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.74/1.33 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.74/1.33 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.74/1.33 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.33 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.74/1.33 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.33 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.33 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.74/1.33 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.74/1.33 ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.74/1.33 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.74/1.33 .
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.74/1.33 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.74/1.33 .
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.74/1.33 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.74/1.33 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.74/1.33 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.33 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.74/1.33 ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.33 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.74/1.33 ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 Y, Z ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 Z, Y ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.74/1.33 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.33 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.74/1.33 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.74/1.33 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.33 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.74/1.33 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.74/1.33 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.74/1.33 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.74/1.33 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.74/1.33 ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.74/1.33 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.74/1.33 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.74/1.33 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.74/1.33 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.74/1.33 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.74/1.33 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.74/1.33 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.74/1.33 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.74/1.33 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.74/1.33 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.74/1.33 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, Z, Y ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, Z, Y ) }.
% 0.74/1.33 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 Y, T ), Z = Y }.
% 0.74/1.33 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 T, Y ), Z = Y }.
% 0.74/1.33 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 T, Y ), Z = Y }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.74/1.33 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.74/1.33 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.74/1.33 , Y, T ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.74/1.33 , T ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.74/1.33 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.74/1.33 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.74/1.33 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.74/1.33 , T, Y ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.74/1.33 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.74/1.33 , Y, T ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.74/1.33 X, Y, Z ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.74/1.33 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.74/1.33 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.74/1.33 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.74/1.33 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, Z, Y ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.74/1.33 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.74/1.33 , T, Y ) ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, T, Y ) }.
% 0.74/1.33 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.74/1.33 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.74/1.33 , Y, Z ) ) }.
% 0.74/1.33 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 Y, Z ), T = Y }.
% 0.74/1.33 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 Y, Z ) }.
% 0.74/1.33 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 T, Y ), Z = Y }.
% 0.74/1.33 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 T, Y ) }.
% 0.74/1.33 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.74/1.33 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.74/1.33 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.74/1.33 c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.33 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.74/1.33 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.74/1.33 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.74/1.33 ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.74/1.33 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.74/1.33 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.74/1.33 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.74/1.33 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.74/1.33 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.74/1.33 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.74/1.33 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.74/1.33 { alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.74/1.33 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.74/1.33 { alpha38( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.74/1.33 ( X, Y ), Z ) ) }.
% 0.74/1.33 { ! alpha38( X, Y, Z ), alpha40( X, Y, Z ), Z = Y }.
% 0.74/1.33 { ! alpha38( X, Y, Z ), alpha40( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.74/1.33 ) ) }.
% 0.74/1.33 { ! alpha40( X, Y, Z ), alpha38( X, Y, Z ) }.
% 0.74/1.33 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha38( X, Y, Z ) }.
% 0.74/1.33 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.74/1.33 }.
% 0.74/1.33 { ! alpha40( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.74/1.33 X, Y ), Z ) ), alpha40( X, Y, Z ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.74/1.33 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.74/1.33 , X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.74/1.33 .
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.74/1.33 .
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.74/1.33 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.74/1.33 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.74/1.33 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.74/1.33 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.74/1.33 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.74/1.33 .
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.74/1.33 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.74/1.33 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.74/1.33 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.74/1.33 ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.74/1.33 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.74/1.33 ) ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.74/1.33 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.74/1.33 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.74/1.33 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.74/1.33 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol2( X, Y ) ) }.
% 0.74/1.33 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.74/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.74/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.74/1.33 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.74/1.33 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.74/1.33 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.33 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.33 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.33 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, Y, X ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.33 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, Y, X ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.74/1.33 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.74/1.33 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.74/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.74/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol3( X, Y ) ) ) }.
% 0.74/1.33 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.74/1.33 .
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.33 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.74/1.33 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.74/1.33 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, Z, X ), Y ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.74/1.33 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.74/1.33 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.74/1.33 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, Z, Y ), X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, X, Z ), Y ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, Z, X ), Y ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.74/1.33 tc_Nat_Onat, X, Y ), Y ) = X }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.74/1.33 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.33 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 0.74/1.33 ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.33 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.74/1.33 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.33 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.74/1.33 ) }.
% 0.74/1.33 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.74/1.33 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.74/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.74/1.33 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.74/1.33 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.33 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.74/1.33 ), Y ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.74/1.33 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.74/1.33 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.74/1.33 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.74/1.33 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.74/1.33 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.74/1.33 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.74/1.33 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.74/1.33 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 0.74/1.33 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 0.74/1.33 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 0.74/1.33 .
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.33 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.74/1.33 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.33 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.74/1.33 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 0.74/1.33 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.33 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 0.74/1.33 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 0.74/1.33 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.33 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 0.74/1.33 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.33 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.74/1.33 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.74/1.33 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.33 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.33 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.74/1.33 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.74/1.33 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.74/1.33 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.74/1.33 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 }.
% 0.74/1.33 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.33 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 }.
% 0.74/1.33 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.33 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.74/1.33 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.74/1.33 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.74/1.33 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.33 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.74/1.34 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.74/1.34 X, W, Z ) ), U ), T ), Y ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), Z ), U ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( X, Z, W ) ), U ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 0.74/1.34 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.74/1.34 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.74/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.74/1.34 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.74/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.74/1.34 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.74/1.34 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.74/1.34 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.74/1.34 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.74/1.34 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.74/1.34 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.74/1.34 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.74/1.34 , alpha1( X, Y, Z ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.74/1.34 , alpha14( X, Y, Z ) }.
% 0.74/1.34 { ! alpha1( X, Y, Z ), ! alpha14( X, Y, Z ), hBOOL( hAPP( Z,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.74/1.34 { ! alpha14( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.74/1.34 T ), hBOOL( hAPP( Z, T ) ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, skol4( T, U, Z ) ) ), alpha14( X, Y, Z ) }.
% 0.74/1.34 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol4( X, Y, Z ) ),
% 0.74/1.34 alpha14( X, Y, Z ) }.
% 0.74/1.34 { ! alpha1( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.74/1.34 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha1( X, Y, Z ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha1
% 0.74/1.34 ( X, Y, Z ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.74/1.34 , ! alpha2( X, Y, Z ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 0.74/1.34 , ! alpha15( X, Y, Z ) }.
% 0.74/1.34 { alpha2( X, Y, Z ), alpha15( X, Y, Z ), hBOOL( hAPP( Z,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.74/1.34 { ! alpha15( X, Y, Z ), ! hBOOL( hAPP( Z, skol5( T, U, Z ) ) ) }.
% 0.74/1.34 { ! alpha15( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.74/1.34 skol5( X, Y, Z ) ) }.
% 0.74/1.34 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 0.74/1.34 ) ), alpha15( X, Y, Z ) }.
% 0.74/1.34 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 0.74/1.34 .
% 0.74/1.34 { ! alpha2( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ) ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha2( X, Y, Z ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.74/1.34 ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.74/1.34 ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.74/1.34 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.74/1.34 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.74/1.34 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.74/1.34 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.74/1.34 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.74/1.34 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.74/1.34 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.74/1.34 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.74/1.34 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.74/1.34 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.74/1.34 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.74/1.34 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.74/1.34 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.74/1.34 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.74/1.34 ), U = Z, T = Y }.
% 0.74/1.34 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.74/1.34 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.74/1.34 ) }.
% 0.74/1.34 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.74/1.34 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.74/1.34 ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.74/1.34 ) ), Z ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.74/1.34 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.34 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.74/1.34 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.74/1.34 ) }.
% 0.74/1.34 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.74/1.34 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.74/1.34 ), ! U = T }.
% 0.74/1.34 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.74/1.34 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.74/1.34 ), ! Z = Y }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.34 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.74/1.34 ) ), T ), Y ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.74/1.34 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.74/1.34 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.74/1.34 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.34 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.34 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.34 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 0.74/1.34 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 0.74/1.34 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.34 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.74/1.34 = Y }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.74/1.34 = Y }.
% 0.74/1.34 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.74/1.34 = Y }.
% 0.74/1.34 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.74/1.34 = Y }.
% 0.74/1.34 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.74/1.34 = Y }.
% 0.74/1.34 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.74/1.34 = Y }.
% 0.74/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 0.74/1.34 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ) ) = X }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), X ) = X }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.74/1.34 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.74/1.34 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.74/1.34 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.74/1.34 = c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.74/1.34 .
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.74/1.34 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.74/1.34 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.74/1.34 .
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.74/1.34 .
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.74/1.34 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.74/1.34 X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.74/1.34 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.74/1.34 }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.74/1.34 ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.74/1.34 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.74/1.34 }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.74/1.34 c_Nat_OSuc( X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.74/1.34 ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.74/1.34 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.74/1.34 , c_Nat_OSuc( X ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.74/1.34 .
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.74/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 0.74/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.74/1.34 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.74/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Nat_Onat, Y, X ), Y ) = X }.
% 0.74/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Nat_Onat, Y, X ), X ) = Y }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Nat_Onat ) ) = Y }.
% 0.74/1.34 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Nat_Onat ) ) = Y }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.74/1.34 ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( tc_Nat_Onat, Y, Z ), X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 0.74/1.34 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 0.74/1.34 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Nat_Onat ) }.
% 0.74/1.34 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Nat_Onat ) }.
% 0.74/1.34 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.74/1.34 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.74/1.34 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.74/1.34 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.74/1.34 , Y ), X ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.74/1.34 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.74/1.34 Z ) ), Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.74/1.34 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.74/1.34 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.74/1.34 tc_Nat_Onat ), X ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.74/1.34 c_Groups_Oone__class_Oone( X ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.74/1.34 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 0.74/1.34 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.74/1.34 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.74/1.34 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 0.74/1.34 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.74/1.34 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 0.74/1.34 ( tc_Nat_Onat ) ) ), X ) ) }.
% 0.74/1.34 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 0.74/1.34 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 0.74/1.34 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 0.74/1.34 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 0.74/1.34 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.74/1.34 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.74/1.34 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.74/1.34 ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.74/1.34 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.74/1.34 ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.74/1.34 Z ) ), U ), T ) = Y }.
% 0.74/1.34 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 0.74/1.34 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), Z ), U ), Y ) }.
% 0.74/1.34 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.74/1.34 W ) ), U ), Y ) }.
% 0.74/1.34 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.74/1.34 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), Z ), U ), Y ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 0.74/1.34 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 0.74/1.34 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.74/1.34 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.74/1.34 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( X ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.74/1.34 .
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.74/1.34 .
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.74/1.34 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( X ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.74/1.34 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( X ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.74/1.34 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha3( X, Y, Z, T ),
% 0.74/1.34 alpha16( X, Y, Z, T ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z, T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.34 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.34 { ! alpha16( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.74/1.34 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha16( X, Y, Z, T ) }.
% 0.74/1.34 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.74/1.34 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.74/1.34 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha3( X, Y, Z, T ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha4( X, Y, Z, T ),
% 0.74/1.34 alpha17( X, Y, Z, T ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z, T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.34 { ! alpha17( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.74/1.34 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha17( X, Y, Z, T ) }.
% 0.74/1.34 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.74/1.34 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.74/1.34 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha4( X, Y, Z, T ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.74/1.34 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.74/1.34 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( X ) ) }.
% 0.74/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.74/1.34 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.74/1.34 , Z, Y ) }.
% 0.74/1.34 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( X ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.34 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.74/1.34 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.74/1.34 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__semiring( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__semiring( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.74/1.34 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__semiring( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.74/1.34 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__semiring( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.74/1.34 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.74/1.34 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( X ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.34 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( X ) ), alpha5( X, Y, Z ), alpha18( X, Y, Z ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( X ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( X ) ) }.
% 0.74/1.34 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.34 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.74/1.34 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( X ), Y ), alpha18( X, Y, Z ) }.
% 0.74/1.34 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.74/1.34 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ), alpha5( X, Y, Z ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha6( X, Y
% 0.74/1.34 , Z ), alpha19( X, Y, Z ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.34 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.34 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.74/1.34 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ), alpha19( X, Y, Z ) }.
% 0.74/1.34 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.74/1.34 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Y ), alpha6( X, Y, Z ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.74/1.34 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.74/1.34 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.74/1.34 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.34 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 0.74/1.34 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.74/1.34 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.34 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.74/1.34 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Nat_Onat, Z, Y ) ) }.
% 0.74/1.34 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.74/1.34 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.74/1.34 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha7( X, Y ), alpha20( X
% 0.74/1.34 , Y ) }.
% 0.74/1.34 { ! alpha7( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.74/1.34 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.34 { ! alpha20( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.74/1.34 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.34 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! alpha20( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ) ) }.
% 0.74/1.34 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 0.74/1.34 { ! alpha7( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ) ) }.
% 0.74/1.34 { ! alpha7( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha7( X, Y ) }.
% 0.74/1.34 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha8( X, Y ), alpha21
% 0.74/1.34 ( X, Y ) }.
% 0.74/1.34 { ! alpha8( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.74/1.34 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! alpha21( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.74/1.34 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ) ) }.
% 0.74/1.34 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 0.74/1.34 { ! alpha8( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ) ) }.
% 0.74/1.34 { ! alpha8( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.34 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.74/1.34 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 0.74/1.34 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.74/1.34 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.74/1.34 c_Nat_OSuc( X ) ) }.
% 0.74/1.34 { ! alpha9( X, Y ), Y = c_Nat_OSuc( skol6( Z, Y ) ) }.
% 0.74/1.34 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol6( X, Y
% 0.74/1.34 ), X ) }.
% 0.74/1.34 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.74/1.34 ), alpha9( X, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol7( X ) ) }.
% 0.74/1.34 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.74/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.74/1.34 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.74/1.34 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.74/1.34 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.74/1.34 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.74/1.34 Y ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), Z ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.74/1.34 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.74/1.34 ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.74/1.34 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.74/1.34 ), X ) ) }.
% 0.74/1.34 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 0.74/1.34 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 0.74/1.34 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.74/1.34 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.74/1.34 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.74/1.34 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.74/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.74/1.34 ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.74/1.34 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.74/1.34 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 X ), Y ), Z = Y }.
% 0.74/1.34 { ! class_Rings_Olinordered__semidom( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.34 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.34 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.74/1.34 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.34 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.74/1.34 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 0.74/1.34 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 0.74/1.34 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.34 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.74/1.34 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 0.74/1.34 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.74/1.34 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.74/1.34 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 0.74/1.34 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.74/1.34 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), Y ) }.
% 0.74/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.74/1.34 ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.74/1.34 , Y ) }.
% 0.74/1.34 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.74/1.34 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.74/1.34 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 0.74/1.34 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.74/1.34 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.74/1.34 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.74/1.34 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.74/1.34 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.74/1.34 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.74/1.34 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.74/1.34 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.74/1.34 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.74/1.34 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.74/1.34 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.74/1.34 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.74/1.34 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.74/1.34 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.74/1.34 ) ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.74/1.34 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.74/1.34 hAPP( Y, U ) ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.74/1.34 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.74/1.34 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.74/1.34 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.74/1.34 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.74/1.34 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.74/1.34 hAPP( Y, U ) ) }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.74/1.34 ( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.74/1.34 ( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.74/1.34 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.74/1.34 hAPP( Y, U ) ) }.
% 0.74/1.34 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.74/1.34 ( Z, skol8( X, Y, Z ) ), hAPP( Y, skol8( X, Y, Z ) ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.74/1.34 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.74/1.34 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.74/1.34 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.74/1.34 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.74/1.34 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.74/1.34 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.74/1.34 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.74/1.34 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.74/1.34 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.74/1.34 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.74/1.34 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.74/1.34 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.74/1.34 , ! Y = Z }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.74/1.34 , ! Z = Y }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.74/1.34 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.74/1.34 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.74/1.34 , ! Z = Y }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.74/1.34 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.74/1.34 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.74/1.34 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.74/1.34 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.74/1.34 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.74/1.34 Y ), ! Z = Y }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.74/1.34 Z ), ! Z = Y }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.74/1.34 Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.74/1.34 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.74/1.34 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.74/1.34 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.74/1.34 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.74/1.34 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.74/1.34 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.74/1.34 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.74/1.34 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.74/1.34 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.74/1.34 ( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.74/1.34 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.74/1.34 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.74/1.34 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.74/1.34 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.74/1.34 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.74/1.34 , ! Z = Y }.
% 0.74/1.34 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.74/1.34 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.74/1.34 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol9( X, Y ) ) }.
% 0.74/1.34 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex
% 0.74/1.34 , v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.74/1.34 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.74/1.34 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol10( Z, Y
% 0.74/1.34 ), Y ) }.
% 0.74/1.34 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.74/1.34 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.74/1.34 skol10( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.74/1.34 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.74/1.34 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.74/1.34 , skol10( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) = c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Nat_Onat, v_k____, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.74/1.34 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.74/1.34 v_pa____ ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.74/1.34 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 0.74/1.34 .
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 0.74/1.34 ( tc_Int_Oint ) ) ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.74/1.34 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.74/1.34 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.74/1.34 .
% 0.74/1.34 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.74/1.34 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.74/1.34 }.
% 0.74/1.34 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.74/1.34 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.74/1.34 }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Int_Oint ) ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.74/1.34 = X }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Int_Oint ) ) ) }.
% 0.74/1.34 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Int_Oint ) ) ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.74/1.34 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.74/1.34 }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Int_Oint ) ), X ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Int_Oint ) ), X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.74/1.34 .
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.74/1.34 .
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.74/1.34 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ) ) = X }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), X ) = X }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.74/1.34 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.74/1.34 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.74/1.34 ( tc_Int_Oint ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.74/1.34 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.74/1.34 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.74/1.34 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.74/1.34 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 0.74/1.34 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Int_Oint, Z, Y ) ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 0.74/1.34 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X, Z
% 0.74/1.34 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 0.74/1.34 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 0.74/1.34 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 0.74/1.34 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 0.74/1.34 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 0.74/1.34 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 0.74/1.34 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.74/1.34 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.74/1.34 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 0.74/1.34 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 0.74/1.34 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 0.74/1.34 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.74/1.34 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.34 T ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.34 T ) ), Y ) ) }.
% 0.74/1.34 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.74/1.34 ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), T ), c_Int_Onumber__class_Onumber__of( X, Y ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.74/1.34 ( X, Y ) ) ) }.
% 0.74/1.34 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 0.74/1.34 Z ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 0.74/1.34 ( X, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 0.74/1.34 { ! class_Int_Onumber( X ), ! class_Rings_Oring( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.34 T ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.34 T ) ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.74/1.34 X, c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.34 Z ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), Z ) ) ), Y ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.34 ( X ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) }.
% 0.74/1.34 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 0.74/1.34 { ! class_Groups_Ozero( X ), !
% 0.74/1.34 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.34 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Polynomial_Opoly( X ) ),
% 0.74/1.34 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.74/1.34 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.74/1.34 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.74/1.34 .
% 0.74/1.34 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.74/1.34 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.74/1.34 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), ! c_Int_Onumber__class_Onumber__of(
% 0.74/1.34 tc_Nat_Onat, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.74/1.34 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.74/1.34 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 0.74/1.34 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.74/1.34 , Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.74/1.34 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.74/1.34 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.74/1.34 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 0.74/1.34 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.34 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.74/1.34 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.74/1.34 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.74/1.34 ( tc_Int_Oint ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.74/1.34 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.74/1.34 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.74/1.34 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.74/1.34 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.74/1.34 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.74/1.34 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.74/1.34 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.74/1.34 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.74/1.34 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.74/1.34 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Int_Oint, X, Y ) ) }.
% 0.74/1.34 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Int_Oint ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.74/1.34 tc_Int_Oint, X, Y ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 0.74/1.34 ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.74/1.34 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.74/1.34 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.74/1.34 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.74/1.34 tc_Complex_Ocomplex, v_p ) ) }.
% 0.74/1.34 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.74/1.34 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.74/1.34 tc_Complex_Ocomplex, v_pa____ ) ) }.
% 0.74/1.34 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.74/1.34 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.74/1.34 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.74/1.34 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.74/1.34 tc_Complex_Ocomplex, v_q____ ) ) }.
% 0.74/1.34 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.74/1.34 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.74/1.34 tc_Complex_Ocomplex, v_q____ ) ) }.
% 0.74/1.34 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.74/1.34 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, X, Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 0.74/1.34 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.74/1.34 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.74/1.34 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 0.74/1.34 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 0.74/1.34 }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.74/1.34 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 0.74/1.34 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, Y, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.74/1.34 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, X, Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.74/1.34 , Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 0.74/1.34 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, Y, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, Y, X ) ) }.
% 0.74/1.34 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha10( X, Y ) }.
% 0.74/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.74/1.34 { ! alpha10( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.74/1.34 { ! alpha10( X, Y ), alpha22( X, Y ), alpha26( X, Y ) }.
% 0.74/1.34 { ! alpha22( X, Y ), alpha10( X, Y ) }.
% 0.74/1.34 { ! alpha26( X, Y ), alpha10( X, Y ) }.
% 0.74/1.34 { ! alpha26( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { ! alpha26( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha26( X, Y ) }.
% 0.74/1.34 { ! alpha22( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.74/1.34 { ! alpha22( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha22( X, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, X, Y ), X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, Z, Y ), X ) }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.74/1.34 ) }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 0.74/1.34 ) }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 0.74/1.34 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.74/1.34 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.74/1.34 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.34 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 0.74/1.34 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 0.74/1.34 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 0.74/1.34 ) }.
% 0.74/1.34 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha39( X,
% 0.74/1.34 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, T, Z ) = Y }.
% 0.74/1.34 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha39( X,
% 0.74/1.34 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Int_Oint, T, Z ) = Y }.
% 0.74/1.34 { ! alpha39( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.74/1.34 { ! alpha39( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha39( X, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 0.74/1.34 , alpha39( X, Y ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.74/1.34 alpha11( X, Z ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 0.74/1.34 alpha23( X, Y, Z ) }.
% 0.74/1.34 { ! alpha11( X, Z ), ! alpha23( X, Y, Z ), hBOOL( hAPP( Z,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 0.74/1.34 { ! alpha23( X, Y, Z ), alpha27( X, Y, Z ) }.
% 0.74/1.34 { ! alpha23( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.74/1.34 { ! alpha27( X, Y, Z ), ! alpha30( X, Y, Z ), alpha23( X, Y, Z ) }.
% 0.74/1.34 { ! alpha30( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha33( X, Y, Z ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha30( X, Y, Z ) }.
% 0.74/1.34 { ! alpha33( X, Y, Z ), alpha30( X, Y, Z ) }.
% 0.74/1.34 { ! alpha33( X, Y, Z ), ! alpha35( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, skol11( T, U, Z ) ) ), alpha33( X, Y, Z ) }.
% 0.74/1.34 { alpha35( X, Y, skol11( X, Y, Z ) ), alpha33( X, Y, Z ) }.
% 0.74/1.34 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.74/1.34 skol12( X, T, U ) ) }.
% 0.74/1.34 { ! alpha35( X, Y, Z ), alpha37( X, Y, Z, skol12( X, Y, Z ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha37( X, Y, Z
% 0.74/1.34 , T ), alpha35( X, Y, Z ) }.
% 0.74/1.34 { ! alpha37( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.74/1.34 { ! alpha37( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.74/1.34 .
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha37( X,
% 0.74/1.34 Y, Z, T ) }.
% 0.74/1.34 { ! alpha27( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha31( X, Y, Z ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Int_Oint ), X ), alpha27( X, Y, Z ) }.
% 0.74/1.34 { ! alpha31( X, Y, Z ), alpha27( X, Y, Z ) }.
% 0.74/1.34 { ! alpha31( X, Y, Z ), ! alpha34( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, skol13( T, U, Z ) ) ), alpha31( X, Y, Z ) }.
% 0.74/1.34 { alpha34( X, Y, skol13( X, Y, Z ) ), alpha31( X, Y, Z ) }.
% 0.74/1.34 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol14( T, U, W ) ) }.
% 0.74/1.34 { ! alpha34( X, Y, Z ), alpha36( X, Y, Z, skol14( X, Y, Z ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha36( X, Y, Z, T )
% 0.74/1.34 , alpha34( X, Y, Z ) }.
% 0.74/1.34 { ! alpha36( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 0.74/1.34 ) }.
% 0.74/1.34 { ! alpha36( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 0.74/1.34 .
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha36( X,
% 0.74/1.34 Y, Z, T ) }.
% 0.74/1.34 { ! alpha11( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 0.74/1.34 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 0.74/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha11( X, Y ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha11
% 0.74/1.34 ( X, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.74/1.34 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 0.74/1.34 tc_Int_Oint, X, Y ) }.
% 0.74/1.34 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.74/1.34 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 0.74/1.34 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Nat_Onat, Z, Y ), X ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_RealDef_Oreal ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 0.74/1.34 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.74/1.34 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 0.74/1.34 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.74/1.34 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.74/1.34 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.74/1.34 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.74/1.34 ( X, Y ) ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 0.74/1.34 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 0.74/1.34 ( X, Y ) ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.74/1.34 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ), !
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 0.74/1.34 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.74/1.34 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.74/1.34 X, T ) = hAPP( X, U ) }.
% 0.74/1.34 { ! hAPP( X, skol15( X ) ) = hAPP( X, skol31( X ) ),
% 0.74/1.34 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 0.74/1.34 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( X, Y, Z ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.74/1.34 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.74/1.34 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 0.74/1.34 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 0.74/1.34 ( X, T, Y ) ) ) ) }.
% 0.74/1.34 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.74/1.34 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Nat_Onat, Y, X ), Y ) }.
% 0.74/1.34 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.74/1.34 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.34 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.74/1.34 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.74/1.34 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.74/1.34 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.74/1.34 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.74/1.34 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.74/1.34 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.74/1.34 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.74/1.34 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 0.74/1.34 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.74/1.34 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.74/1.34 alpha12( X, Z ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.74/1.34 alpha24( X, Y, Z ) }.
% 0.74/1.34 { ! alpha12( X, Z ), ! alpha24( X, Y, Z ), hBOOL( hAPP( Z,
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 0.74/1.34 { ! alpha24( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 alpha28( X, Y, Z ) }.
% 0.74/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha24( X, Y, Z ) }.
% 0.74/1.34 { ! alpha28( X, Y, Z ), alpha24( X, Y, Z ) }.
% 0.74/1.34 { ! alpha28( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 0.74/1.34 ), alpha32( X, Y, Z, T ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol16( X, T, U ), X ),
% 0.74/1.34 alpha28( X, Y, Z ) }.
% 0.74/1.34 { ! alpha32( X, Y, Z, skol16( X, Y, Z ) ), alpha28( X, Y, Z ) }.
% 0.74/1.34 { ! alpha32( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 0.74/1.34 hBOOL( hAPP( Z, U ) ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, skol17( U, W, Z, V0 ) ) ), alpha32( X, Y, Z, T ) }.
% 0.74/1.34 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol17( X, Y, Z, T ) )
% 0.74/1.34 , T ), alpha32( X, Y, Z, T ) }.
% 0.74/1.34 { ! alpha12( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.74/1.34 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.74/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha12( X, Y ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha12
% 0.74/1.34 ( X, Y ) }.
% 0.74/1.34 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 0.74/1.34 alpha13( X, Z ), alpha25( X, Y, Z ) }.
% 0.74/1.34 { ! alpha13( X, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Nat_Onat, Y, X ) ) ) }.
% 0.74/1.34 { ! alpha25( X, Y, Z ), hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Nat_Onat, Y, X ) ) ) }.
% 0.74/1.34 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol18( X
% 0.74/1.34 , Y, T ) ), Y ) }.
% 0.74/1.34 { ! alpha25( X, Y, Z ), alpha29( X, Y, Z, skol18( X, Y, Z ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), T ), Y ), ! alpha29( X
% 0.74/1.34 , Y, Z, T ), alpha25( X, Y, Z ) }.
% 0.74/1.34 { ! alpha29( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc
% 0.74/1.34 ( T ) ) ) }.
% 0.74/1.34 { ! alpha29( X, Y, Z, T ), hBOOL( hAPP( Z, T ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( T ) ) ), !
% 0.74/1.34 hBOOL( hAPP( Z, T ) ), alpha29( X, Y, Z, T ) }.
% 0.74/1.34 { ! alpha13( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! alpha13( X, Y ), hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Nat_Onat ) ) ) }.
% 0.74/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13( X, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ),
% 0.74/1.34 ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ), Z
% 0.74/1.34 = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.74/1.34 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! Z = c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X
% 0.74/1.34 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), c_Nat_OSuc( Z ) ) ) }
% 0.74/1.34 .
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.74/1.34 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 0.74/1.34 , Y ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.74/1.34 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 0.74/1.34 tc_Nat_Onat, Y, X ), X ) ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.74/1.34 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.74/1.34 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.74/1.34 ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.74/1.34 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.74/1.34 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.74/1.34 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.74/1.34 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.74/1.34 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.74/1.34 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.74/1.34 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.74/1.34 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.34 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.74/1.34 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.74/1.34 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex, X
% 0.74/1.34 ), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.74/1.34 tc_Complex_Ocomplex, v_pa____ ) ),
% 0.74/1.34 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 0.74/1.34 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 0.74/1.34 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol19( X ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.74/1.34 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.74/1.34 skol20 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.74/1.34 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.74/1.34 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol20 ), X ) = hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.74/1.34 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), skol21 ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.74/1.34 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.74/1.34 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 0.74/1.34 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.74/1.34 ( X ), T, Z ), Y ) }.
% 0.74/1.34 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.74/1.34 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.74/1.34 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.74/1.34 ) ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.74/1.34 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.74/1.34 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.74/1.34 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.74/1.34 }.
% 0.74/1.34 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.74/1.34 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.74/1.34 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.74/1.34 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.74/1.34 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.74/1.34 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 0.74/1.34 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.74/1.34 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol22( X, Y ) ), Y
% 0.74/1.34 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.74/1.34 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.74/1.34 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.74/1.34 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.34 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.74/1.34 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.74/1.34 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.34 { ! c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X,
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X,
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, X, c_Complex_Oii ) ),
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 0.74/1.34 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, X, c_Complex_Oii ) )
% 0.74/1.34 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.74/1.34 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.74/1.34 skol23 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.74/1.34 tc_Complex_Ocomplex, v_pa____ ) }.
% 0.74/1.34 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol23 ), X ) = hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 0.74/1.34 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 0.74/1.34 { ! c_Complex_Oii = c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex,
% 0.74/1.34 X ) }.
% 0.74/1.34 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.74/1.34 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol24( Y ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol24( X ) ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( Z, T ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol25( X, Y ) ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol26( Z, T ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__algebra( X ),
% 0.74/1.34 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol26( X, Y ) ) ) }.
% 0.74/1.34 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.34 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.74/1.34 tc_Complex_Ocomplex, v_s____ ), v_k____ ), c_Groups_Oone__class_Oone(
% 0.74/1.34 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.74/1.34 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.74/1.34 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.74/1.34 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) = hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.74/1.34 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.74/1.34 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.34 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.74/1.34 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), hAPP
% 0.74/1.34 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 0.74/1.34 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.74/1.34 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.74/1.34 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.34 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.74/1.34 v_q____ ) ), X ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.34 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 0.74/1.34 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 0.74/1.34 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.74/1.34 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.74/1.34 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.74/1.34 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.74/1.34 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.74/1.34 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.34 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.74/1.34 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.74/1.34 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.74/1.34 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.74/1.34 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.74/1.34 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.74/1.34 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.74/1.34 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.74/1.34 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.34 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.74/1.34 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ) }.
% 0.74/1.34 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) ),
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 0.74/1.34 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 0.74/1.34 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.74/1.34 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.74/1.34 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.34 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.74/1.34 v_q____ ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.74/1.34 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.74/1.34 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.74/1.34 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.34 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.74/1.34 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 0.74/1.34 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.74/1.34 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.74/1.34 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.34 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.74/1.34 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.74/1.34 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), v_k____ ) ),
% 0.74/1.34 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.74/1.34 tc_Complex_Ocomplex, v_a____, v_s____ ) ), X ) ) ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 0.74/1.34 c_Rings_Oinverse__class_Oinverse( X, Y ) ) =
% 0.74/1.34 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.74/1.34 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.74/1.34 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.74/1.34 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.74/1.34 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.74/1.34 ) }.
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.74/1.34 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.74/1.34 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.74/1.34 .
% 0.74/1.34 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.74/1.34 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.74/1.34 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.74/1.34 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 0.74/1.35 class_Rings_Odivision__ring__inverse__zero( X ),
% 0.74/1.35 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.74/1.35 Y ) ) = c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.74/1.35 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.74/1.35 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.74/1.35 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.74/1.35 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.74/1.35 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.74/1.35 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.74/1.35 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.74/1.35 ) ), Z ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.74/1.35 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.35 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.74/1.35 ) ), Y ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.74/1.35 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.74/1.35 = Y }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.74/1.35 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.74/1.35 ( X ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.74/1.35 X, Y ) ) = Y }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.74/1.35 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.74/1.35 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.74/1.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.74/1.35 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.74/1.35 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.74/1.35 , Y ) ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.74/1.35 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.74/1.35 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.74/1.35 , Y ) ) = Y }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.74/1.35 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.74/1.35 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.74/1.35 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.74/1.35 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T,
% 0.74/1.35 c_Polynomial_Osmult( X, Y, Z ) ) = c_Polynomial_Osmult( X,
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Divides_Odiv__class_Odiv(
% 0.74/1.35 tc_Polynomial_Opoly( X ), T, Z ) ) }.
% 0.74/1.35 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.74/1.35 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Odiv(
% 0.74/1.35 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.74/1.35 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 0.74/1.35 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.74/1.35 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 0.74/1.35 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.74/1.35 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 0.74/1.35 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.74/1.35 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.74/1.35 c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.74/1.35 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.74/1.35 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.74/1.35 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex
% 0.74/1.35 , v_pa____ ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k____,
% 0.74/1.35 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), c_Orderings_Oord__class_Oless
% 0.74/1.35 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 0.74/1.35 , hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.74/1.35 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.74/1.35 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.35 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.74/1.35 v_q____ ) ), skol27 ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.74/1.35 }.
% 0.74/1.35 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.74/1.35 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.74/1.35 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.35 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.74/1.35 v_q____ ) ), skol28 ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.35 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.74/1.35 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 0.74/1.35 skol32 ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.74/1.35 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.74/1.35 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.74/1.35 Y ) ) }.
% 0.74/1.35 { c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.74/1.35 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.74/1.35 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.74/1.35 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.74/1.35 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.74/1.35 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.74/1.35 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.74/1.35 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.74/1.35 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.74/1.35 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.74/1.35 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.74/1.35 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.74/1.35 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.35 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.74/1.35 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.74/1.35 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.74/1.35 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.74/1.35 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.74/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), T ), hAPP(
% 0.74/1.35 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ), Z ) ) }.
% 0.74/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) ) }.
% 0.74/1.35 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), X ) =
% 0.74/1.35 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.74/1.35 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.74/1.35 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.74/1.35 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.74/1.35 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.74/1.35 .
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.74/1.35 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.74/1.35 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.74/1.35 .
% 0.74/1.35 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 0.74/1.35 c_RealVector_Onorm__class_Onorm( X, Y ) ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.35 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 0.74/1.35 Y ) ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Z ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.74/1.35 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.74/1.35 }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.35 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 0.74/1.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.74/1.35 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.74/1.35 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.35 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.74/1.35 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.74/1.35 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.74/1.35 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.35 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.74/1.35 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.74/1.35 = c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.74/1.35 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.74/1.35 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.74/1.35 ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.74/1.35 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.74/1.35 .
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.74/1.35 ( X ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.74/1.35 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.74/1.35 .
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.74/1.35 , Y ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.74/1.35 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.74/1.35 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.74/1.35 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.74/1.35 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.74/1.35 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.74/1.35 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.74/1.35 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.74/1.35 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.74/1.35 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.74/1.35 , Y ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.74/1.35 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 0.74/1.35 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.74/1.35 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.74/1.35 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.74/1.35 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.74/1.35 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.35 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.74/1.35 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.74/1.35 ) ) }.
% 0.74/1.35 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.74/1.35 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.74/1.35 c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.74/1.35 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.74/1.35 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.74/1.35 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 0.74/1.35 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.74/1.35 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.74/1.35 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.74/1.35 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.74/1.35 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.74/1.35 { ! skol29 = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { ! skol33 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.74/1.35 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.74/1.35 tc_Nat_Onat, c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.74/1.35 tc_Complex_Ocomplex, skol34 ), skol33 ), c_Groups_Oone__class_Oone(
% 0.74/1.35 tc_Nat_Onat ) ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 0.74/1.35 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 0.74/1.35 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 0.74/1.35 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.74/1.35 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.74/1.35 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.35 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.74/1.35 v_q____ ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, hAPP
% 0.74/1.35 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 0.74/1.35 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 0.74/1.35 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 0.74/1.35 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 0.74/1.35 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ), hAPP(
% 0.74/1.35 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP( hAPP(
% 0.74/1.35 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ), skol33 ) ),
% 0.74/1.35 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_OpCons(
% 0.74/1.35 tc_Complex_Ocomplex, skol29, skol34 ) ), X ) ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.74/1.35 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.74/1.35 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.74/1.35 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.74/1.35 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.74/1.35 , Y ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.74/1.35 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.74/1.35 }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.74/1.35 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.74/1.35 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.74/1.35 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.74/1.35 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.74/1.35 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.74/1.35 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.74/1.35 ), c_Orderings_Oord__class_Oless__eq( X, T, skol30( X, U, W, T ) ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, V0 ) ),
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.74/1.35 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.74/1.35 ) ) }.
% 0.74/1.35 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 0.74/1.35 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_RealVector_Onorm__class_Onorm( Y, c_Groups_Ominus__class_Ominus( Y,
% 0.74/1.35 hAPP( Z, T ), hAPP( Z, skol30( X, Y, Z, T ) ) ) ),
% 0.74/1.35 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, U ) ),
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 0.74/1.35 ( tc_RealDef_Oreal ), c_RealVector_Onorm__class_Onorm( Y, hAPP( Z, T ) )
% 0.74/1.35 ) ) }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.74/1.35 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.74/1.35 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.74/1.35 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.74/1.35 { c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ) =
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 X, Y ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.74/1.35 X, Z, Y ) }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 0.74/1.35 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 0.74/1.35 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Y ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 0.74/1.35 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 X, Y ) ) }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 0.74/1.35 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 0.74/1.35 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.74/1.35 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.74/1.35 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), Y ) }.
% 0.74/1.35 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.74/1.35 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.74/1.35 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 0.74/1.35 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.74/1.35 ( X ), Z, Y ) ) }.
% 0.74/1.35 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 0.74/1.35 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 0.74/1.35 ( X ), Z, Y ) ) }.
% 0.74/1.35 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.74/1.35 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( tc_Int_Oint, Y ), X ) }.
% 0.74/1.35 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 0.74/1.35 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 0.74/1.35 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 0.74/1.35 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 0.74/1.35 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 0.74/1.35 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.74/1.35 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.74/1.35 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.74/1.35 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.35 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.35 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.74/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.74/1.35 c_Groups_Oone__class_Oone( X ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.74/1.35 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.74/1.35 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.74/1.35 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.74/1.35 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.74/1.35 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.74/1.35 ) ) }.
% 0.74/1.35 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Y ), Z = Y }.
% 0.74/1.35 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Y ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.74/1.35 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.74/1.35 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.74/1.35 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.74/1.35 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 = Y }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.74/1.35 ( X ) }.
% 0.74/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Y ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.74/1.35 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.74/1.35 = Y }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.74/1.35 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Y ), Z ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.74/1.35 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Z ), Y ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.74/1.35 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.74/1.35 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.74/1.35 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.74/1.35 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.74/1.35 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.74/1.35 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.74/1.35 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.74/1.35 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.74/1.35 ) ), Y ) }.
% 0.74/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.74/1.35 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.35 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.74/1.35 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.35 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.74/1.35 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.74/1.35 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.74/1.35 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.74/1.35 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.74/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.74/1.35 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Z ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.74/1.35 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 Z ) = Y }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.74/1.35 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Y ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 X ) }.
% 0.74/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.74/1.35 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , Y ) }.
% 0.74/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.74/1.35 , Y ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.74/1.35 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.74/1.35 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.74/1.35 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.74/1.35 .
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.74/1.35 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.74/1.35 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.74/1.35 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.74/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.74/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Y ), Y ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.74/1.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.74/1.35 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.35 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.74/1.35 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.74/1.35 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.74/1.35 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.74/1.35 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.74/1.35 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.74/1.35 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.74/1.35 Y ) ) = Y }.
% 0.74/1.35 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.35 Z, Y ) ) = Y }.
% 0.74/1.35 { ! class_RealVector_Oreal__normed__vector( X ),
% 0.74/1.35 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 0.74/1.35 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.74/1.35 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.74/1.35 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.74/1.35 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.74/1.35 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.74/1.35 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.74/1.35 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.35 ( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 c_Int_Onumber__class_Onumber__of( X, Z ) ) ), Y ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Z ) ) ), Y ) }.
% 0.74/1.35 { ! class_Int_Onumber__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.74/1.35 c_Int_Onumber__class_Onumber__of( X, c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 tc_Int_Oint, Y ) ) }.
% 0.74/1.35 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.74/1.35 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.74/1.35 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.74/1.35 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.35 Y ) ) }.
% 0.74/1.35 { c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex, Y, X ) =
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) ) }.
% 0.74/1.35 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, c_Complex_Oii ) =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, c_Complex_Oii ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.74/1.35 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.74/1.35 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.74/1.35 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.74/1.35 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.35 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.74/1.35 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.74/1.35 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.74/1.35 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.74/1.35 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.74/1.35 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.74/1.35 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.74/1.35 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.74/1.35 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.74/1.35 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.74/1.35 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.74/1.35 { ! class_Int_Onumber__ring( X ), c_Groups_Ominus__class_Ominus( X,
% 0.74/1.35 c_Int_Onumber__class_Onumber__of( X, Z ),
% 0.74/1.35 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 0.74/1.35 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 0.74/1.35 tc_Int_Oint, Z, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) }.
% 0.74/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.74/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.74/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.74/1.35 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.74/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.74/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.74/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.74/1.35 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.74/1.35 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.74/1.35 { c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 0.74/1.35 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 0.74/1.35 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 0.74/1.35 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.74/1.35 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.74/1.35 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 0.74/1.35 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 0.74/1.35 .
% 0.74/1.35 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 0.74/1.35 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.74/1.35 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 0.74/1.35 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 0.74/1.35 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 0.74/1.35 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Ominus__class_Ominus(
% 0.74/1.35 X, Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) =
% 0.74/1.35 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 0.74/1.35 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ), Z ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 0.74/1.35 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 0.74/1.35 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.74/1.35 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 0.74/1.35 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.74/1.35 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.74/1.35 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.74/1.35 Y ) ) ), Y ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 0.74/1.35 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.74/1.35 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.74/1.35 Y ) ) ), Y ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.74/1.35 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.74/1.35 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.74/1.35 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.74/1.35 , Z ) ) }.
% 0.74/1.35 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.74/1.35 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 0.74/1.35 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 0.74/1.35 , Z ) ) }.
% 0.74/1.35 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 0.74/1.35 , Y ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.74/1.35 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.74/1.35 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 0.74/1.35 , Z, Y ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 0.74/1.35 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 0.74/1.35 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 0.74/1.35 ( X, Z, Y ) = T }.
% 0.74/1.35 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.74/1.35 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 0.74/1.35 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 0.74/1.35 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 0.74/1.35 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 0.74/1.35 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.74/1.35 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 0.74/1.35 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 0.74/1.35 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 0.74/1.35 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.74/1.35 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 0.74/1.35 tc_Polynomial_Opoly( X ), T, Y ) }.
% 0.74/1.35 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 0.74/1.35 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 0.74/1.35 X, T, Z ), Y ) }.
% 0.74/1.35 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.74/1.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.74/1.35 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 0.74/1.35 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.74/1.35 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.74/1.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 0.74/1.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 0.74/1.35 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.74/1.35 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 0.74/1.35 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 0.74/1.35 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 0.74/1.35 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.74/1.35 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 0.74/1.35 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.74/1.35 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 0.74/1.35 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.74/1.35 ), T ), U ), Y ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.74/1.35 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 0.74/1.35 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.74/1.35 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 0.74/1.35 .
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 0.74/1.35 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.74/1.35 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 0.74/1.35 .
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.74/1.35 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.74/1.35 }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 0.74/1.35 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.74/1.35 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 0.74/1.35 }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.74/1.35 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.74/1.35 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.74/1.35 }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 0.74/1.35 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.74/1.35 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 0.74/1.35 }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.74/1.35 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 0.74/1.35 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.74/1.35 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.74/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 0.74/1.35 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.74/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 0.74/1.35 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 0.74/1.35 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.74/1.35 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.74/1.35 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 0.74/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.74/1.35 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.74/1.35 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.74/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 0.74/1.35 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 0.74/1.35 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 0.74/1.35 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 0.74/1.35 Z, T ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 0.74/1.35 c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.74/1.35 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.74/1.35 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 0.74/1.35 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.74/1.35 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.74/1.35 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 0.74/1.35 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.74/1.35 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 0.74/1.35 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 0.74/1.35 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 0.74/1.35 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 0.74/1.35 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.74/1.35 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 0.74/1.35 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 0.74/1.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.74/1.35 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 0.74/1.35 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.74/1.35 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.74/1.35 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 0.74/1.35 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 0.74/1.35 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 0.74/1.35 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.74/1.35 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 0.74/1.35 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.74/1.35 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.74/1.35 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.74/1.35 ( tc_fun( Y, X ) ) }.
% 0.74/1.35 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.74/1.35 ) ) }.
% 0.74/1.35 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.74/1.35 .
% 0.74/1.35 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.74/1.35 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.74/1.35 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 0.74/1.35 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.74/1.35 tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.74/1.35 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.74/1.35 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.74/1.35 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.74/1.35 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.74/1.35 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.74/1.35 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.74/1.35 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.74/1.35 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Ominus( tc_Int_Oint ) }.
% 0.74/1.35 { class_Power_Opower( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.74/1.35 { class_Int_Onumber( tc_Int_Oint ) }.
% 0.74/1.35 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.74/1.35 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.74/1.35 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.74/1.35 tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Int_Onumber( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.74/1.35 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.74/1.35 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.74/1.35 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.74/1.35 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.74/1.35 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.74/1.35 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 0.74/1.35 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.74/1.35 tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.74/1.35 .
% 0.74/1.35 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Int_Onumber__ring( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Ominus( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Int_Onumber( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 0.74/1.35 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.74/1.35 tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Ominus( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ),
% 0.74/1.35 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.74/1.35 ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.74/1.35 X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.74/1.35 ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.74/1.35 }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.74/1.35 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ),
% 0.74/1.35 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.74/1.35 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.74/1.35 ( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.74/1.35 ( tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.74/1.35 ( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber__ring(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.74/1.35 }.
% 0.74/1.35 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.74/1.35 ) ) }.
% 0.74/1.35 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.74/1.35 .
% 0.74/1.35 { ! class_Rings_Ocomm__ring__1( X ), class_Int_Onumber( tc_Polynomial_Opoly
% 0.74/1.35 ( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.74/1.35 tc_Polynomial_Opoly( X ) ) }.
% 0.74/1.35 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ),
% 0.74/1.35 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), X ),
% 0.74/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____, c_Nat_OSuc(
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 0.74/1.35 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), hAPP( hAPP(
% 0.74/1.35 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), Y ),
% 0.74/1.35 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, v_k____, c_Nat_OSuc(
% 0.74/1.35 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) }.
% 0.74/1.35
% 0.74/1.35 *** allocated 15000 integers for clauses
% 0.74/1.35 *** allocated 22500 integers for clauses
% 0.74/1.35 *** allocated 33750 integers for clauses
% 0.74/1.35 *** allocated 50625 integers for clauses
% 0.74/1.35 *** allocated 75937 integers for clauses
% 0.74/1.35 percentage equality = 0.262817, percentage horn = 0.910590
% 0.74/1.35 This is a problem with some equality
% 0.74/1.35
% 0.74/1.35
% 0.74/1.35
% 0.74/1.35 Options Used:
% 0.74/1.35
% 0.74/1.35 useres = 1
% 0.74/1.35 useparamod = 1
% 0.74/1.35 useeqrefl = 1
% 0.74/1.35 useeqfact = 1
% 0.74/1.35 usefactor = 1
% 0.74/1.35 usesimpsplitting = 0
% 0.74/1.35 usesimpdemod = 5
% 0.74/1.35 usesimpres = 3
% 0.74/1.35
% 0.74/1.35 resimpinuse = 1000
% 0.74/1.35 resimpclauses = 20000
% 0.74/1.35 substype = eqrewr
% 0.74/1.35 backwardsubs = 1
% 0.74/1.35 selectoldest = 5
% 0.74/1.35
% 0.74/1.35 litorderings [0] = split
% 0.74/1.35 litorderings [1] = extend the termordering, first sorting on arguments
% 0.74/1.35
% 0.74/1.35 termordering = kbo
% 0.74/1.35
% 0.74/1.35 litapriori = 0
% 0.74/1.35 termapriori = 1
% 0.74/1.35 litaposteriori = 0
% 0.74/1.35 termaposteriori = 0
% 0.74/1.35 demodaposteriori = 0
% 0.74/1.35 ordereqreflfact = 0
% 0.74/1.35
% 0.74/1.35 litselect = negord
% 0.74/1.35
% 0.74/1.35 maxweight = 15
% 0.74/1.35 maxdepth = 30000
% 0.74/1.35 maxlength = 115
% 0.74/1.35 maxnrvars = 195
% 0.74/1.35 excuselevel = 1
% 0.74/1.35 increasemaxweight = 1
% 0.74/1.35
% 0.74/1.35 maxselected = 10000000
% 0.74/1.35 maxnrclauses = 10000000
% 0.74/1.35
% 0.74/1.35 showgenerated = 0
% 0.74/1.35 showkept = 0
% 0.74/1.35 showselected = 0
% 0.74/1.35 showdeleted = 0
% 0.74/1.35 showresimp = 1
% 0.74/1.35 showstatus = 2000
% 0.74/1.35
% 0.74/1.35 prologoutput = 0
% 0.74/1.35 nrgoals = 5000000
% 0.74/1.35 totalproof = 1
% 0.74/1.35
% 0.74/1.35 Symbols occurring in the translation:
% 0.74/1.35
% 0.74/1.35 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.74/1.35 . [1, 2] (w:1, o:210, a:1, s:1, b:0),
% 0.74/1.35 ! [4, 1] (w:0, o:120, a:1, s:1, b:0),
% 0.74/1.35 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.35 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.74/1.35 hAPP [38, 2] (w:1, o:234, a:1, s:1, b:0),
% 0.74/1.35 v_k____ [39, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.74/1.35 tc_Nat_Onat [40, 0] (w:1, o:22, a:1, s:1, b:0),
% 0.74/1.35 c_Groups_Ozero__class_Ozero [41, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.74/1.35 v_a____ [42, 0] (w:1, o:23, a:1, s:1, b:0),
% 0.74/1.35 tc_Complex_Ocomplex [43, 0] (w:1, o:24, a:1, s:1, b:0),
% 0.74/1.35 class_Power_Opower [47, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.74/1.35 c_Power_Opower__class_Opower [48, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.74/1.35 c_Nat_OSuc [49, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.74/1.35 c_Groups_Otimes__class_Otimes [50, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Ocomm__semiring__1 [53, 1] (w:1, o:137, a:1, s:1, b:0),
% 0.74/1.35 class_Groups_Omonoid__mult [54, 1] (w:1, o:143, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Osemiring__0 [55, 1] (w:1, o:148, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Omult__zero [58, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Ono__zero__divisors [59, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.74/1.35
% 0.74/1.35 class_Rings_Ozero__neq__one [60, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.74/1.35 c_Groups_Ominus__class_Ominus [62, 3] (w:1, o:265, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Oring__1__no__zero__divisors [78, 1] (w:1, o:144, a:1, s:
% 0.74/1.35 1, b:0),
% 0.74/1.35 class_Groups_Ocomm__monoid__mult [79, 1] (w:1, o:161, a:1, s:1, b:0)
% 0.74/1.35 ,
% 0.74/1.35 class_RealVector_Oreal__normed__algebra [83, 1] (w:1, o:162, a:1, s:1
% 0.74/1.35 , b:0),
% 0.74/1.35 class_Groups_Ogroup__add [88, 1] (w:1, o:163, a:1, s:1, b:0),
% 0.74/1.35 class_Groups_Oab__group__add [89, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Oring__no__zero__divisors [90, 1] (w:1, o:145, a:1, s:1
% 0.74/1.35 , b:0),
% 0.74/1.35 class_Groups_Ozero [91, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.74/1.35 class_Groups_Oab__semigroup__mult [93, 1] (w:1, o:166, a:1, s:1, b:0)
% 0.74/1.35 ,
% 0.74/1.35 c_Groups_Oone__class_Oone [96, 1] (w:1, o:167, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Ocomm__ring__1 [97, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.74/1.35 c_Groups_Oplus__class_Oplus [98, 3] (w:1, o:266, a:1, s:1, b:0),
% 0.74/1.35 tc_Int_Oint [100, 0] (w:1, o:76, a:1, s:1, b:0),
% 0.74/1.35 c_Orderings_Oord__class_Oless__eq [101, 3] (w:1, o:267, a:1, s:1, b:0
% 0.74/1.35 ),
% 0.74/1.35 class_Groups_Ominus [105, 1] (w:1, o:168, a:1, s:1, b:0),
% 0.74/1.35 tc_fun [106, 2] (w:1, o:244, a:1, s:1, b:0),
% 0.74/1.35 class_Lattices_Oab__semigroup__idem__mult [107, 1] (w:1, o:169, a:1
% 0.74/1.35 , s:1, b:0),
% 0.74/1.35 c_Orderings_Oord__class_Oless [108, 3] (w:1, o:268, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Olinordered__semidom [109, 1] (w:1, o:151, a:1, s:1, b:0)
% 0.74/1.35 ,
% 0.74/1.35 class_Groups_Olinordered__ab__group__add [110, 1] (w:1, o:142, a:1
% 0.74/1.35 , s:1, b:0),
% 0.74/1.35 class_Groups_Oordered__comm__monoid__add [112, 1] (w:1, o:170, a:1
% 0.74/1.35 , s:1, b:0),
% 0.74/1.35 class_Rings_Olinordered__semiring__1__strict [119, 1] (w:1, o:152, a:
% 0.74/1.35 1, s:1, b:0),
% 0.74/1.35 class_Groups_Oordered__ab__semigroup__add__imp__le [120, 1] (w:1, o:
% 0.74/1.35 171, a:1, s:1, b:0),
% 0.74/1.35 class_Groups_Ocancel__semigroup__add [121, 1] (w:1, o:172, a:1, s:1
% 0.74/1.35 , b:0),
% 0.74/1.35 class_Groups_Ocancel__ab__semigroup__add [122, 1] (w:1, o:173, a:1
% 0.74/1.35 , s:1, b:0),
% 0.74/1.35 class_Groups_Oordered__ab__semigroup__add [124, 1] (w:1, o:174, a:1
% 0.74/1.35 , s:1, b:0),
% 0.74/1.35 class_Groups_Oordered__cancel__ab__semigroup__add [125, 1] (w:1, o:
% 0.74/1.35 175, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Olinordered__idom [126, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.74/1.35 class_Groups_Oab__semigroup__add [127, 1] (w:1, o:176, a:1, s:1, b:0)
% 0.74/1.35 ,
% 0.74/1.35 class_Groups_Oone [128, 1] (w:1, o:177, a:1, s:1, b:0),
% 0.74/1.35 hBOOL [130, 1] (w:1, o:178, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Olinordered__semiring__1 [135, 1] (w:1, o:154, a:1, s:1
% 0.74/1.35 , b:0),
% 0.74/1.35 class_Rings_Oring__1 [136, 1] (w:1, o:146, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Olinordered__ring__strict [137, 1] (w:1, o:149, a:1, s:1
% 0.74/1.35 , b:0),
% 0.74/1.35 class_Rings_Olinordered__ring [138, 1] (w:1, o:150, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Olinordered__semiring__strict [139, 1] (w:1, o:155, a:1
% 0.74/1.35 , s:1, b:0),
% 0.74/1.35 class_Rings_Olinordered__semiring [140, 1] (w:1, o:156, a:1, s:1, b:0
% 0.74/1.35 ),
% 0.74/1.35 class_Rings_Oordered__ring [142, 1] (w:1, o:179, a:1, s:1, b:0),
% 0.74/1.35 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.74/1.35 145, 1] (w:1, o:192, a:1, s:1, b:0),
% 0.74/1.35 class_Groups_Ocomm__monoid__add [146, 1] (w:1, o:193, a:1, s:1, b:0)
% 0.74/1.35 ,
% 0.74/1.35 class_Groups_Omonoid__add [147, 1] (w:1, o:194, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Osemiring [151, 1] (w:1, o:180, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Ocomm__semiring [152, 1] (w:1, o:181, a:1, s:1, b:0),
% 0.74/1.35 class_Groups_Oordered__ab__group__add [153, 1] (w:1, o:195, a:1, s:1
% 0.74/1.35 , b:0),
% 0.74/1.35 class_Rings_Oring [154, 1] (w:1, o:147, a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Olinordered__comm__semiring__strict [155, 1] (w:1, o:157
% 0.74/1.35 , a:1, s:1, b:0),
% 0.74/1.35 class_Rings_Oordered__cancel__semiring [156, 1] (w:1, o:182, a:1, s:1
% 0.74/1.35 , b:0),
% 0.74/1.35 class_Rings_Oordered__semiring [157, 1] (w:1, o:183, a:1, s:1, b:0),
% 0.74/1.35
% 0.74/1.35 class_Rings_Oordered__comm__semiring [158, 1] (w:1, o:184, a:1, s:1
% 0.74/1.35 , b:0),
% 0.74/1.35 class_Orderings_Opreorder [161, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.74/1.35 c_Power_Opower_Opower [162, 3] (w:1, o:269, a:1, s:1, b:0),
% 0.74/1.35 class_Orderings_Olinorder [163, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.74/1.35 class_Orderings_Oord [170, 1] (w:1, o:126, a:1, s:1, b:0),
% 0.74/1.35 class_Orderings_Oorder [171, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.74/1.35 v_pa____ [174, 0] (w:1, o:103, a:1, s:1, b:0),
% 0.74/1.35 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [175, 2] (w:1, o:
% 0.74/1.35 245, a:1, s:1, b:0),
% 0.74/1.35 c_Int_Onumber__class_Onumber__of [177, 2] (w:1, o:246, a:1, s:1, b:0)
% 0.74/1.35 ,
% 0.74/1.35 class_Int_Onumber__ring [180, 1] (w:1, o:196, a:1, s:1, b:0),
% 0.74/1.35 class_Int_Oring__char__0 [181, 1] (w:1, o:197, a:1, s:1, b:0),
% 0.74/1.35 class_Int_Onumber [182, 1] (w:1, o:198, a:1, s:1, b:0),
% 0.74/1.35 tc_Polynomial_Opoly [185, 1] (w:1, o:204, a:1, s:1, b:0),
% 0.74/1.35 v_q____ [186, 0] (w:1, o:106, a:1, s:1, b:0),
% 0.74/1.35 c_Nat__Transfer_Otsub [189, 2] (w:1, o:247, a:1, s:1, b:0),
% 0.74/1.35 c_Divides_Odiv__class_Odiv [190, 3] (w:1, o:270, a:1, s:1, b:0),
% 0.74/1.35 c_Polynomial_Opoly [191, 2] (w:1, o:248, a:1, s:1, b:0),
% 0.74/1.35 v_p [192, 0] (w:1, o:105, a:1, s:1, b:0),
% 0.74/1.35 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [193, 3] (w:1
% 0.74/1.35 , o:264, a:1, s:1, b:0),
% 0.74/1.35 v_c____ [194, 0] (w:1, o:107, a:1, s:1, b:0),
% 3.82/4.19 class_Divides_Osemiring__div [195, 1] (w:1, o:206, a:1, s:1, b:0),
% 3.82/4.19 tc_RealDef_Oreal [200, 0] (w:1, o:108, a:1, s:1, b:0),
% 3.82/4.19 c_RealVector_Onorm__class_Onorm [201, 2] (w:1, o:249, a:1, s:1, b:0)
% 3.82/4.19 ,
% 3.82/4.19 class_Rings_Ocomm__semiring__0 [202, 1] (w:1, o:136, a:1, s:1, b:0),
% 3.82/4.19
% 3.82/4.19 class_RealVector_Oreal__normed__vector [203, 1] (w:1, o:185, a:1, s:1
% 3.82/4.19 , b:0),
% 3.82/4.19 class_RealVector_Oreal__normed__algebra__1 [204, 1] (w:1, o:186, a:1
% 3.82/4.19 , s:1, b:0),
% 3.82/4.19 class_RealVector_Oreal__normed__div__algebra [206, 1] (w:1, o:187, a:
% 3.82/4.19 1, s:1, b:0),
% 3.82/4.19 class_Rings_Oidom [208, 1] (w:1, o:188, a:1, s:1, b:0),
% 3.82/4.19 class_Rings_Ocomm__ring [210, 1] (w:1, o:135, a:1, s:1, b:0),
% 3.82/4.19 class_Fields_Ofield [212, 1] (w:1, o:138, a:1, s:1, b:0),
% 3.82/4.19 c_Polynomial_Oorder [213, 3] (w:1, o:271, a:1, s:1, b:0),
% 3.82/4.19 c_Complex_Oii [214, 0] (w:1, o:112, a:1, s:1, b:0),
% 3.82/4.19 v_s____ [218, 0] (w:1, o:116, a:1, s:1, b:0),
% 3.82/4.19 c_Rings_Oinverse__class_Oinverse [219, 2] (w:1, o:250, a:1, s:1, b:0)
% 3.82/4.19 ,
% 3.82/4.19 c_Polynomial_Osmult [220, 3] (w:1, o:272, a:1, s:1, b:0),
% 3.82/4.19 c_Polynomial_OpCons [221, 3] (w:1, o:273, a:1, s:1, b:0),
% 3.82/4.19 class_Rings_Odivision__ring__inverse__zero [222, 1] (w:1, o:189, a:1
% 3.82/4.19 , s:1, b:0),
% 3.82/4.19 class_Rings_Odivision__ring [223, 1] (w:1, o:190, a:1, s:1, b:0),
% 3.82/4.19 class_Fields_Olinordered__field__inverse__zero [225, 1] (w:1, o:139
% 3.82/4.19 , a:1, s:1, b:0),
% 3.82/4.19 class_Fields_Ofield__inverse__zero [226, 1] (w:1, o:140, a:1, s:1, b:
% 3.82/4.19 0),
% 3.82/4.19 class_Fields_Olinordered__field [227, 1] (w:1, o:141, a:1, s:1, b:0)
% 3.82/4.19 ,
% 3.82/4.19 c_Polynomial_Opcompose [228, 3] (w:1, o:274, a:1, s:1, b:0),
% 3.82/4.19 c_Polynomial_Osynthetic__div [229, 3] (w:1, o:275, a:1, s:1, b:0),
% 3.82/4.19 c_Groups_Ouminus__class_Ouminus [230, 2] (w:1, o:251, a:1, s:1, b:0)
% 3.82/4.19 ,
% 3.82/4.19 class_Lattices_Oboolean__algebra [233, 1] (w:1, o:207, a:1, s:1, b:0)
% 3.82/4.19 ,
% 3.82/4.19 class_Groups_Ouminus [234, 1] (w:1, o:208, a:1, s:1, b:0),
% 3.82/4.19 c_Rings_Odvd__class_Odvd [235, 3] (w:1, o:276, a:1, s:1, b:0),
% 3.82/4.19 class_Divides_Oring__div [236, 1] (w:1, o:205, a:1, s:1, b:0),
% 3.82/4.19 class_Rings_Odvd [237, 1] (w:1, o:191, a:1, s:1, b:0),
% 3.82/4.19 class_Groups_Ocancel__comm__monoid__add [239, 1] (w:1, o:209, a:1, s:
% 3.82/4.19 1, b:0),
% 3.82/4.19 tc_HOL_Obool [241, 0] (w:1, o:75, a:1, s:1, b:0),
% 3.82/4.19 alpha1 [242, 3] (w:1, o:277, a:1, s:1, b:1),
% 3.82/4.19 alpha2 [243, 3] (w:1, o:282, a:1, s:1, b:1),
% 3.82/4.19 alpha3 [244, 4] (w:1, o:307, a:1, s:1, b:1),
% 3.82/4.19 alpha4 [245, 4] (w:1, o:311, a:1, s:1, b:1),
% 3.82/4.19 alpha5 [246, 3] (w:1, o:284, a:1, s:1, b:1),
% 3.82/4.19 alpha6 [247, 3] (w:1, o:285, a:1, s:1, b:1),
% 3.82/4.19 alpha7 [248, 2] (w:1, o:252, a:1, s:1, b:1),
% 3.82/4.19 alpha8 [249, 2] (w:1, o:253, a:1, s:1, b:1),
% 3.82/4.19 alpha9 [250, 2] (w:1, o:254, a:1, s:1, b:1),
% 3.82/4.19 alpha10 [251, 2] (w:1, o:255, a:1, s:1, b:1),
% 3.82/4.19 alpha11 [252, 2] (w:1, o:256, a:1, s:1, b:1),
% 3.82/4.19 alpha12 [253, 2] (w:1, o:257, a:1, s:1, b:1),
% 3.82/4.19 alpha13 [254, 2] (w:1, o:258, a:1, s:1, b:1),
% 3.82/4.19 alpha14 [255, 3] (w:1, o:278, a:1, s:1, b:1),
% 3.82/4.19 alpha15 [256, 3] (w:1, o:279, a:1, s:1, b:1),
% 3.82/4.19 alpha16 [257, 4] (w:1, o:312, a:1, s:1, b:1),
% 3.82/4.19 alpha17 [258, 4] (w:1, o:313, a:1, s:1, b:1),
% 3.82/4.19 alpha18 [259, 3] (w:1, o:280, a:1, s:1, b:1),
% 3.82/4.19 alpha19 [260, 3] (w:1, o:281, a:1, s:1, b:1),
% 3.82/4.19 alpha20 [261, 2] (w:1, o:259, a:1, s:1, b:1),
% 3.82/4.19 alpha21 [262, 2] (w:1, o:260, a:1, s:1, b:1),
% 3.82/4.19 alpha22 [263, 2] (w:1, o:261, a:1, s:1, b:1),
% 3.82/4.19 alpha23 [264, 3] (w:1, o:286, a:1, s:1, b:1),
% 3.82/4.19 alpha24 [265, 3] (w:1, o:287, a:1, s:1, b:1),
% 3.82/4.19 alpha25 [266, 3] (w:1, o:288, a:1, s:1, b:1),
% 3.82/4.19 alpha26 [267, 2] (w:1, o:262, a:1, s:1, b:1),
% 3.82/4.19 alpha27 [268, 3] (w:1, o:289, a:1, s:1, b:1),
% 3.82/4.19 alpha28 [269, 3] (w:1, o:290, a:1, s:1, b:1),
% 3.82/4.19 alpha29 [270, 4] (w:1, o:306, a:1, s:1, b:1),
% 3.82/4.19 alpha30 [271, 3] (w:1, o:291, a:1, s:1, b:1),
% 3.82/4.19 alpha31 [272, 3] (w:1, o:292, a:1, s:1, b:1),
% 3.82/4.19 alpha32 [273, 4] (w:1, o:308, a:1, s:1, b:1),
% 3.82/4.19 alpha33 [274, 3] (w:1, o:293, a:1, s:1, b:1),
% 3.82/4.19 alpha34 [275, 3] (w:1, o:294, a:1, s:1, b:1),
% 3.82/4.19 alpha35 [276, 3] (w:1, o:295, a:1, s:1, b:1),
% 17.85/18.27 alpha36 [277, 4] (w:1, o:309, a:1, s:1, b:1),
% 17.85/18.27 alpha37 [278, 4] (w:1, o:310, a:1, s:1, b:1),
% 17.85/18.27 alpha38 [279, 3] (w:1, o:296, a:1, s:1, b:1),
% 17.85/18.27 alpha39 [280, 2] (w:1, o:263, a:1, s:1, b:1),
% 17.85/18.27 alpha40 [281, 3] (w:1, o:283, a:1, s:1, b:1),
% 17.85/18.27 skol1 [282, 2] (w:1, o:235, a:1, s:1, b:1),
% 17.85/18.27 skol2 [283, 2] (w:1, o:237, a:1, s:1, b:1),
% 17.85/18.27 skol3 [284, 2] (w:1, o:241, a:1, s:1, b:1),
% 17.85/18.27 skol4 [285, 3] (w:1, o:297, a:1, s:1, b:1),
% 17.85/18.27 skol5 [286, 3] (w:1, o:298, a:1, s:1, b:1),
% 17.85/18.27 skol6 [287, 2] (w:1, o:242, a:1, s:1, b:1),
% 17.85/18.27 skol7 [288, 1] (w:1, o:199, a:1, s:1, b:1),
% 17.85/18.27 skol8 [289, 3] (w:1, o:299, a:1, s:1, b:1),
% 17.85/18.27 skol9 [290, 2] (w:1, o:243, a:1, s:1, b:1),
% 17.85/18.27 skol10 [291, 2] (w:1, o:236, a:1, s:1, b:1),
% 17.85/18.27 skol11 [292, 3] (w:1, o:300, a:1, s:1, b:1),
% 17.85/18.27 skol12 [293, 3] (w:1, o:301, a:1, s:1, b:1),
% 17.85/18.27 skol13 [294, 3] (w:1, o:302, a:1, s:1, b:1),
% 17.85/18.27 skol14 [295, 3] (w:1, o:303, a:1, s:1, b:1),
% 17.85/18.27 skol15 [296, 1] (w:1, o:200, a:1, s:1, b:1),
% 17.85/18.27 skol16 [297, 3] (w:1, o:304, a:1, s:1, b:1),
% 17.85/18.27 skol17 [298, 4] (w:1, o:314, a:1, s:1, b:1),
% 17.85/18.27 skol18 [299, 3] (w:1, o:305, a:1, s:1, b:1),
% 17.85/18.27 skol19 [300, 1] (w:1, o:201, a:1, s:1, b:1),
% 17.85/18.27 skol20 [301, 0] (w:1, o:13, a:1, s:1, b:1),
% 17.85/18.27 skol21 [302, 0] (w:1, o:14, a:1, s:1, b:1),
% 17.85/18.27 skol22 [303, 2] (w:1, o:238, a:1, s:1, b:1),
% 17.85/18.27 skol23 [304, 0] (w:1, o:15, a:1, s:1, b:1),
% 17.85/18.27 skol24 [305, 1] (w:1, o:202, a:1, s:1, b:1),
% 17.85/18.27 skol25 [306, 2] (w:1, o:239, a:1, s:1, b:1),
% 17.85/18.27 skol26 [307, 2] (w:1, o:240, a:1, s:1, b:1),
% 17.85/18.27 skol27 [308, 0] (w:1, o:16, a:1, s:1, b:1),
% 17.85/18.27 skol28 [309, 0] (w:1, o:17, a:1, s:1, b:1),
% 17.85/18.27 skol29 [310, 0] (w:1, o:18, a:1, s:1, b:1),
% 17.85/18.27 skol30 [311, 4] (w:1, o:315, a:1, s:1, b:1),
% 17.85/18.27 skol31 [312, 1] (w:1, o:203, a:1, s:1, b:1),
% 17.85/18.27 skol32 [313, 0] (w:1, o:19, a:1, s:1, b:1),
% 17.85/18.27 skol33 [314, 0] (w:1, o:20, a:1, s:1, b:1),
% 17.85/18.27 skol34 [315, 0] (w:1, o:21, a:1, s:1, b:1).
% 17.85/18.27
% 17.85/18.27
% 17.85/18.27 Starting Search:
% 17.85/18.27
% 17.85/18.27 *** allocated 113905 integers for clauses
% 17.85/18.27 *** allocated 170857 integers for clauses
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27
% 17.85/18.27 Intermediate Status:
% 17.85/18.27 Generated: 3095
% 17.85/18.27 Kept: 2069
% 17.85/18.27 Inuse: 46
% 17.85/18.27 Deleted: 0
% 17.85/18.27 Deletedinuse: 0
% 17.85/18.27
% 17.85/18.27 *** allocated 256285 integers for clauses
% 17.85/18.27 *** allocated 170857 integers for termspace/termends
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27
% 17.85/18.27 Intermediate Status:
% 17.85/18.27 Generated: 14100
% 17.85/18.27 Kept: 4076
% 17.85/18.27 Inuse: 135
% 17.85/18.27 Deleted: 4
% 17.85/18.27 Deletedinuse: 1
% 17.85/18.27
% 17.85/18.27 *** allocated 384427 integers for clauses
% 17.85/18.27 *** allocated 256285 integers for termspace/termends
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27
% 17.85/18.27 Intermediate Status:
% 17.85/18.27 Generated: 21616
% 17.85/18.27 Kept: 6079
% 17.85/18.27 Inuse: 223
% 17.85/18.27 Deleted: 14
% 17.85/18.27 Deletedinuse: 1
% 17.85/18.27
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27 *** allocated 576640 integers for clauses
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27 *** allocated 384427 integers for termspace/termends
% 17.85/18.27
% 17.85/18.27 Intermediate Status:
% 17.85/18.27 Generated: 28647
% 17.85/18.27 Kept: 8166
% 17.85/18.27 Inuse: 283
% 17.85/18.27 Deleted: 14
% 17.85/18.27 Deletedinuse: 1
% 17.85/18.27
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27
% 17.85/18.27 Intermediate Status:
% 17.85/18.27 Generated: 33394
% 17.85/18.27 Kept: 10418
% 17.85/18.27 Inuse: 308
% 17.85/18.27 Deleted: 14
% 17.85/18.27 Deletedinuse: 1
% 17.85/18.27
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27 *** allocated 864960 integers for clauses
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27
% 17.85/18.27 Intermediate Status:
% 17.85/18.27 Generated: 45804
% 17.85/18.27 Kept: 12718
% 17.85/18.27 Inuse: 328
% 17.85/18.27 Deleted: 14
% 17.85/18.27 Deletedinuse: 1
% 17.85/18.27
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27 *** allocated 576640 integers for termspace/termends
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27
% 17.85/18.27 Intermediate Status:
% 17.85/18.27 Generated: 53174
% 17.85/18.27 Kept: 14727
% 17.85/18.27 Inuse: 377
% 17.85/18.27 Deleted: 15
% 17.85/18.27 Deletedinuse: 2
% 17.85/18.27
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27
% 17.85/18.27 Intermediate Status:
% 17.85/18.27 Generated: 59904
% 17.85/18.27 Kept: 16776
% 17.85/18.27 Inuse: 448
% 17.85/18.27 Deleted: 20
% 17.85/18.27 Deletedinuse: 2
% 17.85/18.27
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27 *** allocated 1297440 integers for clauses
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27
% 17.85/18.27 Intermediate Status:
% 17.85/18.27 Generated: 66692
% 17.85/18.27 Kept: 18891
% 17.85/18.27 Inuse: 513
% 17.85/18.27 Deleted: 20
% 17.85/18.27 Deletedinuse: 2
% 17.85/18.27
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27 Resimplifying inuse:
% 17.85/18.27 Done
% 17.85/18.27
% 17.85/18.27 Resimplifying clauses:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 *** allocated 864960 integers for termspace/termends
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 76476
% 72.74/73.12 Kept: 21354
% 72.74/73.12 Inuse: 550
% 72.74/73.12 Deleted: 369
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 84208
% 72.74/73.12 Kept: 23372
% 72.74/73.12 Inuse: 605
% 72.74/73.12 Deleted: 369
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 90999
% 72.74/73.12 Kept: 25458
% 72.74/73.12 Inuse: 635
% 72.74/73.12 Deleted: 369
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 97974
% 72.74/73.12 Kept: 27469
% 72.74/73.12 Inuse: 657
% 72.74/73.12 Deleted: 369
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 *** allocated 1946160 integers for clauses
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 *** allocated 1297440 integers for termspace/termends
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 108736
% 72.74/73.12 Kept: 30431
% 72.74/73.12 Inuse: 665
% 72.74/73.12 Deleted: 369
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 119155
% 72.74/73.12 Kept: 33528
% 72.74/73.12 Inuse: 710
% 72.74/73.12 Deleted: 369
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 126094
% 72.74/73.12 Kept: 35629
% 72.74/73.12 Inuse: 755
% 72.74/73.12 Deleted: 369
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 134478
% 72.74/73.12 Kept: 40142
% 72.74/73.12 Inuse: 775
% 72.74/73.12 Deleted: 369
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying clauses:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 141381
% 72.74/73.12 Kept: 42152
% 72.74/73.12 Inuse: 822
% 72.74/73.12 Deleted: 573
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 *** allocated 2919240 integers for clauses
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 153150
% 72.74/73.12 Kept: 45036
% 72.74/73.12 Inuse: 845
% 72.74/73.12 Deleted: 573
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 160448
% 72.74/73.12 Kept: 49035
% 72.74/73.12 Inuse: 855
% 72.74/73.12 Deleted: 573
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 *** allocated 1946160 integers for termspace/termends
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 175911
% 72.74/73.12 Kept: 52915
% 72.74/73.12 Inuse: 895
% 72.74/73.12 Deleted: 573
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 184292
% 72.74/73.12 Kept: 54925
% 72.74/73.12 Inuse: 930
% 72.74/73.12 Deleted: 573
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 193755
% 72.74/73.12 Kept: 56959
% 72.74/73.12 Inuse: 972
% 72.74/73.12 Deleted: 573
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 205955
% 72.74/73.12 Kept: 58988
% 72.74/73.12 Inuse: 990
% 72.74/73.12 Deleted: 573
% 72.74/73.12 Deletedinuse: 2
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying clauses:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 214510
% 72.74/73.12 Kept: 61018
% 72.74/73.12 Inuse: 1026
% 72.74/73.12 Deleted: 907
% 72.74/73.12 Deletedinuse: 3
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 223727
% 72.74/73.12 Kept: 63368
% 72.74/73.12 Inuse: 1034
% 72.74/73.12 Deleted: 907
% 72.74/73.12 Deletedinuse: 3
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 *** allocated 4378860 integers for clauses
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 232261
% 72.74/73.12 Kept: 68024
% 72.74/73.12 Inuse: 1045
% 72.74/73.12 Deleted: 907
% 72.74/73.12 Deletedinuse: 3
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 240814
% 72.74/73.12 Kept: 70032
% 72.74/73.12 Inuse: 1096
% 72.74/73.12 Deleted: 907
% 72.74/73.12 Deletedinuse: 3
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 255257
% 72.74/73.12 Kept: 73144
% 72.74/73.12 Inuse: 1120
% 72.74/73.12 Deleted: 908
% 72.74/73.12 Deletedinuse: 4
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 263333
% 72.74/73.12 Kept: 76075
% 72.74/73.12 Inuse: 1140
% 72.74/73.12 Deleted: 908
% 72.74/73.12 Deletedinuse: 4
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 *** allocated 2919240 integers for termspace/termends
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 274830
% 72.74/73.12 Kept: 78250
% 72.74/73.12 Inuse: 1165
% 72.74/73.12 Deleted: 908
% 72.74/73.12 Deletedinuse: 4
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12 Resimplifying inuse:
% 72.74/73.12 Done
% 72.74/73.12
% 72.74/73.12
% 72.74/73.12 Intermediate Status:
% 72.74/73.12 Generated: 282577
% 72.74/73.12 Kept: 80307
% 72.74/73.12 Inuse: 1185
% 72.74/73.12 Deleted: 910
% 211.62/212.09 Deletedinuse: 6
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying clauses:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 295901
% 211.62/212.09 Kept: 82953
% 211.62/212.09 Inuse: 1195
% 211.62/212.09 Deleted: 1732
% 211.62/212.09 Deletedinuse: 6
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 308803
% 211.62/212.09 Kept: 86415
% 211.62/212.09 Inuse: 1215
% 211.62/212.09 Deleted: 1733
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 316126
% 211.62/212.09 Kept: 88421
% 211.62/212.09 Inuse: 1226
% 211.62/212.09 Deleted: 1733
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 328296
% 211.62/212.09 Kept: 91577
% 211.62/212.09 Inuse: 1235
% 211.62/212.09 Deleted: 1733
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 334714
% 211.62/212.09 Kept: 93837
% 211.62/212.09 Inuse: 1260
% 211.62/212.09 Deleted: 1733
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 342855
% 211.62/212.09 Kept: 95983
% 211.62/212.09 Inuse: 1280
% 211.62/212.09 Deleted: 1733
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 *** allocated 6568290 integers for clauses
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 351528
% 211.62/212.09 Kept: 98032
% 211.62/212.09 Inuse: 1300
% 211.62/212.09 Deleted: 1733
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 *** allocated 4378860 integers for termspace/termends
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 357873
% 211.62/212.09 Kept: 100532
% 211.62/212.09 Inuse: 1320
% 211.62/212.09 Deleted: 1733
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying clauses:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 363948
% 211.62/212.09 Kept: 102612
% 211.62/212.09 Inuse: 1335
% 211.62/212.09 Deleted: 2360
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 369893
% 211.62/212.09 Kept: 104654
% 211.62/212.09 Inuse: 1350
% 211.62/212.09 Deleted: 2360
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 376832
% 211.62/212.09 Kept: 107011
% 211.62/212.09 Inuse: 1365
% 211.62/212.09 Deleted: 2360
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 383210
% 211.62/212.09 Kept: 109068
% 211.62/212.09 Inuse: 1380
% 211.62/212.09 Deleted: 2360
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 389069
% 211.62/212.09 Kept: 111157
% 211.62/212.09 Inuse: 1410
% 211.62/212.09 Deleted: 2360
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 395494
% 211.62/212.09 Kept: 113340
% 211.62/212.09 Inuse: 1449
% 211.62/212.09 Deleted: 2361
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 403318
% 211.62/212.09 Kept: 115512
% 211.62/212.09 Inuse: 1483
% 211.62/212.09 Deleted: 2362
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 411338
% 211.62/212.09 Kept: 119805
% 211.62/212.09 Inuse: 1493
% 211.62/212.09 Deleted: 2362
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 460639
% 211.62/212.09 Kept: 126268
% 211.62/212.09 Inuse: 1533
% 211.62/212.09 Deleted: 2362
% 211.62/212.09 Deletedinuse: 7
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying clauses:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 470771
% 211.62/212.09 Kept: 128272
% 211.62/212.09 Inuse: 1552
% 211.62/212.09 Deleted: 3084
% 211.62/212.09 Deletedinuse: 12
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 478887
% 211.62/212.09 Kept: 130275
% 211.62/212.09 Inuse: 1572
% 211.62/212.09 Deleted: 3084
% 211.62/212.09 Deletedinuse: 12
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 485975
% 211.62/212.09 Kept: 132294
% 211.62/212.09 Inuse: 1599
% 211.62/212.09 Deleted: 3084
% 211.62/212.09 Deletedinuse: 12
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 494501
% 211.62/212.09 Kept: 134411
% 211.62/212.09 Inuse: 1626
% 211.62/212.09 Deleted: 3089
% 211.62/212.09 Deletedinuse: 15
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 501523
% 211.62/212.09 Kept: 138276
% 211.62/212.09 Inuse: 1631
% 211.62/212.09 Deleted: 3089
% 211.62/212.09 Deletedinuse: 15
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 508838
% 211.62/212.09 Kept: 142209
% 211.62/212.09 Inuse: 1636
% 211.62/212.09 Deleted: 3089
% 211.62/212.09 Deletedinuse: 15
% 211.62/212.09
% 211.62/212.09 Resimplifying inuse:
% 211.62/212.09 Done
% 211.62/212.09
% 211.62/212.09
% 211.62/212.09 Intermediate Status:
% 211.62/212.09 Generated: 516081
% 211.62/212.09 Kept: 146124
% 211.62/212.09 Inuse: 1641
% 211.62/212.09 Deleted: 3089Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------