TSTP Solution File: SWW242+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW242+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:30 EDT 2022
% Result : Timeout 300.10s 300.49s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW242+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jun 4 07:27:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.02/1.55 *** allocated 10000 integers for termspace/termends
% 1.02/1.55 *** allocated 10000 integers for clauses
% 1.02/1.55 *** allocated 10000 integers for justifications
% 1.02/1.55 *** allocated 15000 integers for termspace/termends
% 1.02/1.55 *** allocated 22500 integers for termspace/termends
% 1.02/1.55 *** allocated 33750 integers for termspace/termends
% 1.02/1.55 Bliksem 1.12
% 1.02/1.55
% 1.02/1.55
% 1.02/1.55 Automatic Strategy Selection
% 1.02/1.55
% 1.02/1.55 *** allocated 50625 integers for termspace/termends
% 1.02/1.55 *** allocated 75937 integers for termspace/termends
% 1.02/1.55 *** allocated 113905 integers for termspace/termends
% 1.02/1.55
% 1.02/1.55 Clauses:
% 1.02/1.55
% 1.02/1.55 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.02/1.55 { ! class_Rings_Oidom( t_a ), v_c____ = c_Groups_Ozero__class_Ozero( t_a )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Rings_Oidom( t_a ), ! skol2 = c_Groups_Ozero__class_Ozero( t_a )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a, v_p ), skol2
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.02/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.55 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 1.02/1.55 c_Polynomial_Odegree( X, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.02/1.55 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.02/1.55 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha1( X, Y ), alpha23
% 1.02/1.55 ( X, Y ) }.
% 1.02/1.55 { ! alpha1( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.55 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! alpha23( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.55 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! alpha23( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! alpha23( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha23( X, Y ) }.
% 1.02/1.55 { ! alpha1( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! alpha1( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 1.02/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y ), alpha24( X
% 1.02/1.55 , Y ) }.
% 1.02/1.55 { ! alpha2( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! alpha24( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! alpha24( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! alpha24( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha24( X, Y ) }.
% 1.02/1.55 { ! alpha2( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 1.02/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.55 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.55 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.02/1.55 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.02/1.55 .
% 1.02/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.02/1.55 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.02/1.55 .
% 1.02/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.02/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.02/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.02/1.55 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.55 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.02/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.55 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.55 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.02/1.55 tc_Nat_Onat ) }.
% 1.02/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.02/1.55 tc_Nat_Onat ) }.
% 1.02/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.02/1.55 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.55 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.55 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.02/1.55 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.55 , Y ), X ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.02/1.55 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.02/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.02/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.02/1.55 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.02/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.02/1.55 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.02/1.55 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.55 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.02/1.55 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 1.02/1.55 c_Polynomial_Odegree( X, Z ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.55 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.02/1.55 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.55 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.55 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.55 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.02/1.55 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.02/1.55 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.02/1.55 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.02/1.55 { ! c_Nat_OSuc( X ) = X }.
% 1.02/1.55 { ! X = c_Nat_OSuc( X ) }.
% 1.02/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.02/1.55 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.02/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.02/1.55 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.02/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.02/1.55 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.02/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.02/1.55 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.55 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.55 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.55 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.55 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.55 ), U = Z, T = Y }.
% 1.02/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.55 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.55 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.02/1.55 ) ), Z ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.55 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.55 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.55 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.55 ), ! U = T }.
% 1.02/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.55 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.55 ), ! Z = Y }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.55 = Y }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.55 = Y }.
% 1.02/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( X ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.55 = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.02/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.02/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.02/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( tc_Nat_Onat ) ) = X }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ), X ) = X }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.55 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.02/1.55 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), !
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.02/1.55 tc_Nat_Onat ) ) = Y }.
% 1.02/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.02/1.55 tc_Nat_Onat ) ) = Y }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.02/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.02/1.55 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.02/1.55 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.02/1.55 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.02/1.55 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.02/1.55 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.02/1.55 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.02/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.02/1.55 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.55 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.55 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.02/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.55 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.55 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.02/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.55 .
% 1.02/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.55 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.55 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.55 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.02/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.55 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.02/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.55 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.55 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_Rings_Oidom( t_a ), ! skol3 = c_Groups_Ozero__class_Ozero( t_a )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a,
% 1.02/1.55 c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) ), skol3 ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.55 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.02/1.55 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.02/1.55 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 1.02/1.55 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( t_a ), ! skol4 = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.02/1.55 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 1.02/1.55 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( t_a ), ! v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.02/1.55 t_a ) ), c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If(
% 1.02/1.55 tc_Nat_Onat, c_fequal( skol27, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( t_a ) ) ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.02/1.55 ), c_Nat_OSuc( c_Polynomial_Odegree( t_a, skol27 ) ) ), skol23 ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 1.02/1.55 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( t_a ), v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a
% 1.02/1.55 ) ), c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If(
% 1.02/1.55 tc_Nat_Onat, c_fequal( skol27, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( t_a ) ) ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.02/1.55 ), c_Nat_OSuc( c_Polynomial_Odegree( t_a, skol27 ) ) ), skol23 ) ) =
% 1.02/1.55 c_Nat_OSuc( c_Polynomial_Odegree( t_a, v_cs____ ) ) }.
% 1.02/1.55 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 1.02/1.55 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( t_a ), hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( t_a ), Y ), skol23 ) ), hAPP(
% 1.02/1.55 c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, skol4, skol27 ) ), Y )
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.55 = Y }.
% 1.02/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.55 = Y }.
% 1.02/1.55 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.55 = Y }.
% 1.02/1.55 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.55 = Y }.
% 1.02/1.55 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.02/1.55 ) ), T ), Y ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.55 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.55 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.55 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.02/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.02/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.02/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.02/1.55 ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.02/1.55 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.02/1.55 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.02/1.55 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.02/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.02/1.55 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.02/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.02/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.55 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.02/1.55 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.02/1.55 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 1.02/1.55 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.02/1.55 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.02/1.55 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.02/1.55 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.02/1.55 ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.02/1.55 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 T, Y ), Z = Y }.
% 1.02/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 T, Y ) }.
% 1.02/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 Y, Z ), T = Y }.
% 1.02/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 Y, Z ) }.
% 1.02/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 T, Y ), Z = Y }.
% 1.02/1.55 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 T, Y ), Z = Y }.
% 1.02/1.55 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 Y, T ), Z = Y }.
% 1.02/1.55 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.02/1.55 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.02/1.55 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 1.02/1.55 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.55 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.02/1.55 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.55 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.55 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.02/1.55 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.02/1.55 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.02/1.55 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.02/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.02/1.55 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.02/1.55 .
% 1.02/1.55 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.02/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.02/1.55 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.02/1.55 X, Z ), Y ) ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.02/1.55 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 1.02/1.55 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.02/1.55 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.02/1.55 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.02/1.55 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.55 ( X ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.55 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.55 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.02/1.55 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.02/1.55 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.02/1.55 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.02/1.55 c_Polynomial_Ocoeff( X, Y ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.02/1.55 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol5( X
% 1.02/1.55 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol5( X, Y, Z ) ), Z = Y
% 1.02/1.55 }.
% 1.02/1.55 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.55 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ) ) = Z }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.55 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 1.02/1.55 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.02/1.55 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 1.02/1.55 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.02/1.55 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.55 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.02/1.55 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.55 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.55 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.55 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.02/1.55 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.02/1.55 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.55 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.02/1.55 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.02/1.55 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.02/1.55 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.02/1.55 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.02/1.55 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.02/1.55 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.02/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.02/1.55 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.02/1.55 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.02/1.55 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.55 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.02/1.55 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 1.02/1.55 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 1.02/1.55 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 1.02/1.55 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.02/1.55 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.02/1.55 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 1.02/1.55 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.55 ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.02/1.55 .
% 1.02/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.02/1.55 .
% 1.02/1.55 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ) }.
% 1.02/1.55 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.02/1.55 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.02/1.55 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 1.02/1.55 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 1.02/1.55 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 1.02/1.55 , Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.55 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.02/1.55 .
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.02/1.55 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.02/1.55 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.02/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.02/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.55 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.02/1.55 ) ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.02/1.55 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.02/1.55 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.02/1.55 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.55 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.55 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.55 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.55 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.55 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.55 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 = Y }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( X ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.55 , Y ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.55 = Y }.
% 1.02/1.55 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.55 ( X, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.55 ) ), Y ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.55 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.55 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.55 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.55 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.55 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.55 ( X, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.55 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.55 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.02/1.55 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.02/1.55 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.02/1.55 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.55 Y ) ) = Y }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 Z, Y ) ) = Y }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.55 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.02/1.55 c_Polynomial_Odegree( X, Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.02/1.55 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.55 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.02/1.55 .
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.02/1.55 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 X ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.55 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.55 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.02/1.55 ( X, Y ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.55 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 Z ) = Y }.
% 1.02/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.55 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.55 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.55 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 1.02/1.55 Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.55 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.02/1.55 ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.55 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.02/1.55 , Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 1.02/1.55 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.55 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.55 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.02/1.55 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.55 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.02/1.55 c_Polynomial_Odegree( X, Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.55 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.55 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 1.02/1.55 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.02/1.55 .
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.55 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.55 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.02/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.02/1.55 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.02/1.55 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.55 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.02/1.55 ( X, Z ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.55 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.02/1.55 Y ) ) ), Y ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.55 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 1.02/1.55 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.55 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.02/1.55 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.02/1.55 Y ) ) ), Y ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.02/1.55 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 1.02/1.55 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.55 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.02/1.55 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.02/1.55 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 1.02/1.55 c_Polynomial_OpCons( X, T,
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.02/1.55 .
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.55 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.55 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 1.02/1.55 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.55 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.55 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.55 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.55 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.02/1.55 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.02/1.55 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.55 Z, T ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.02/1.55 ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( tc_Int_Oint ) ) = X }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Int_Oint ), X ) = X }.
% 1.02/1.55 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.55 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.02/1.55 ( tc_Int_Oint ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.02/1.55 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.55 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 1.02/1.55 , Z, Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.55 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.55 , Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.55 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.55 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.55 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.55 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.55 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 1.02/1.55 X, T, Z ), Y ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.02/1.55 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.02/1.55 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.02/1.55 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.55 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), !
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 1.02/1.55 c_Polynomial_Odegree( X, Z ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha3( X
% 1.02/1.55 , Y, T ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha25( X
% 1.02/1.55 , Y, Z, T ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! alpha3( X, Y, T ), ! alpha25( X, Y, Z, T )
% 1.02/1.55 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 1.02/1.55 ( X, T, Z ), Y ) }.
% 1.02/1.55 { ! alpha25( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.55 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha25( X, Y, Z, T ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha25( X
% 1.02/1.55 , Y, Z, T ) }.
% 1.02/1.55 { ! alpha3( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 1.02/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha3( X
% 1.02/1.55 , Y, Z ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 1.02/1.55 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.55 , Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.02/1.55 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.02/1.55 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.55 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 X ) }.
% 1.02/1.55 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 1.02/1.55 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 1.02/1.55 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.02/1.55 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.02/1.55 hAPP( Z, skol6( U, W, Z ) ) ) }.
% 1.02/1.55 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.02/1.55 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol6( X
% 1.02/1.55 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.02/1.55 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.02/1.55 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol24( X,
% 1.02/1.55 Y, Z ) ) ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, Y ), alpha56( X, Y, Z, T ), ! Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, Y ), alpha56( X, Y, Z, T ), ! hAPP(
% 1.02/1.55 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 1.02/1.55 .
% 1.02/1.55 { ! alpha56( X, Y, Z, T ), alpha58( X, Y, Z, T ), alpha53( X, Y, T ) }.
% 1.02/1.55 { ! alpha56( X, Y, Z, T ), alpha58( X, Y, Z, T ), ! hAPP(
% 1.02/1.55 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! alpha58( X, Y, Z, T ), alpha56( X, Y, Z, T ) }.
% 1.02/1.55 { ! alpha53( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.02/1.55 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 alpha56( X, Y, Z, T ) }.
% 1.02/1.55 { ! alpha58( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.55 ( X ), Z, T ), alpha59( X, Y, Z, T ) }.
% 1.02/1.55 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha58( X, Y
% 1.02/1.55 , Z, T ) }.
% 1.02/1.55 { ! alpha59( X, Y, Z, T ), alpha58( X, Y, Z, T ) }.
% 1.02/1.55 { ! alpha59( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.02/1.55 ), skol7( X, Y, U, W ), Y ) }.
% 1.02/1.55 { ! alpha59( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.02/1.55 ), skol7( X, Y, U, T ), T ) }.
% 1.02/1.55 { ! alpha59( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.55 ( X ), skol7( X, Y, Z, T ), Z ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha59( X, Y
% 1.02/1.55 , Z, T ) }.
% 1.02/1.55 { ! alpha53( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! alpha53( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha53( X, Y, Z
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.55 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 1.02/1.55 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.02/1.55 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.55 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.55 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.02/1.55 ( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X
% 1.02/1.55 , Z, Y ) ) = c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) }
% 1.02/1.55 .
% 1.02/1.55 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.55 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 1.02/1.55 .
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.02/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 1.02/1.55 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 1.02/1.55 ) ) }.
% 1.02/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.55 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.55 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.02/1.55 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.02/1.55 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 1.02/1.55 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.55 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.02/1.55 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.55 , Y ) ) = Y }.
% 1.02/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.02/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.55 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.55 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.02/1.55 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.55 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.55 X, Y ) ) = Y }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.55 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( X ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.55 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.55 = Y }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.02/1.55 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.55 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.55 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.02/1.55 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 1.02/1.55 ) ), Y ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.55 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.55 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.55 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.55 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.55 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Int_Oint, Y, X ) }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.02/1.55 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.55 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.55 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.55 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.55 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.55 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.02/1.55 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.55 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.02/1.55 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 1.02/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 1.02/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.55 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.55 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.55 ) ), Z ) }.
% 1.02/1.55 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.55 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.55 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.02/1.55 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.55 W ) ), U ), Y ) }.
% 1.02/1.55 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.55 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), Z ), U ), Y ) }.
% 1.02/1.55 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.55 Z ) ), U ), T ) = Y }.
% 1.02/1.55 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.55 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), Z ), U ), Y ) }.
% 1.02/1.55 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.55 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.55 Z ) ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.55 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.02/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.55 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.02/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.02/1.55 }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.55 X, Y ) }.
% 1.02/1.55 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.55 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.02/1.55 X, Y ) ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.02/1.55 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.55 , Y ) ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.55 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.55 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.55 X, Z, Y ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.02/1.55 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.02/1.55 , Z ), X ) ), T ) ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Int_Oint, U, T ) ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.55 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.55 X ) ) }.
% 1.02/1.55 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ) ) = Y }.
% 1.02/1.55 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), c_Nat_OSuc( X ) ) = hAPP( Y, X )
% 1.02/1.55 }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.55 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.02/1.55 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.02/1.55 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.02/1.55 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Y ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.55 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.02/1.55 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.02/1.55 .
% 1.02/1.55 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.02/1.55 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 1.02/1.55 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 1.02/1.55 tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.02/1.55 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.55 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.02/1.55 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.55 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.02/1.55 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.02/1.55 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.02/1.55 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.55 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.02/1.55 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.55 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.55 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.55 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.02/1.55 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.02/1.55 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.55 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Nat_Onat, Z, X ) }.
% 1.02/1.55 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Nat_Onat, Y, Z ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.02/1.55 , Z ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.02/1.55 Z, Y ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.55 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Nat_Onat, Y, Z ) }.
% 1.02/1.55 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Nat_Onat, Y, Z ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.55 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.55 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.55 { ! alpha4( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! alpha4( X, Y ), ! Y = X }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha4( X, Y ) }
% 1.02/1.55 .
% 1.02/1.55 { ! alpha4( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! alpha4( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), alpha4( X, Y ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha5( X, Y ), Y = X }
% 1.02/1.55 .
% 1.02/1.55 { ! alpha5( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! alpha5( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! alpha5( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.55 ( tc_Nat_Onat, X, Y ), alpha5( X, Y ) }.
% 1.02/1.55 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 1.02/1.55 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 1.02/1.55 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.55 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ) ) }.
% 1.02/1.55 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.02/1.55 tc_Nat_Onat ), X ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.55 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.02/1.55 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.55 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.55 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 1.02/1.55 , Y = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 1.02/1.55 = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.55 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Int_Oint, Z, X ) }.
% 1.02/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.02/1.55 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.02/1.55 ) }.
% 1.02/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.55 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.55 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.02/1.55 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.55 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 1.02/1.55 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 1.02/1.55 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 1.02/1.55 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X, Z, Y ) =
% 1.02/1.55 c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 1.02/1.55 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.02/1.55 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.55 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.02/1.55 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.02/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.02/1.55 X ) ) }.
% 1.02/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.55 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, Z, Y ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.02/1.55 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, Z, Y ) }.
% 1.02/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.55 , T ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.55 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.55 , T, Y ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.55 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.55 , Y, T ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.55 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, Z, Y ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.55 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.55 , T, Y ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, T, Y ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.55 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.55 , Y, Z ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.55 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.02/1.55 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.55 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.02/1.55 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.55 ( X, Y ), Z ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.55 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.55 ( X, Z ), Y ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.55 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 1.02/1.55 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.02/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ), X ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Nat_Onat ), X ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.02/1.55 .
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.02/1.55 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.02/1.55 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.02/1.55 .
% 1.02/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.02/1.55 .
% 1.02/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.02/1.55 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.02/1.55 X ) ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.55 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.02/1.55 }.
% 1.02/1.55 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.02/1.55 , X ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.02/1.55 .
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.02/1.55 .
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.55 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.02/1.55 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.55 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.02/1.55 .
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.55 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.55 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.55 ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.55 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.55 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 1.02/1.55 ( X ), Z, Y ) ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.02/1.55 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.02/1.55 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.55 { alpha54( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.02/1.55 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.02/1.55 { alpha54( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.02/1.55 ( X, Y ), Z ) ) }.
% 1.02/1.55 { ! alpha54( X, Y, Z ), alpha57( X, Y, Z ), Z = Y }.
% 1.02/1.55 { ! alpha54( X, Y, Z ), alpha57( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.02/1.55 ) ) }.
% 1.02/1.55 { ! alpha57( X, Y, Z ), alpha54( X, Y, Z ) }.
% 1.02/1.55 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha54( X, Y, Z ) }.
% 1.02/1.55 { ! alpha57( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.02/1.55 }.
% 1.02/1.55 { ! alpha57( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.02/1.55 X, Y ), Z ) ), alpha57( X, Y, Z ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.02/1.55 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.02/1.55 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 1.02/1.55 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.55 X, Y, Z ) }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.02/1.55 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.55 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.55 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 1.02/1.55 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.55 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.02/1.55 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.02/1.55 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.55 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.55 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.02/1.55 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 1.02/1.55 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 1.02/1.55 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 1.02/1.55 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 1.02/1.55 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.55 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha6( X, Y, Z, T ),
% 1.02/1.55 alpha26( X, Y, Z, T ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z, T ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha26( X, Y, Z, T ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.55 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.55 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha26( X, Y, Z, T ) }.
% 1.02/1.55 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.55 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.55 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha6( X, Y, Z, T ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha7( X, Y, Z, T ),
% 1.02/1.55 alpha27( X, Y, Z, T ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z, T ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha27( X, Y, Z, T ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.55 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.55 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.55 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha27( X, Y, Z, T ) }.
% 1.02/1.55 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.02/1.55 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.55 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.02/1.55 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha7( X, Y, Z, T ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.55 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.55 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.55 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.55 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( X ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.55 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( X ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.02/1.55 .
% 1.02/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.55 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.02/1.55 .
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.55 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.55 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.55 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.55 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( X ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.02/1.55 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.55 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.55 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.02/1.55 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.55 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.55 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.55 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.55 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.55 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.55 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.55 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.02/1.55 ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.55 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.55 ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.55 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.55 ( X ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.55 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.55 , Z, Y ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.55 .
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.55 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.55 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.55 , Y ) }.
% 1.02/1.55 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.55 , Y ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.55 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.55 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.55 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.55 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.55 .
% 1.02/1.55 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.55 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.55 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.55 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.55 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.55 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.55 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.55 ) }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.02/1.55 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.02/1.55 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.02/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.55 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.55 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.55 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.55 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.56 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.56 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.56 , Y ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.56 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( X ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol8( X ) ) }.
% 1.02/1.56 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 1.02/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.56 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.56 c_Nat_OSuc( X ) ) }.
% 1.02/1.56 { ! alpha8( X, Y ), Y = c_Nat_OSuc( skol9( Z, Y ) ) }.
% 1.02/1.56 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol9( X, Y
% 1.02/1.56 ), X ) }.
% 1.02/1.56 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.02/1.56 ), alpha8( X, Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.02/1.56 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ), Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) ) }.
% 1.02/1.56 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ), Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ), Z ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.56 Y ), X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.56 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.56 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.56 tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.56 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.56 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.56 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.56 ), X ) ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.56 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.56 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.02/1.56 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.02/1.56 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.02/1.56 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.02/1.56 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.02/1.56 ), X ) ) }.
% 1.02/1.56 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.02/1.56 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.02/1.56 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.02/1.56 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.02/1.56 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.02/1.56 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.02/1.56 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.02/1.56 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.02/1.56 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.56 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.56 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.02/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.56 X, W, Z ) ), U ), T ), Y ) }.
% 1.02/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), Z ), U ), Y ) ) }.
% 1.02/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.02/1.56 ( X, Z, W ) ), U ), Y ) ) }.
% 1.02/1.56 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.02/1.56 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.56 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.56 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.56 ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.02/1.56 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.02/1.56 ) ) = X }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.02/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.02/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.56 , ! alpha9( X, Y, Z ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.56 , ! alpha28( X, Y, Z ) }.
% 1.02/1.56 { alpha9( X, Y, Z ), alpha28( X, Y, Z ), hBOOL( hAPP( Z,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.56 { ! alpha28( X, Y, Z ), ! hBOOL( hAPP( Z, skol11( T, U, Z ) ) ) }.
% 1.02/1.56 { ! alpha28( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.56 skol11( X, Y, Z ) ) }.
% 1.02/1.56 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.02/1.56 ) ), alpha28( X, Y, Z ) }.
% 1.02/1.56 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.02/1.56 .
% 1.02/1.56 { ! alpha9( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ) ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha9( X, Y, Z ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.56 , alpha10( X, Y, Z ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.56 , alpha29( X, Y, Z ) }.
% 1.02/1.56 { ! alpha10( X, Y, Z ), ! alpha29( X, Y, Z ), hBOOL( hAPP( Z,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.56 { ! alpha29( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.56 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Z, skol12( T, U, Z ) ) ), alpha29( X, Y, Z ) }.
% 1.02/1.56 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol12( X, Y, Z ) ),
% 1.02/1.56 alpha29( X, Y, Z ) }.
% 1.02/1.56 { ! alpha10( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.02/1.56 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha10( X, Y, Z ) }
% 1.02/1.56 .
% 1.02/1.56 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha10
% 1.02/1.56 ( X, Y, Z ) }.
% 1.02/1.56 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.02/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.02/1.56 c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.02/1.56 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.02/1.56 ( X ), Y ), Z ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.02/1.56 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.02/1.56 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.02/1.56 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.02/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.02/1.56 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.02/1.56 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ), Y ) }.
% 1.02/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.02/1.56 ), X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 X ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 X ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 1.02/1.56 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ) }.
% 1.02/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.02/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.56 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 1.02/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 1.02/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.56 tc_Nat_Onat, Y, X ), X ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.02/1.56 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.02/1.56 tc_Int_Oint, Z, X ), Y ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.02/1.56 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.02/1.56 tc_Int_Oint, Z, Y ), X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.56 tc_Nat_Onat, Y, X ), X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.56 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.56 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.56 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol13( X, Y ) ) }.
% 1.02/1.56 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 1.02/1.56 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.56 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol14( X, Y ) ) }.
% 1.02/1.56 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 1.02/1.56 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 1.02/1.56 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.56 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 1.02/1.56 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.56 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.56 ( tc_Int_Oint, Y ), X ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.56 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 1.02/1.56 ( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 1.02/1.56 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 1.02/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 1.02/1.56 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 1.02/1.56 }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.02/1.56 ( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.56 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), c_Rings_Odvd__class_Odvd
% 1.02/1.56 ( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus
% 1.02/1.56 ( tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y )
% 1.02/1.56 = c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.02/1.56 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.02/1.56 ( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.56 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Int_Oint, Y, X ), X ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.56 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.02/1.56 = X }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.56 tc_Int_Oint ) ) ) }.
% 1.02/1.56 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.56 tc_Int_Oint ) ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.02/1.56 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.02/1.56 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.02/1.56 alpha11( X, Y, Z ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.02/1.56 alpha30( X, Y, Z ) }.
% 1.02/1.56 { ! alpha11( X, Y, Z ), ! alpha30( X, Y, Z ), hBOOL( hAPP( Z,
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.56 { ! alpha30( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.56 alpha41( X, Y, Z ) }.
% 1.02/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha30( X, Y, Z ) }.
% 1.02/1.56 { ! alpha41( X, Y, Z ), alpha30( X, Y, Z ) }.
% 1.02/1.56 { ! alpha41( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.02/1.56 ), alpha47( X, Y, Z, T ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol15( X, T, U ), X ),
% 1.02/1.56 alpha41( X, Y, Z ) }.
% 1.02/1.56 { ! alpha47( X, Y, Z, skol15( X, Y, Z ) ), alpha41( X, Y, Z ) }.
% 1.02/1.56 { ! alpha47( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.02/1.56 hBOOL( hAPP( Z, T ) ) }.
% 1.02/1.56 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol16( X, Y, T ) ), T
% 1.02/1.56 ), alpha47( X, Y, Z, T ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Z, T ) ), alpha47( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha11( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.56 hBOOL( hAPP( Z, Y ) ) }.
% 1.02/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y, Z ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Z, Y ) ), alpha11( X, Y, Z ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.02/1.56 tc_Nat_Onat ), X ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X )
% 1.02/1.56 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.56 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.56 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.56 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.02/1.56 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 1.02/1.56 X, Z, Y ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 1.02/1.56 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.02/1.56 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.02/1.56 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 1.02/1.56 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.02/1.56 ), Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 1.02/1.56 , Y ) ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.02/1.56 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.02/1.56 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 1.02/1.56 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 1.02/1.56 ), Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 1.02/1.56 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.56 T, Y ), Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 1.02/1.56 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.56 T, Z ), Y ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.02/1.56 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.02/1.56 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.02/1.56 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.02/1.56 ), Z ), Y ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.02/1.56 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 1.02/1.56 , Y ) ), Y ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 1.02/1.56 ( X, Y, Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 1.02/1.56 ( X, Z, Y ) }.
% 1.02/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.02/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 1.02/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 1.02/1.56 Y ) ), Y ) }.
% 1.02/1.56 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.02/1.56 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 1.02/1.56 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 1.02/1.56 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 1.02/1.56 , U ), Z ) }.
% 1.02/1.56 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.02/1.56 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 1.02/1.56 , Y ) ), Y ) }.
% 1.02/1.56 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.02/1.56 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 1.02/1.56 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 1.02/1.56 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.56 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 1.02/1.56 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 1.02/1.56 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.56 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.02/1.56 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.02/1.56 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Polynomial_Osmult( X,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.56 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ),
% 1.02/1.56 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y )
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.56 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.56 , alpha42( X, Y, Z, T ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha42( X, Y, Z, T ),
% 1.02/1.56 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.02/1.56 { ! alpha42( X, Y, Z, T ), alpha12( X, Z, T ) }.
% 1.02/1.56 { ! alpha42( X, Y, Z, T ), alpha31( X, Y, T ) }.
% 1.02/1.56 { ! alpha12( X, Z, T ), ! alpha31( X, Y, T ), alpha42( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha31( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), alpha43( X, Y, Z ) }.
% 1.02/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha31( X
% 1.02/1.56 , Y, Z ) }.
% 1.02/1.56 { ! alpha43( X, Y, Z ), alpha31( X, Y, Z ) }.
% 1.02/1.56 { ! alpha43( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.02/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha43( X
% 1.02/1.56 , Y, Z ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.02/1.56 ), c_Polynomial_Odegree( X, Z ) ), alpha43( X, Y, Z ) }.
% 1.02/1.56 { ! alpha12( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha12( X,
% 1.02/1.56 Y, Z ) }.
% 1.02/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha12( X
% 1.02/1.56 , Y, Z ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.56 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 1.02/1.56 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.02/1.56 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.02/1.56 , Y, Z ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.02/1.56 , Y, Z ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 1.02/1.56 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha13( X, Y, Z ), alpha32( X,
% 1.02/1.56 Y, Z ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.02/1.56 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.02/1.56 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.56 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.56 ), alpha32( X, Y, Z ) }.
% 1.02/1.56 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.56 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 ), alpha13( X, Y, Z ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha14( X, Y, Z ), alpha33
% 1.02/1.56 ( X, Y, Z ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha14( X, Y, Z
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha33( X, Y, Z
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.56 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.56 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 ), alpha33( X, Y, Z ) }.
% 1.02/1.56 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.56 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.56 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.56 ), alpha14( X, Y, Z ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 1.02/1.56 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha34( X, Y, Z, T ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha15( X, Y, Z ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha34( X, Y, Z, T ), !
% 1.02/1.56 alpha15( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 1.02/1.56 { ! alpha34( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.02/1.56 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha34( X, Y, Z, T ) }.
% 1.02/1.56 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha34(
% 1.02/1.56 X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha15( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { Z = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 1.02/1.56 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha35( X, Y, Z, T ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha16( X, Y, T ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha35( X, Y, Z, T ), !
% 1.02/1.56 alpha16( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.02/1.56 { ! alpha35( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.02/1.56 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha35( X, Y, Z, T ) }.
% 1.02/1.56 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha35(
% 1.02/1.56 X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha16( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { Y = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 1.02/1.56 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.02/1.56 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.02/1.56 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 1.02/1.56 ( X ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.02/1.56 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.02/1.56 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 1.02/1.56 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.56 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.02/1.56 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 1.02/1.56 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 1.02/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Y, Z ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 1.02/1.56 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.02/1.56 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.56 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.02/1.56 { ! class_RealVector_Oreal__normed__field( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.56 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.02/1.56 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 1.02/1.56 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.02/1.56 { ! class_RealVector_Oreal__normed__field( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.56 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.56 ), Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 1.02/1.56 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.02/1.56 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.02/1.56 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.56 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.56 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.02/1.56 { ! class_RealVector_Oreal__normed__field( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.56 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 1.02/1.56 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.56 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 1.02/1.56 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_RealVector_Oreal__normed__field( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.02/1.56 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Z
% 1.02/1.56 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.56 Y ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X )
% 1.02/1.56 , Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 Z, Y ) ), alpha36( X, Y, Z, T ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 Z, Y ) ), alpha44( X, Y, Z, T ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 1.02/1.56 , T ), ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.56 { ! alpha44( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), alpha48( X, Y, Z, T ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.02/1.56 , alpha44( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha48( X, Y, Z, T ), alpha44( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha48( X, Y, Z, T ), alpha51( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha48( X, Y, Z, T ), alpha17( X, Y, T ) }.
% 1.02/1.56 { ! alpha51( X, Y, Z, T ), ! alpha17( X, Y, T ), alpha48( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha51( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.56 alpha51( X, Y, Z, T ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha51( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha36( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.56 alpha36( X, Y, Z, T ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha36( X, Y, Z, T )
% 1.02/1.56 }.
% 1.02/1.56 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.56 , alpha17( X, Y, Z ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.56 , alpha17( X, Y, Z ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.02/1.56 Z ), Y ), alpha37( X, Y, Z, T ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.02/1.56 Z ), Y ), alpha45( X, Y, Z, T ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 1.02/1.56 , T ), ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.02/1.56 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), alpha49( X, Y, Z, T ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.56 , alpha45( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha49( X, Y, Z, T ), alpha45( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha49( X, Y, Z, T ), alpha52( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha49( X, Y, Z, T ), alpha18( X, Y, Z ) }.
% 1.02/1.56 { ! alpha52( X, Y, Z, T ), ! alpha18( X, Y, Z ), alpha49( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha52( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.56 alpha52( X, Y, Z, T ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha52( X, Y, Z, T )
% 1.02/1.56 }.
% 1.02/1.56 { ! alpha37( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.56 alpha37( X, Y, Z, T ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha37( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.56 , alpha18( X, Y, Z ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.02/1.56 , alpha18( X, Y, Z ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 Z, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.02/1.56 Y ), Z ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.02/1.56 Y ), Z ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 Z, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 Z, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.02/1.56 Y ), Z ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.02/1.56 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.02/1.56 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 1.02/1.56 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.02/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 1.02/1.56 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.02/1.56 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.02/1.56 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.02/1.56 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.56 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.02/1.56 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.56 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.02/1.56 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 1.02/1.56 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 1.02/1.56 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.56 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.02/1.56 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.02/1.56 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.56 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.56 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 1.02/1.56 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 1.02/1.56 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 1.02/1.56 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 1.02/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 1.02/1.56 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.02/1.56 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 1.02/1.56 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 1.02/1.56 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Z ) ), T ) =
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.56 Y ) ), c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus
% 1.02/1.56 ( X, Y, Z ), T ) ) ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.56 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.56 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.56 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.56 alpha19( X, Y, Z ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.56 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! alpha19( X, Y, Z ),
% 1.02/1.56 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.02/1.56 { ! alpha19( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.56 alpha19( X, Y, Z ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.56 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.56 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.56 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ), Y ) = hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ),
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 1.02/1.56 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, Z ) ),
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.02/1.56 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.02/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y,
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.56 ( tc_Int_Oint, Y ), X ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.56 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) }.
% 1.02/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 1.02/1.56 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 1.02/1.56 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 1.02/1.56 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.02/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, X, Y ) ) = c_Divides_Odiv__class_Odiv( tc_Int_Oint,
% 1.02/1.56 c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ), c_Groups_Oabs__class_Oabs(
% 1.02/1.56 tc_Int_Oint, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.56 ) ) = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X
% 1.02/1.56 , Y ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.02/1.56 ( hAPP( c_Power_Opower__class_Opower( X ),
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) ) =
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.56 ), Z ), Y ) ) }.
% 1.02/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.02/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), c_Groups_Oabs__class_Oabs
% 1.02/1.56 ( tc_Int_Oint, Y ) = c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Oinverse( X, Y ) )
% 1.02/1.56 = c_Rings_Oinverse__class_Oinverse( X, c_Groups_Oabs__class_Oabs( X, Y )
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.02/1.56 = c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z )
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oabs__class_Oabs( X, Y ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), c_Rings_Odvd__class_Odvd( X, c_Groups_Oabs__class_Oabs( X, Z ), Y ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oabs__class_Oabs( X, Z )
% 1.02/1.56 = c_Groups_Oabs__class_Oabs( X, Y ), c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Oabs__class_Oabs( X, Y ) ) =
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.02/1.56 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( X ), c_Groups_Oabs__class_Oabs( X, Z ) ), Y
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X,
% 1.02/1.56 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) )
% 1.02/1.56 = c_Groups_Oplus__class_Oplus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 1.02/1.56 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.02/1.56 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 1.02/1.56 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, Y, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.02/1.56 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 1.02/1.56 , Z ) ) }.
% 1.02/1.56 { ! class_Divides_Oring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z
% 1.02/1.56 ) = c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Odiv( X, Y
% 1.02/1.56 , Z ) ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( X ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 1.02/1.56 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 1.02/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.56 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.02/1.56 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 1.02/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.02/1.56 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.02/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.56 tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) =
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.56 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, X ) = c_Groups_Oone__class_Oone
% 1.02/1.56 ( tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, X,
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.56 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) = X }.
% 1.02/1.56 { ! c_Groups_Oabs__class_Oabs( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), c_Groups_Oabs__class_Oabs(
% 1.02/1.56 tc_Int_Oint, X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z, Y )
% 1.02/1.56 ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z
% 1.02/1.56 ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 X ), c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.02/1.56 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs(
% 1.02/1.56 X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, Z, Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.56 X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Z ), Y )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Oabs__class_Oabs( X, Z ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Groups_Oabs__class_Oabs( X, U ), T ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oabs__class_Oabs( X, Z ) ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, U ) ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ), ! Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.02/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Int_Oint ) ) = X }.
% 1.02/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Int_Oint ), Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Groups_Oabs__if( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.56 { ! class_Groups_Oabs__if( X ), c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Oabs__class_Oabs( X, Y ) = Y
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.56 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oabs__class_Oabs( X, Z ), Y
% 1.02/1.56 ) = c_Groups_Oabs__class_Oabs( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.02/1.56 , Y ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, X, Y ), X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, Z, Y ), X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.02/1.56 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oabs__class_Oabs(
% 1.02/1.56 tc_Int_Oint, X ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 1.02/1.56 tc_Int_Oint, X ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Groups_Oabs__class_Oabs(
% 1.02/1.56 tc_Int_Oint, X ) = X }.
% 1.02/1.56 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.02/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.56 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 1.02/1.56 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 1.02/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) =
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.02/1.56 ( tc_Int_Oint, X, Y ) ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Divides_Odiv__class_Odiv
% 1.02/1.56 ( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 1.02/1.56 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.02/1.56 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 1.02/1.56 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.02/1.56 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 1.02/1.56 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 1.02/1.56 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 1.02/1.56 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 1.02/1.56 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 1.02/1.56 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 1.02/1.56 ( X, Z, Y ) = T }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.56 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 1.02/1.56 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 1.02/1.56 , Z ) ) = Y }.
% 1.02/1.56 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.56 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 1.02/1.56 ), Y ) ) = Z }.
% 1.02/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.02/1.56 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 1.02/1.56 tc_Int_Oint ) }.
% 1.02/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.02/1.56 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) = c_Groups_Oone__class_Oone(
% 1.02/1.56 tc_Int_Oint ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ), X ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 1.02/1.56 , c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ), ! Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.56 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 1.02/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( tc_Int_Oint, Y ) ), X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 1.02/1.56 ) ) }.
% 1.02/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.02/1.56 ( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.02/1.56 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.02/1.56 ( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) =
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint,
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Odiv
% 1.02/1.56 ( tc_Int_Oint, Y, X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Groups_Oplus__class_Oplus
% 1.02/1.56 ( tc_Int_Oint, c_Groups_Oabs__class_Oabs( tc_Int_Oint,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ),
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 1.02/1.56 ), Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus
% 1.02/1.56 ( X, Z, Y ), T ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, T, Z )
% 1.02/1.56 ), Y ), c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus
% 1.02/1.56 ( X, Z, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Ominus__class_Ominus( X, Z, Y ), T ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.02/1.56 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oabs__class_Oabs( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, T, Z ) ), Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), c_Groups_Osgn__class_Osgn(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Oone__class_Oone(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.56 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), Y ), c_Groups_Osgn__class_Osgn(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.56 tc_Polynomial_Opoly( X ), c_Groups_Oone__class_Oone( tc_Polynomial_Opoly
% 1.02/1.56 ( X ) ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Osgn__class_Osgn( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Z, Y,
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) = X }.
% 1.02/1.56 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.56 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 1.02/1.56 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Oabs__class_Oabs( X, Y ) =
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.02/1.56 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Y ) ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) = Y }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Y ) ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.56 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.02/1.56 ( X ), Z, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.56 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.02/1.56 ( X ), Z, Y ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.02/1.56 ( X ), T, Z ), Y ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.02/1.56 { ! class_Groups_Osgn__if( X ), c_Groups_Osgn__class_Osgn( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.02/1.56 ( X, c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.02/1.56 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.56 X ), c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.02/1.56 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Groups_Osgn__class_Osgn( X, Y ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), c_Groups_Osgn__class_Osgn( X, Z ) ),
% 1.02/1.56 c_Groups_Osgn__class_Osgn( X, Y ) ) }.
% 1.02/1.56 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.02/1.56 c_Groups_Osgn__class_Osgn( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.56 X ), Z ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.56 c_Groups_Osgn__class_Osgn( X, Z ) ), c_Groups_Osgn__class_Osgn( X, Y ) )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.02/1.56 c_Groups_Osgn__class_Osgn( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.02/1.56 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.56 { ! class_RealVector_Oreal__normed__vector( X ), c_Groups_Osgn__class_Osgn
% 1.02/1.56 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Osgn__class_Osgn( X, Y ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), c_Groups_Osgn__class_Osgn( X,
% 1.02/1.56 c_Groups_Osgn__class_Osgn( X, Y ) ) = c_Groups_Osgn__class_Osgn( X, Y ) }
% 1.02/1.56 .
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.02/1.56 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 1.02/1.56 ) ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.02/1.56 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Divides_Odiv__class_Odiv
% 1.02/1.56 ( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.02/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Divides_Odiv__class_Omod
% 1.02/1.56 ( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.56 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), X ) =
% 1.02/1.56 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Divides_Odiv__class_Omod
% 1.02/1.56 ( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T,
% 1.02/1.56 c_Polynomial_Osmult( X, Y, Z ) ) = c_Polynomial_Osmult( X,
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Polynomial_Opoly( X ), T, Z ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.02/1.56 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), Z, Y ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.02/1.56 = c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 1.02/1.56 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , c_Groups_Ozero__class_Ozero( X ), Y ), c_Groups_Osgn__class_Osgn( X, Y
% 1.02/1.56 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ), Z ), c_Divides_Odiv__class_Omod(
% 1.02/1.56 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.02/1.56 ( X ), T, Z ), Y ) ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X
% 1.02/1.56 ), T, Z ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.02/1.56 ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.56 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.02/1.56 , c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.56 tc_Nat_Onat, Y, X ), X ) ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.02/1.56 alpha20( X, Z ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.02/1.56 alpha38( X, Y, Z ) }.
% 1.02/1.56 { ! alpha20( X, Z ), ! alpha38( X, Y, Z ), hBOOL( hAPP( Z,
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.56 { ! alpha38( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.56 alpha46( X, Y, Z ) }.
% 1.02/1.56 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha38( X, Y, Z ) }.
% 1.02/1.56 { ! alpha46( X, Y, Z ), alpha38( X, Y, Z ) }.
% 1.02/1.56 { ! alpha46( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.02/1.56 ), alpha50( X, Y, Z, T ) }.
% 1.02/1.56 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol17( X, T, U ), X ),
% 1.02/1.56 alpha46( X, Y, Z ) }.
% 1.02/1.56 { ! alpha50( X, Y, Z, skol17( X, Y, Z ) ), alpha46( X, Y, Z ) }.
% 1.02/1.56 { ! alpha50( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.02/1.56 hBOOL( hAPP( Z, U ) ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Z, skol18( U, W, Z, V0 ) ) ), alpha50( X, Y, Z, T ) }.
% 1.02/1.56 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol18( X, Y, Z, T ) )
% 1.02/1.56 , T ), alpha50( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha20( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.56 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.56 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha20( X, Y ) }.
% 1.02/1.56 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha20
% 1.02/1.56 ( X, Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) ), c_Groups_Oabs__class_Oabs(
% 1.02/1.56 tc_Polynomial_Opoly( X ), Y ) = Y }.
% 1.02/1.56 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ),
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.56 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) ), X ) ) }.
% 1.02/1.56 { ! class_Groups_Osgn__if( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.56 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.56 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.56 { ! class_Groups_Osgn__if( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.56 c_Groups_Osgn__class_Osgn( X, Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.56 c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Osgn__class_Osgn( X, Y )
% 1.02/1.56 = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 1.02/1.56 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.56 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Osgn__class_Osgn( X, Y
% 1.02/1.56 ) = c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.56 }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 1.02/1.56 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 1.02/1.56 ) ), ! alpha21( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), alpha21( X, Y, skol19( X, Y, Z ), skol25( X, Y, Z )
% 1.02/1.56 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 1.02/1.56 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.56 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol19( X, Y, Z ) ), skol25
% 1.02/1.56 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 1.02/1.56 ) }.
% 1.02/1.56 { ! alpha21( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 1.02/1.56 { ! alpha21( X, Y, Z, T ), alpha39( X, Y, Z, T ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha39( X, Y, Z, T )
% 1.02/1.56 , alpha21( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha39( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.02/1.56 ) }.
% 1.02/1.56 { ! alpha39( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.02/1.56 .
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha39( X,
% 1.02/1.56 Y, Z, T ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha22( X, Y, T,
% 1.02/1.56 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha22( X, Y, skol20( X, Y
% 1.02/1.56 , Z ), skol26( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.02/1.56 skol20( X, Y, Z ) ), skol26( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 1.02/1.56 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.02/1.56 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.02/1.56 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 1.02/1.56 ) }.
% 1.02/1.56 { ! alpha22( X, Y, Z, T ), alpha40( X, Y, Z, T ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha40( X, Y, Z
% 1.02/1.56 , T ), alpha22( X, Y, Z, T ) }.
% 1.02/1.56 { ! alpha40( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.56 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.56 { ! alpha40( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.02/1.56 .
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha40( X,
% 1.02/1.56 Y, Z, T ) }.
% 1.02/1.56 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.02/1.56 tc_Int_Oint, X, Y ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) ), c_Groups_Oabs__class_Oabs( X,
% 1.02/1.56 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Z, Y ) )
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, c_Groups_Ominus__class_Ominus( X, Y, Z ) )
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.56 , Y ), c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.02/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.02/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.56 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.56 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Z ), Y ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.02/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X,
% 1.02/1.56 c_Groups_Oplus__class_Oplus( X, Z, Y ) ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.56 , c_Groups_Oabs__class_Oabs( X, Z ), c_Groups_Oabs__class_Oabs( X, Y ) )
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oabs__class_Oabs( X, Y
% 1.02/1.56 ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Z ),
% 1.02/1.56 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oabs__class_Oabs( X, Y ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.56 c_Groups_Oabs__class_Oabs( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.56 ), c_Groups_Oabs__class_Oabs( X, Y ) = Y }.
% 1.02/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.56 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.56 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.56 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.56 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.56 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.56 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.56 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.56 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.56 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.56 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.56 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.56 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.56 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.56 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.56 ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.56 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.56 ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.56 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.56 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.56 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.56 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.56 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.56 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.56 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.56 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ),
% 1.02/1.56 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__ab__semigroup__add( X ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors( X ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__semigroup__add( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__mult( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__mult( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__add( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__add( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__1( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__0( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Oab__group__add( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Ozero__neq__one( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__mult( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring__1( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__add( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Osemiring__0( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Ogroup__add( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Omult__zero( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Osemiring( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oring__1( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Power_Opower( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Ozero( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oring( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Oone( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Odvd( X ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__comm__monoid__add( X ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.56 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.56 tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.02/1.56 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.02/1.56 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.02/1.56 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Osgn__if( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Oabs__if( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.02/1.56 { class_Power_Opower( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.02/1.56 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.02/1.56 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.02/1.56 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.56 tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.02/1.56 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ),
% 1.02/1.56 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.56 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.02/1.56 ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.56 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.02/1.56 X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.56 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.02/1.56 ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.56 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.56 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.56 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.56 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.56 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.56 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.56 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.56 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.02/1.56 ( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.02/1.56 ( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.02/1.56 ( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), class_Groups_Osgn__if(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Olinordered__idom( X ), class_Groups_Oabs__if(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.02/1.56 }.
% 1.02/1.56 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.02/1.56 ) ) }.
% 1.02/1.56 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.02/1.56 .
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.02/1.56 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.56 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.02/1.56 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.02/1.56 { ! hBOOL( c_fFalse ) }.
% 1.02/1.56 { hBOOL( c_fTrue ) }.
% 1.02/1.56 { ! v_z = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.02/1.56 { ! c_Groups_Oplus__class_Oplus( t_a, v_a, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( t_a ), v_z ), hAPP( c_Polynomial_Opoly(
% 1.02/1.56 t_a, v_q ), v_z ) ) ) = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.02/1.56 { ! v_a = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.02/1.56 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If( tc_Nat_Onat, c_fequal(
% 1.02/1.56 v_q, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) ),
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Nat_OSuc(
% 1.02/1.56 c_Polynomial_Odegree( t_a, v_q ) ) ), v_k ) = c_Polynomial_Odegree( t_a,
% 1.02/1.56 v_cs____ ) }.
% 1.02/1.56 { hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( t_a ), X ), v_k ) ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( t_a, v_a, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( t_a ), X ), hAPP( c_Polynomial_Opoly( t_a
% 1.02/1.56 , v_q ), X ) ) ) ) }.
% 1.02/1.56 { ! v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) }
% 1.02/1.56 .
% 1.02/1.56 { X = c_Groups_Ozero__class_Ozero( t_a ), alpha55( X, Y ), ! Y =
% 1.02/1.56 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) }.
% 1.02/1.56 { X = c_Groups_Ozero__class_Ozero( t_a ), alpha55( X, Y ), !
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( t_a, Y )
% 1.02/1.56 , c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k,
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = c_Polynomial_Odegree( t_a
% 1.02/1.56 , v_cs____ ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( t_a ), skol21
% 1.02/1.56 ( X, Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP
% 1.02/1.56 ( c_Power_Opower__class_Opower( t_a ), skol21( X, Y ) ), v_k ) ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( t_a, v_a, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( t_a ), skol21( X, Y ) ), hAPP(
% 1.02/1.56 c_Polynomial_Opoly( t_a, v_q ), skol21( X, Y ) ) ) ) ) ) = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( t_a ), skol21( X, Y ) ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k, c_Groups_Oone__class_Oone
% 1.02/1.56 ( tc_Nat_Onat ) ) ) ), c_Groups_Oplus__class_Oplus( t_a, X, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( t_a ), skol21( X, Y ) ), hAPP(
% 1.02/1.56 c_Polynomial_Opoly( t_a, Y ), skol21( X, Y ) ) ) ) ) }.
% 1.02/1.56 { ! alpha55( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.02/1.56 t_a ) ) }.
% 1.02/1.56 { ! alpha55( X, Y ), ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k,
% 1.02/1.56 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = c_Nat_OSuc(
% 1.02/1.56 c_Polynomial_Odegree( t_a, v_cs____ ) ), ! hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( t_a ), skol22( X ) ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( t_a ), skol22( X ) ), v_k ) ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( t_a, v_a, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( t_a ), skol22( X ) ), hAPP(
% 1.02/1.56 c_Polynomial_Opoly( t_a, v_q ), skol22( X ) ) ) ) ) ) = hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( t_a ), skol22( X ) ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k, c_Groups_Oone__class_Oone
% 1.02/1.56 ( tc_Nat_Onat ) ) ) ), X ) }.
% 1.02/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k, c_Groups_Oone__class_Oone
% 1.02/1.56 ( tc_Nat_Onat ) ) = c_Nat_OSuc( c_Polynomial_Odegree( t_a, v_cs____ ) ),
% 1.02/1.56 alpha55( X, Y ) }.
% 1.02/1.56 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ), hAPP(
% 1.02/1.56 hAPP( c_Groups_Otimes__class_Otimes( t_a ), Z ), hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.02/1.56 c_Power_Opower__class_Opower( t_a ), Z ), v_k ) ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( t_a, v_a, hAPP( hAPP(
% 1.02/1.56 c_Groups_Otimes__class_Otimes( t_a ), Z ), hAPP( c_Polynomial_Opoly( t_a
% 1.02/1.56 , v_q ), Z ) ) ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( t_a ),
% 1.02/1.56 hAPP( hAPP( c_Power_Opower__class_Opower( t_a ), Z ),
% 1.02/1.56 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, v_k, c_Groups_Oone__class_Oone
% 1.02/1.56 ( tc_Nat_Onat ) ) ) ), X ), alpha55( X, Y ) }.
% 1.02/1.56 { class_Rings_Oidom( t_a ) }.
% 1.02/1.56
% 1.02/1.56 *** allocated 15000 integers for clauses
% 1.02/1.56 *** allocated 22500 integers for clauses
% 1.02/1.56 *** allocated 33750 integers for clauses
% 1.02/1.56 *** allocated 50625 integers for clauses
% 1.02/1.56 *** allocated 75937 integers for clauses
% 1.02/1.56 *** allocated 113905 integers for clauses
% 1.02/1.56 percentage equality = 0.345643, percentage horn = 0.864935
% 1.02/1.56 This is a problem with some equality
% 1.02/1.56
% 1.02/1.56
% 1.02/1.56
% 1.02/1.56 Options Used:
% 1.02/1.56
% 1.02/1.56 useres = 1
% 1.02/1.56 useparamod = 1
% 1.02/1.56 useeqrefl = 1
% 1.02/1.56 useeqfact = 1
% 1.02/1.56 usefactor = 1
% 1.02/1.56 usesimpsplitting = 0
% 1.02/1.56 usesimpdemod = 5
% 1.02/1.56 usesimpres = 3
% 1.02/1.56
% 1.02/1.56 resimpinuse = 1000
% 1.02/1.56 resimpclauses = 20000
% 1.02/1.56 substype = eqrewr
% 1.02/1.56 backwardsubs = 1
% 1.02/1.56 selectoldest = 5
% 1.02/1.56
% 1.02/1.56 litorderings [0] = split
% 1.02/1.56 litorderings [1] = extend the termordering, first sorting on arguments
% 1.02/1.56
% 1.02/1.56 termordering = kbo
% 1.02/1.56
% 1.02/1.56 litapriori = 0
% 1.02/1.56 termapriori = 1
% 1.02/1.56 litaposteriori = 0
% 1.02/1.56 termaposteriori = 0
% 1.02/1.56 demodaposteriori = 0
% 1.02/1.56 ordereqreflfact = 0
% 1.02/1.56
% 1.02/1.56 litselect = negord
% 1.02/1.56
% 1.02/1.56 maxweight = 15
% 1.02/1.56 maxdepth = 30000
% 1.02/1.56 maxlength = 115
% 1.02/1.56 maxnrvars = 195
% 1.02/1.56 excuselevel = 1
% 1.02/1.56 increasemaxweight = 1
% 1.02/1.56
% 1.02/1.56 maxselected = 10000000
% 1.02/1.56 maxnrclauses = 10000000
% 1.02/1.56
% 1.02/1.56 showgenerated = 0
% 1.02/1.56 showkept = 0
% 1.02/1.56 showselected = 0
% 1.02/1.56 showdeleted = 0
% 1.02/1.56 showresimp = 1
% 1.02/1.56 showstatus = 2000
% 1.02/1.56
% 1.02/1.56 prologoutput = 0
% 1.02/1.56 nrgoals = 5000000
% 1.02/1.56 totalproof = 1
% 1.02/1.56
% 1.02/1.56 Symbols occurring in the translation:
% 1.02/1.56
% 1.02/1.56 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.02/1.56 . [1, 2] (w:1, o:190, a:1, s:1, b:0),
% 1.02/1.56 ! [4, 1] (w:0, o:112, a:1, s:1, b:0),
% 1.02/1.56 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.56 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.56 hAPP [38, 2] (w:1, o:214, a:1, s:1, b:0),
% 1.02/1.56 t_a [39, 0] (w:1, o:19, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Oidom [40, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.02/1.56 v_c____ [41, 0] (w:1, o:20, a:1, s:1, b:0),
% 1.02/1.56 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.02/1.56 v_p [44, 0] (w:1, o:22, a:1, s:1, b:0),
% 1.02/1.56 c_Polynomial_Opoly [45, 2] (w:1, o:215, a:1, s:1, b:0),
% 1.02/1.56 class_Power_Opower [48, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Osemiring__0 [49, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.02/1.56 tc_Nat_Onat [50, 0] (w:1, o:31, a:1, s:1, b:0),
% 1.02/1.56 c_Power_Opower__class_Opower [51, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.02/1.56 c_Groups_Oone__class_Oone [52, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.02/1.56 class_Groups_Ozero [54, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.02/1.56 tc_Polynomial_Opoly [55, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.02/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [56, 2] (w:1, o:216
% 1.02/1.56 , a:1, s:1, b:0),
% 1.02/1.56 c_Polynomial_Odegree [57, 2] (w:1, o:218, a:1, s:1, b:0),
% 1.02/1.56 c_Nat_OSuc [58, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Ocomm__semiring__0 [60, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.02/1.56 c_Groups_Oplus__class_Oplus [61, 3] (w:1, o:243, a:1, s:1, b:0),
% 1.02/1.56 class_Groups_Omonoid__mult [66, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.02/1.56 c_Groups_Otimes__class_Otimes [67, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Ocomm__semiring__1 [69, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.02/1.56 class_Int_Oring__char__0 [87, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.02/1.56 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [90
% 1.02/1.56 , 1] (w:1, o:166, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Oring__1__no__zero__divisors [96, 1] (w:1, o:120, a:1, s:
% 1.02/1.56 1, b:0),
% 1.02/1.56 class_Groups_Ocomm__monoid__mult [97, 1] (w:1, o:167, a:1, s:1, b:0)
% 1.02/1.56 ,
% 1.02/1.56 class_Rings_Olinordered__ring__strict [101, 1] (w:1, o:144, a:1, s:1
% 1.02/1.56 , b:0),
% 1.02/1.56 class_Rings_Omult__zero [102, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Ono__zero__divisors [103, 1] (w:1, o:152, a:1, s:1, b:0)
% 1.02/1.56 ,
% 1.02/1.56 class_Rings_Ozero__neq__one [104, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.02/1.56 v_cs____ [105, 0] (w:1, o:75, a:1, s:1, b:0),
% 1.02/1.56 c_Polynomial_OpCons [106, 3] (w:1, o:247, a:1, s:1, b:0),
% 1.02/1.56 c_Polynomial_Oorder [107, 3] (w:1, o:246, a:1, s:1, b:0),
% 1.02/1.56 c_Power_Opower_Opower [108, 3] (w:1, o:248, a:1, s:1, b:0),
% 1.02/1.56 c_fequal [112, 2] (w:1, o:219, a:1, s:1, b:0),
% 1.02/1.56 c_If [113, 4] (w:1, o:297, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Osemiring [115, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.02/1.56 class_RealVector_Oreal__normed__algebra [117, 1] (w:1, o:155, a:1, s:
% 1.02/1.56 1, b:0),
% 1.02/1.56 class_Rings_Ocomm__semiring [119, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.02/1.56 class_Groups_Ocomm__monoid__add [120, 1] (w:1, o:168, a:1, s:1, b:0)
% 1.02/1.56 ,
% 1.02/1.56 class_Groups_Oab__semigroup__mult [123, 1] (w:1, o:169, a:1, s:1, b:0
% 1.02/1.56 ),
% 1.02/1.56 class_Groups_Oab__semigroup__add [124, 1] (w:1, o:170, a:1, s:1, b:0)
% 1.02/1.56 ,
% 1.02/1.56 class_Groups_Ocancel__semigroup__add [125, 1] (w:1, o:171, a:1, s:1
% 1.02/1.56 , b:0),
% 1.02/1.56 class_Groups_Ocancel__ab__semigroup__add [126, 1] (w:1, o:172, a:1
% 1.02/1.56 , s:1, b:0),
% 1.02/1.56 class_Groups_Oone [127, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Oring__no__zero__divisors [128, 1] (w:1, o:121, a:1, s:1
% 1.02/1.56 , b:0),
% 1.02/1.56 class_Groups_Omonoid__add [129, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.02/1.56 class_Groups_Olinordered__ab__group__add [130, 1] (w:1, o:139, a:1
% 1.02/1.56 , s:1, b:0),
% 1.02/1.56 c_Polynomial_Opcompose [133, 3] (w:1, o:249, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Ocomm__ring__1 [137, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.02/1.56 c_Polynomial_Omonom [138, 3] (w:1, o:250, a:1, s:1, b:0),
% 1.02/1.56 c_Polynomial_Opoly__rec [140, 5] (w:1, o:325, a:1, s:1, b:0),
% 1.02/1.56 c_Polynomial_Osynthetic__div [141, 3] (w:1, o:251, a:1, s:1, b:0),
% 1.02/1.56 c_Nat_Onat_Onat__size [143, 1] (w:1, o:175, a:1, s:1, b:0),
% 1.02/1.56 c_Polynomial_Ocoeff [144, 2] (w:1, o:217, a:1, s:1, b:0),
% 1.02/1.56 tc_Int_Oint [146, 0] (w:1, o:96, a:1, s:1, b:0),
% 1.02/1.56 c_Groups_Ouminus__class_Ouminus [147, 2] (w:1, o:220, a:1, s:1, b:0)
% 1.02/1.56 ,
% 1.02/1.56 c_Nat_Osize__class_Osize [148, 2] (w:1, o:221, a:1, s:1, b:0),
% 1.02/1.56 class_Fields_Ofield [149, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.02/1.56 c_Polynomial_Opoly__gcd [150, 3] (w:1, o:252, a:1, s:1, b:0),
% 1.02/1.56 c_fFalse [151, 0] (w:1, o:97, a:1, s:1, b:0),
% 1.02/1.56 c_HOL_Obool_Obool__size [152, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.02/1.56 c_fTrue [153, 0] (w:1, o:98, a:1, s:1, b:0),
% 1.02/1.56 c_Polynomial_Osmult [154, 3] (w:1, o:253, a:1, s:1, b:0),
% 1.02/1.56 class_Groups_Oab__group__add [155, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Ocomm__ring [160, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.02/1.56 class_Groups_Ogroup__add [161, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Oring [162, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Oring__1 [163, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.02/1.56 c_Rings_Odvd__class_Odvd [164, 3] (w:1, o:254, a:1, s:1, b:0),
% 1.02/1.56 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [166, 3] (w:
% 1.02/1.56 1, o:242, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Odvd [167, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.02/1.56 hBOOL [171, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.02/1.56 c_Rings_Oinverse__class_Oinverse [172, 2] (w:1, o:222, a:1, s:1, b:0)
% 1.02/1.56 ,
% 1.02/1.56 c_Groups_Ominus__class_Ominus [173, 3] (w:1, o:255, a:1, s:1, b:0),
% 1.02/1.56 c_Nat_Onat_Onat__case [174, 3] (w:1, o:256, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Odivision__ring [176, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Odivision__ring__inverse__zero [177, 1] (w:1, o:159, a:1
% 1.02/1.56 , s:1, b:0),
% 1.02/1.56 class_Fields_Ofield__inverse__zero [182, 1] (w:1, o:128, a:1, s:1, b:
% 1.02/1.56 0),
% 1.02/1.56 c_Divides_Odiv__class_Omod [183, 3] (w:1, o:257, a:1, s:1, b:0),
% 1.02/1.56 c_Polynomial_OAbs__poly [184, 2] (w:1, o:223, a:1, s:1, b:0),
% 1.02/1.56 c_Orderings_Oord__class_Oless [185, 3] (w:1, o:244, a:1, s:1, b:0),
% 1.02/1.56 class_Groups_Oordered__ab__semigroup__add__imp__le [186, 1] (w:1, o:
% 1.02/1.56 180, a:1, s:1, b:0),
% 1.02/1.56 class_Groups_Oordered__cancel__ab__semigroup__add [187, 1] (w:1, o:
% 1.02/1.56 181, a:1, s:1, b:0),
% 1.02/1.56 class_Groups_Oordered__ab__group__add [188, 1] (w:1, o:182, a:1, s:1
% 1.02/1.56 , b:0),
% 1.02/1.56 class_Rings_Olinordered__idom [192, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Olinordered__semidom [194, 1] (w:1, o:147, a:1, s:1, b:0)
% 1.02/1.56 ,
% 1.02/1.56 class_Rings_Olinordered__ring [195, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.02/1.56 class_Rings_Olinordered__semiring__strict [196, 1] (w:1, o:148, a:1
% 1.02/1.56 , s:1, b:0),
% 1.02/1.56 class_Rings_Olinordered__comm__semiring__strict [197, 1] (w:1, o:149
% 1.02/1.56 , a:1, s:1, b:0),
% 1.02/1.56 class_Groups_Oordered__comm__monoid__add [198, 1] (w:1, o:183, a:1
% 1.02/1.56 , s:1, b:0),
% 1.02/1.56 class_Fields_Olinordered__field__inverse__zero [199, 1] (w:1, o:129
% 1.02/1.56 , a:1, s:1, b:0),
% 1.02/1.56 class_Fields_Olinordered__field [200, 1] (w:1, o:130, a:1, s:1, b:0)
% 1.02/1.56 ,
% 1.02/1.56 class_Rings_Oordered__ring [205, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.02/1.57 class_Divides_Osemiring__div [207, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.02/1.57 class_Divides_Oring__div [210, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.02/1.57 c_Rings_Oinverse__class_Odivide [211, 3] (w:1, o:258, a:1, s:1, b:0)
% 1.02/1.57 ,
% 1.02/1.57 c_Polynomial_Opdivmod__rel [213, 5] (w:1, o:326, a:1, s:1, b:0),
% 1.02/1.57 class_RealVector_Oreal__normed__field [214, 1] (w:1, o:161, a:1, s:1
% 1.02/1.57 , b:0),
% 1.02/1.57 class_RealVector_Oreal__field [219, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.02/1.57 c_Polynomial_Opos__poly [222, 2] (w:1, o:224, a:1, s:1, b:0),
% 1.02/1.57 c_Divides_Odiv__class_Odiv [223, 3] (w:1, o:259, a:1, s:1, b:0),
% 1.02/1.57 c_Groups_Oabs__class_Oabs [224, 2] (w:1, o:225, a:1, s:1, b:0),
% 1.02/1.57 class_Groups_Oordered__ab__group__add__abs [225, 1] (w:1, o:186, a:1
% 1.02/1.57 , s:1, b:0),
% 1.02/1.57 class_Groups_Oabs__if [226, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.02/1.57 c_Groups_Osgn__class_Osgn [227, 2] (w:1, o:226, a:1, s:1, b:0),
% 1.02/1.57 class_Groups_Osgn__if [228, 1] (w:1, o:188, a:1, s:1, b:0),
% 1.02/1.57 class_RealVector_Oreal__normed__vector [229, 1] (w:1, o:163, a:1, s:1
% 1.02/1.57 , b:0),
% 1.02/1.57 class_RealVector_Oreal__normed__div__algebra [230, 1] (w:1, o:164, a:
% 1.02/1.57 1, s:1, b:0),
% 1.02/1.57 class_RealVector_Oreal__normed__algebra__1 [231, 1] (w:1, o:165, a:1
% 1.02/1.57 , s:1, b:0),
% 1.02/1.57 c_Orderings_Oord__class_Oless__eq [232, 3] (w:1, o:245, a:1, s:1, b:0
% 1.02/1.57 ),
% 1.02/1.57 class_Rings_Olinordered__semiring [233, 1] (w:1, o:150, a:1, s:1, b:0
% 1.02/1.57 ),
% 1.02/1.57 class_Groups_Ocancel__comm__monoid__add [235, 1] (w:1, o:189, a:1, s:
% 1.02/1.57 1, b:0),
% 1.02/1.57 v_z [237, 0] (w:1, o:108, a:1, s:1, b:0),
% 1.02/1.57 v_a [238, 0] (w:1, o:109, a:1, s:1, b:0),
% 1.02/1.57 v_q [239, 0] (w:1, o:110, a:1, s:1, b:0),
% 1.02/1.57 v_k [240, 0] (w:1, o:111, a:1, s:1, b:0),
% 1.02/1.57 alpha1 [241, 2] (w:1, o:227, a:1, s:1, b:1),
% 1.02/1.57 alpha2 [242, 2] (w:1, o:228, a:1, s:1, b:1),
% 1.02/1.57 alpha3 [243, 3] (w:1, o:262, a:1, s:1, b:1),
% 1.02/1.57 alpha4 [244, 2] (w:1, o:229, a:1, s:1, b:1),
% 1.02/1.57 alpha5 [245, 2] (w:1, o:230, a:1, s:1, b:1),
% 1.02/1.57 alpha6 [246, 4] (w:1, o:304, a:1, s:1, b:1),
% 1.02/1.57 alpha7 [247, 4] (w:1, o:305, a:1, s:1, b:1),
% 10.39/10.77 alpha8 [248, 2] (w:1, o:231, a:1, s:1, b:1),
% 10.39/10.77 alpha9 [249, 3] (w:1, o:263, a:1, s:1, b:1),
% 10.39/10.77 alpha10 [250, 3] (w:1, o:264, a:1, s:1, b:1),
% 10.39/10.77 alpha11 [251, 3] (w:1, o:265, a:1, s:1, b:1),
% 10.39/10.77 alpha12 [252, 3] (w:1, o:266, a:1, s:1, b:1),
% 10.39/10.77 alpha13 [253, 3] (w:1, o:267, a:1, s:1, b:1),
% 10.39/10.77 alpha14 [254, 3] (w:1, o:268, a:1, s:1, b:1),
% 10.39/10.77 alpha15 [255, 3] (w:1, o:269, a:1, s:1, b:1),
% 10.39/10.77 alpha16 [256, 3] (w:1, o:270, a:1, s:1, b:1),
% 10.39/10.77 alpha17 [257, 3] (w:1, o:271, a:1, s:1, b:1),
% 10.39/10.77 alpha18 [258, 3] (w:1, o:272, a:1, s:1, b:1),
% 10.39/10.77 alpha19 [259, 3] (w:1, o:273, a:1, s:1, b:1),
% 10.39/10.77 alpha20 [260, 2] (w:1, o:232, a:1, s:1, b:1),
% 10.39/10.77 alpha21 [261, 4] (w:1, o:306, a:1, s:1, b:1),
% 10.39/10.77 alpha22 [262, 4] (w:1, o:307, a:1, s:1, b:1),
% 10.39/10.77 alpha23 [263, 2] (w:1, o:233, a:1, s:1, b:1),
% 10.39/10.77 alpha24 [264, 2] (w:1, o:234, a:1, s:1, b:1),
% 10.39/10.77 alpha25 [265, 4] (w:1, o:308, a:1, s:1, b:1),
% 10.39/10.77 alpha26 [266, 4] (w:1, o:309, a:1, s:1, b:1),
% 10.39/10.77 alpha27 [267, 4] (w:1, o:310, a:1, s:1, b:1),
% 10.39/10.77 alpha28 [268, 3] (w:1, o:260, a:1, s:1, b:1),
% 10.39/10.77 alpha29 [269, 3] (w:1, o:261, a:1, s:1, b:1),
% 10.39/10.77 alpha30 [270, 3] (w:1, o:274, a:1, s:1, b:1),
% 10.39/10.77 alpha31 [271, 3] (w:1, o:275, a:1, s:1, b:1),
% 10.39/10.77 alpha32 [272, 3] (w:1, o:276, a:1, s:1, b:1),
% 10.39/10.77 alpha33 [273, 3] (w:1, o:277, a:1, s:1, b:1),
% 10.39/10.77 alpha34 [274, 4] (w:1, o:311, a:1, s:1, b:1),
% 10.39/10.77 alpha35 [275, 4] (w:1, o:312, a:1, s:1, b:1),
% 10.39/10.77 alpha36 [276, 4] (w:1, o:313, a:1, s:1, b:1),
% 10.39/10.77 alpha37 [277, 4] (w:1, o:314, a:1, s:1, b:1),
% 10.39/10.77 alpha38 [278, 3] (w:1, o:278, a:1, s:1, b:1),
% 10.39/10.77 alpha39 [279, 4] (w:1, o:315, a:1, s:1, b:1),
% 10.39/10.77 alpha40 [280, 4] (w:1, o:316, a:1, s:1, b:1),
% 10.39/10.77 alpha41 [281, 3] (w:1, o:279, a:1, s:1, b:1),
% 10.39/10.77 alpha42 [282, 4] (w:1, o:317, a:1, s:1, b:1),
% 10.39/10.77 alpha43 [283, 3] (w:1, o:280, a:1, s:1, b:1),
% 10.39/10.77 alpha44 [284, 4] (w:1, o:318, a:1, s:1, b:1),
% 10.39/10.77 alpha45 [285, 4] (w:1, o:319, a:1, s:1, b:1),
% 10.39/10.77 alpha46 [286, 3] (w:1, o:281, a:1, s:1, b:1),
% 10.39/10.77 alpha47 [287, 4] (w:1, o:320, a:1, s:1, b:1),
% 10.39/10.77 alpha48 [288, 4] (w:1, o:321, a:1, s:1, b:1),
% 10.39/10.77 alpha49 [289, 4] (w:1, o:322, a:1, s:1, b:1),
% 10.39/10.77 alpha50 [290, 4] (w:1, o:298, a:1, s:1, b:1),
% 10.39/10.77 alpha51 [291, 4] (w:1, o:299, a:1, s:1, b:1),
% 10.39/10.77 alpha52 [292, 4] (w:1, o:300, a:1, s:1, b:1),
% 10.39/10.77 alpha53 [293, 3] (w:1, o:282, a:1, s:1, b:1),
% 10.39/10.77 alpha54 [294, 3] (w:1, o:283, a:1, s:1, b:1),
% 10.39/10.77 alpha55 [295, 2] (w:1, o:235, a:1, s:1, b:1),
% 10.39/10.77 alpha56 [296, 4] (w:1, o:301, a:1, s:1, b:1),
% 10.39/10.77 alpha57 [297, 3] (w:1, o:284, a:1, s:1, b:1),
% 10.39/10.77 alpha58 [298, 4] (w:1, o:302, a:1, s:1, b:1),
% 10.39/10.77 alpha59 [299, 4] (w:1, o:303, a:1, s:1, b:1),
% 10.39/10.77 skol1 [300, 2] (w:1, o:236, a:1, s:1, b:1),
% 10.39/10.77 skol2 [301, 0] (w:1, o:14, a:1, s:1, b:1),
% 10.39/10.77 skol3 [302, 0] (w:1, o:17, a:1, s:1, b:1),
% 10.39/10.77 skol4 [303, 0] (w:1, o:18, a:1, s:1, b:1),
% 10.39/10.77 skol5 [304, 3] (w:1, o:285, a:1, s:1, b:1),
% 10.39/10.77 skol6 [305, 3] (w:1, o:286, a:1, s:1, b:1),
% 10.39/10.77 skol7 [306, 4] (w:1, o:323, a:1, s:1, b:1),
% 10.39/10.77 skol8 [307, 1] (w:1, o:132, a:1, s:1, b:1),
% 10.39/10.77 skol9 [308, 2] (w:1, o:237, a:1, s:1, b:1),
% 10.39/10.77 skol10 [309, 2] (w:1, o:238, a:1, s:1, b:1),
% 10.39/10.77 skol11 [310, 3] (w:1, o:287, a:1, s:1, b:1),
% 10.39/10.77 skol12 [311, 3] (w:1, o:288, a:1, s:1, b:1),
% 10.39/10.77 skol13 [312, 2] (w:1, o:239, a:1, s:1, b:1),
% 10.39/10.77 skol14 [313, 2] (w:1, o:240, a:1, s:1, b:1),
% 10.39/10.77 skol15 [314, 3] (w:1, o:289, a:1, s:1, b:1),
% 10.39/10.77 skol16 [315, 3] (w:1, o:290, a:1, s:1, b:1),
% 10.39/10.77 skol17 [316, 3] (w:1, o:291, a:1, s:1, b:1),
% 10.39/10.77 skol18 [317, 4] (w:1, o:324, a:1, s:1, b:1),
% 10.39/10.77 skol19 [318, 3] (w:1, o:292, a:1, s:1, b:1),
% 10.39/10.77 skol20 [319, 3] (w:1, o:293, a:1, s:1, b:1),
% 10.39/10.77 skol21 [320, 2] (w:1, o:241, a:1, s:1, b:1),
% 10.39/10.77 skol22 [321, 1] (w:1, o:133, a:1, s:1, b:1),
% 10.39/10.77 skol23 [322, 0] (w:1, o:15, a:1, s:1, b:1),
% 10.39/10.77 skol24 [323, 3] (w:1, o:294, a:1, s:1, b:1),
% 10.39/10.77 skol25 [324, 3] (w:1, o:295, a:1, s:1, b:1),
% 10.39/10.77 skol26 [325, 3] (w:1, o:296, a:1, s:1, b:1),
% 34.90/35.24 skol27 [326, 0] (w:1, o:16, a:1, s:1, b:1).
% 34.90/35.24
% 34.90/35.24
% 34.90/35.24 Starting Search:
% 34.90/35.24
% 34.90/35.24 *** allocated 170857 integers for clauses
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24
% 34.90/35.24 Intermediate Status:
% 34.90/35.24 Generated: 3057
% 34.90/35.24 Kept: 2039
% 34.90/35.24 Inuse: 37
% 34.90/35.24 Deleted: 4
% 34.90/35.24 Deletedinuse: 0
% 34.90/35.24
% 34.90/35.24 *** allocated 256285 integers for clauses
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24 *** allocated 170857 integers for termspace/termends
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24 *** allocated 384427 integers for clauses
% 34.90/35.24
% 34.90/35.24 Intermediate Status:
% 34.90/35.24 Generated: 8688
% 34.90/35.24 Kept: 4261
% 34.90/35.24 Inuse: 171
% 34.90/35.24 Deleted: 5
% 34.90/35.24 Deletedinuse: 0
% 34.90/35.24
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24 *** allocated 256285 integers for termspace/termends
% 34.90/35.24
% 34.90/35.24 Intermediate Status:
% 34.90/35.24 Generated: 20730
% 34.90/35.24 Kept: 6428
% 34.90/35.24 Inuse: 231
% 34.90/35.24 Deleted: 10
% 34.90/35.24 Deletedinuse: 0
% 34.90/35.24
% 34.90/35.24 *** allocated 576640 integers for clauses
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24
% 34.90/35.24 Intermediate Status:
% 34.90/35.24 Generated: 26582
% 34.90/35.24 Kept: 8449
% 34.90/35.24 Inuse: 273
% 34.90/35.24 Deleted: 10
% 34.90/35.24 Deletedinuse: 0
% 34.90/35.24
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24 *** allocated 384427 integers for termspace/termends
% 34.90/35.24
% 34.90/35.24 Intermediate Status:
% 34.90/35.24 Generated: 42505
% 34.90/35.24 Kept: 11048
% 34.90/35.24 Inuse: 321
% 34.90/35.24 Deleted: 11
% 34.90/35.24 Deletedinuse: 1
% 34.90/35.24
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24 *** allocated 864960 integers for clauses
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24
% 34.90/35.24 Intermediate Status:
% 34.90/35.24 Generated: 49983
% 34.90/35.24 Kept: 13074
% 34.90/35.24 Inuse: 377
% 34.90/35.24 Deleted: 15
% 34.90/35.24 Deletedinuse: 1
% 34.90/35.24
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24
% 34.90/35.24 Intermediate Status:
% 34.90/35.24 Generated: 57860
% 34.90/35.24 Kept: 15076
% 34.90/35.24 Inuse: 401
% 34.90/35.24 Deleted: 15
% 34.90/35.24 Deletedinuse: 1
% 34.90/35.24
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24
% 34.90/35.24 Intermediate Status:
% 34.90/35.24 Generated: 66951
% 34.90/35.24 Kept: 17229
% 34.90/35.24 Inuse: 427
% 34.90/35.24 Deleted: 15
% 34.90/35.24 Deletedinuse: 1
% 34.90/35.24
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24 *** allocated 576640 integers for termspace/termends
% 34.90/35.24 *** allocated 1297440 integers for clauses
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24
% 34.90/35.24 Intermediate Status:
% 34.90/35.24 Generated: 72078
% 34.90/35.24 Kept: 19249
% 34.90/35.24 Inuse: 460
% 34.90/35.24 Deleted: 15
% 34.90/35.24 Deletedinuse: 1
% 34.90/35.24
% 34.90/35.24 Resimplifying inuse:
% 34.90/35.24 Done
% 34.90/35.24
% 34.90/35.24 Resimplifying clauses:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25
% 34.90/35.25 Intermediate Status:
% 34.90/35.25 Generated: 91843
% 34.90/35.25 Kept: 21282
% 34.90/35.25 Inuse: 473
% 34.90/35.25 Deleted: 309
% 34.90/35.25 Deletedinuse: 1
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25
% 34.90/35.25 Intermediate Status:
% 34.90/35.25 Generated: 101238
% 34.90/35.25 Kept: 23801
% 34.90/35.25 Inuse: 502
% 34.90/35.25 Deleted: 309
% 34.90/35.25 Deletedinuse: 1
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25 *** allocated 864960 integers for termspace/termends
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25
% 34.90/35.25 Intermediate Status:
% 34.90/35.25 Generated: 108415
% 34.90/35.25 Kept: 26743
% 34.90/35.25 Inuse: 522
% 34.90/35.25 Deleted: 309
% 34.90/35.25 Deletedinuse: 1
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25 *** allocated 1946160 integers for clauses
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25
% 34.90/35.25 Intermediate Status:
% 34.90/35.25 Generated: 113505
% 34.90/35.25 Kept: 28775
% 34.90/35.25 Inuse: 545
% 34.90/35.25 Deleted: 309
% 34.90/35.25 Deletedinuse: 1
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25
% 34.90/35.25 Intermediate Status:
% 34.90/35.25 Generated: 118135
% 34.90/35.25 Kept: 30781
% 34.90/35.25 Inuse: 561
% 34.90/35.25 Deleted: 309
% 34.90/35.25 Deletedinuse: 1
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25
% 34.90/35.25 Intermediate Status:
% 34.90/35.25 Generated: 139171
% 34.90/35.25 Kept: 33078
% 34.90/35.25 Inuse: 577
% 34.90/35.25 Deleted: 309
% 34.90/35.25 Deletedinuse: 1
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25
% 34.90/35.25 Intermediate Status:
% 34.90/35.25 Generated: 148278
% 34.90/35.25 Kept: 35285
% 34.90/35.25 Inuse: 587
% 34.90/35.25 Deleted: 309
% 34.90/35.25 Deletedinuse: 1
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25 *** allocated 1297440 integers for termspace/termends
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25
% 34.90/35.25 Intermediate Status:
% 34.90/35.25 Generated: 156694
% 34.90/35.25 Kept: 37321
% 34.90/35.25 Inuse: 604
% 34.90/35.25 Deleted: 309
% 34.90/35.25 Deletedinuse: 1
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25
% 34.90/35.25 Intermediate Status:
% 34.90/35.25 Generated: 169787
% 34.90/35.25 Kept: 39909
% 34.90/35.25 Inuse: 617
% 34.90/35.25 Deleted: 309
% 34.90/35.25 Deletedinuse: 1
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25 Resimplifying clauses:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25
% 34.90/35.25 Intermediate Status:
% 34.90/35.25 Generated: 176647
% 34.90/35.25 Kept: 41910
% 34.90/35.25 Inuse: 640
% 34.90/35.25 Deleted: 465
% 34.90/35.25 Deletedinuse: 1
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25 *** allocated 2919240 integers for clauses
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25
% 34.90/35.25 Intermediate Status:
% 34.90/35.25 Generated: 184388
% 34.90/35.25 Kept: 43934
% 34.90/35.25 Inuse: 656
% 34.90/35.25 Deleted: 465
% 34.90/35.25 Deletedinuse: 1
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 34.90/35.25 Resimplifying inuse:
% 34.90/35.25 Done
% 34.90/35.25
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 191498
% 118.35/118.75 Kept: 45947
% 118.35/118.75 Inuse: 680
% 118.35/118.75 Deleted: 465
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 199291
% 118.35/118.75 Kept: 47985
% 118.35/118.75 Inuse: 700
% 118.35/118.75 Deleted: 465
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 208610
% 118.35/118.75 Kept: 50074
% 118.35/118.75 Inuse: 712
% 118.35/118.75 Deleted: 465
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 221269
% 118.35/118.75 Kept: 52656
% 118.35/118.75 Inuse: 722
% 118.35/118.75 Deleted: 465
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 *** allocated 1946160 integers for termspace/termends
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 228987
% 118.35/118.75 Kept: 54977
% 118.35/118.75 Inuse: 747
% 118.35/118.75 Deleted: 465
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 240351
% 118.35/118.75 Kept: 57099
% 118.35/118.75 Inuse: 777
% 118.35/118.75 Deleted: 465
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 250571
% 118.35/118.75 Kept: 59246
% 118.35/118.75 Inuse: 797
% 118.35/118.75 Deleted: 465
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying clauses:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 267253
% 118.35/118.75 Kept: 62449
% 118.35/118.75 Inuse: 817
% 118.35/118.75 Deleted: 519
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 *** allocated 4378860 integers for clauses
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 289169
% 118.35/118.75 Kept: 65441
% 118.35/118.75 Inuse: 847
% 118.35/118.75 Deleted: 519
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 309217
% 118.35/118.75 Kept: 67934
% 118.35/118.75 Inuse: 862
% 118.35/118.75 Deleted: 519
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 315578
% 118.35/118.75 Kept: 69967
% 118.35/118.75 Inuse: 877
% 118.35/118.75 Deleted: 519
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 325588
% 118.35/118.75 Kept: 71987
% 118.35/118.75 Inuse: 908
% 118.35/118.75 Deleted: 519
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 333436
% 118.35/118.75 Kept: 74033
% 118.35/118.75 Inuse: 917
% 118.35/118.75 Deleted: 519
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 *** allocated 2919240 integers for termspace/termends
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 349470
% 118.35/118.75 Kept: 76823
% 118.35/118.75 Inuse: 947
% 118.35/118.75 Deleted: 519
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 368738
% 118.35/118.75 Kept: 80879
% 118.35/118.75 Inuse: 962
% 118.35/118.75 Deleted: 519
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying clauses:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 383465
% 118.35/118.75 Kept: 83518
% 118.35/118.75 Inuse: 977
% 118.35/118.75 Deleted: 578
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 393759
% 118.35/118.75 Kept: 85550
% 118.35/118.75 Inuse: 1007
% 118.35/118.75 Deleted: 578
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 400740
% 118.35/118.75 Kept: 87583
% 118.35/118.75 Inuse: 1018
% 118.35/118.75 Deleted: 578
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 409521
% 118.35/118.75 Kept: 89725
% 118.35/118.75 Inuse: 1032
% 118.35/118.75 Deleted: 578
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 419321
% 118.35/118.75 Kept: 91747
% 118.35/118.75 Inuse: 1048
% 118.35/118.75 Deleted: 578
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 428650
% 118.35/118.75 Kept: 93757
% 118.35/118.75 Inuse: 1068
% 118.35/118.75 Deleted: 578
% 118.35/118.75 Deletedinuse: 1
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 442180
% 118.35/118.75 Kept: 96461
% 118.35/118.75 Inuse: 1087
% 118.35/118.75 Deleted: 580
% 118.35/118.75 Deletedinuse: 3
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 *** allocated 6568290 integers for clauses
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 455933
% 118.35/118.75 Kept: 99567
% 118.35/118.75 Inuse: 1102
% 118.35/118.75 Deleted: 580
% 118.35/118.75 Deletedinuse: 3
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 118.35/118.75
% 118.35/118.75
% 118.35/118.75 Intermediate Status:
% 118.35/118.75 Generated: 469266
% 118.35/118.75 Kept: 102374
% 118.35/118.75 Inuse: 1112
% 118.35/118.75 Deleted: 580
% 118.35/118.75 Deletedinuse: 3
% 118.35/118.75
% 118.35/118.75 Resimplifying inuse:
% 118.35/118.75 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying clauses:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 480072
% 234.47/234.87 Kept: 104782
% 234.47/234.87 Inuse: 1127
% 234.47/234.87 Deleted: 845
% 234.47/234.87 Deletedinuse: 3
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 490489
% 234.47/234.87 Kept: 106976
% 234.47/234.87 Inuse: 1152
% 234.47/234.87 Deleted: 845
% 234.47/234.87 Deletedinuse: 3
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 *** allocated 4378860 integers for termspace/termends
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 500242
% 234.47/234.87 Kept: 109059
% 234.47/234.87 Inuse: 1177
% 234.47/234.87 Deleted: 845
% 234.47/234.87 Deletedinuse: 3
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 518426
% 234.47/234.87 Kept: 113747
% 234.47/234.87 Inuse: 1217
% 234.47/234.87 Deleted: 845
% 234.47/234.87 Deletedinuse: 3
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 530192
% 234.47/234.87 Kept: 116619
% 234.47/234.87 Inuse: 1222
% 234.47/234.87 Deleted: 845
% 234.47/234.87 Deletedinuse: 3
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 540166
% 234.47/234.87 Kept: 120417
% 234.47/234.87 Inuse: 1237
% 234.47/234.87 Deleted: 845
% 234.47/234.87 Deletedinuse: 3
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 548416
% 234.47/234.87 Kept: 123819
% 234.47/234.87 Inuse: 1247
% 234.47/234.87 Deleted: 845
% 234.47/234.87 Deletedinuse: 3
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying clauses:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 581561
% 234.47/234.87 Kept: 127972
% 234.47/234.87 Inuse: 1267
% 234.47/234.87 Deleted: 907
% 234.47/234.87 Deletedinuse: 3
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 597653
% 234.47/234.87 Kept: 130005
% 234.47/234.87 Inuse: 1286
% 234.47/234.87 Deleted: 907
% 234.47/234.87 Deletedinuse: 3
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 609122
% 234.47/234.87 Kept: 133131
% 234.47/234.87 Inuse: 1297
% 234.47/234.87 Deleted: 943
% 234.47/234.87 Deletedinuse: 4
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 616946
% 234.47/234.87 Kept: 135198
% 234.47/234.87 Inuse: 1301
% 234.47/234.87 Deleted: 956
% 234.47/234.87 Deletedinuse: 4
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 624045
% 234.47/234.87 Kept: 137501
% 234.47/234.87 Inuse: 1309
% 234.47/234.87 Deleted: 961
% 234.47/234.87 Deletedinuse: 4
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 637126
% 234.47/234.87 Kept: 139508
% 234.47/234.87 Inuse: 1314
% 234.47/234.87 Deleted: 971
% 234.47/234.87 Deletedinuse: 4
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 653111
% 234.47/234.87 Kept: 141936
% 234.47/234.87 Inuse: 1316
% 234.47/234.87 Deleted: 975
% 234.47/234.87 Deletedinuse: 5
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 *** allocated 9852435 integers for clauses
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 681502
% 234.47/234.87 Kept: 145747
% 234.47/234.87 Inuse: 1321
% 234.47/234.87 Deleted: 995
% 234.47/234.87 Deletedinuse: 5
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying clauses:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 691573
% 234.47/234.87 Kept: 148042
% 234.47/234.87 Inuse: 1346
% 234.47/234.87 Deleted: 1383
% 234.47/234.87 Deletedinuse: 5
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 700594
% 234.47/234.87 Kept: 150105
% 234.47/234.87 Inuse: 1356
% 234.47/234.87 Deleted: 1383
% 234.47/234.87 Deletedinuse: 5
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 713817
% 234.47/234.87 Kept: 153024
% 234.47/234.87 Inuse: 1371
% 234.47/234.87 Deleted: 1383
% 234.47/234.87 Deletedinuse: 5
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 724621
% 234.47/234.87 Kept: 155664
% 234.47/234.87 Inuse: 1381
% 234.47/234.87 Deleted: 1383
% 234.47/234.87 Deletedinuse: 5
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 749988
% 234.47/234.87 Kept: 157681
% 234.47/234.87 Inuse: 1417
% 234.47/234.87 Deleted: 1383
% 234.47/234.87 Deletedinuse: 5
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 *** allocated 6568290 integers for termspace/termends
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 761322
% 234.47/234.87 Kept: 159694
% 234.47/234.87 Inuse: 1450
% 234.47/234.87 Deleted: 1383
% 234.47/234.87 Deletedinuse: 5
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 775414
% 234.47/234.87 Kept: 164807
% 234.47/234.87 Inuse: 1471
% 234.47/234.87 Deleted: 1383
% 234.47/234.87 Deletedinuse: 5
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying clauses:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 783393
% 234.47/234.87 Kept: 166853
% 234.47/234.87 Inuse: 1495
% 234.47/234.87 Deleted: 1849
% 234.47/234.87 Deletedinuse: 5
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87 Resimplifying inuse:
% 234.47/234.87 Done
% 234.47/234.87
% 234.47/234.87
% 234.47/234.87 Intermediate Status:
% 234.47/234.87 Generated: 788986
% 234.47/234.87 Kept: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------