%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW243+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n019.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 23:21:31 EDT 2022
% Result : Timeout 300.09s 300.60s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW243+1 : TPTP v8.1.0. Released v5.2.0.
% 0.14/0.13 % Command : bliksem %s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.20/0.35 % DateTime : Mon Jun 6 07:55:40 EDT 2022
% 0.20/0.35 % CPUTime :
% 0.98/1.61 *** allocated 10000 integers for termspace/termends
% 0.98/1.61 *** allocated 10000 integers for clauses
% 0.98/1.61 *** allocated 10000 integers for justifications
% 0.98/1.61 *** allocated 15000 integers for termspace/termends
% 0.98/1.61 *** allocated 22500 integers for termspace/termends
% 0.98/1.61 *** allocated 33750 integers for termspace/termends
% 0.98/1.61 Bliksem 1.12
% 0.98/1.61
% 0.98/1.61
% 0.98/1.61 Automatic Strategy Selection
% 0.98/1.61
% 0.98/1.61 *** allocated 50625 integers for termspace/termends
% 0.98/1.61 *** allocated 75937 integers for termspace/termends
% 0.98/1.61 *** allocated 113905 integers for termspace/termends
% 0.98/1.61
% 0.98/1.61 Clauses:
% 0.98/1.61
% 0.98/1.61 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.98/1.61 { ! class_Rings_Oidom( t_a ), v_c____ = c_Groups_Ozero__class_Ozero( t_a )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Oidom( t_a ), ! skol2 = c_Groups_Ozero__class_Ozero( t_a )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a, v_p ), skol2
% 0.98/1.61 ) = c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.61 X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.61 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ),
% 0.98/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ),
% 0.98/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.98/1.61 c_Polynomial_Odegree( X, Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol3( X, Y ) ) ) }.
% 0.98/1.61 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.98/1.61 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.98/1.61 .
% 0.98/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.98/1.61 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.98/1.61 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.98/1.61 .
% 0.98/1.61 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.98/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.98/1.61 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.98/1.61 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.98/1.61 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.98/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.98/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.98/1.61 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.98/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.98/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.98/1.61 Y ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.61 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.98/1.61 ), X ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.98/1.61 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.98/1.61 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.61 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.98/1.61 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.61 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.98/1.61 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.98/1.61 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.98/1.61 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.98/1.61 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.98/1.61 c_Polynomial_Odegree( X, Z ) ) }.
% 0.98/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.98/1.61 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.98/1.61 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.98/1.61 { ! c_Nat_OSuc( X ) = X }.
% 0.98/1.61 { ! X = c_Nat_OSuc( X ) }.
% 0.98/1.61 { alpha59( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.98/1.61 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.61 { alpha59( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.98/1.61 ( X, Y ), Z ) ) }.
% 0.98/1.61 { ! alpha59( X, Y, Z ), alpha61( X, Y, Z ), Z = Y }.
% 0.98/1.61 { ! alpha59( X, Y, Z ), alpha61( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.98/1.61 ) ) }.
% 0.98/1.61 { ! alpha61( X, Y, Z ), alpha59( X, Y, Z ) }.
% 0.98/1.61 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha59( X, Y, Z ) }.
% 0.98/1.61 { ! alpha61( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.98/1.61 }.
% 0.98/1.61 { ! alpha61( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.98/1.61 X, Y ), Z ) ), alpha61( X, Y, Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.61 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.61 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.98/1.61 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.98/1.61 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.98/1.61 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.98/1.61 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.98/1.61 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.98/1.61 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.98/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.61 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.98/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.98/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.98/1.61 .
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.98/1.61 .
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.98/1.61 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.98/1.61 X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.98/1.61 }.
% 0.98/1.61 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ) ) = X }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), X ) = X }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.61 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.98/1.61 , X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.98/1.61 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.98/1.61 .
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), !
% 0.98/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ),
% 0.98/1.61 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.98/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.98/1.61 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.98/1.61 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.98/1.61 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.98/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.98/1.61 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.98/1.61 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.98/1.61 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.98/1.61 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.61 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.98/1.61 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 0.98/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.98/1.61 c_Nat_OSuc( X ) ) }.
% 0.98/1.61 { ! alpha1( X, Y ), Y = c_Nat_OSuc( skol4( Z, Y ) ) }.
% 0.98/1.61 { ! alpha1( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol4( X, Y
% 0.98/1.61 ), X ) }.
% 0.98/1.61 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.98/1.61 ), alpha1( X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol5( X ) ) }.
% 0.98/1.61 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.61 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y ), alpha25( X
% 0.98/1.61 , Y ) }.
% 0.98/1.61 { ! alpha2( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! alpha25( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! alpha25( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! alpha25( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha25( X, Y ) }.
% 0.98/1.61 { ! alpha2( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 0.98/1.61 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha3( X, Y ), alpha26
% 0.98/1.61 ( X, Y ) }.
% 0.98/1.61 { ! alpha3( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! alpha26( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.98/1.61 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.98/1.61 { ! alpha26( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! alpha26( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha26( X, Y ) }.
% 0.98/1.61 { ! alpha3( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! alpha3( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha3( X, Y ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Y, X ) ) }.
% 0.98/1.61 { ! class_Rings_Oidom( t_a ), ! skol6 = c_Groups_Ozero__class_Ozero( t_a )
% 0.98/1.61 }.
% 0.98/1.61 { ! class_Rings_Oidom( t_a ), ! hAPP( c_Polynomial_Opoly( t_a,
% 0.98/1.61 c_Polynomial_OpCons( t_a, v_c____, v_cs____ ) ), skol6 ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( t_a ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Z, Y ) ) }.
% 0.98/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.98/1.61 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.98/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.98/1.61 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.98/1.61 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.98/1.61 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.98/1.61 .
% 0.98/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.61 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ) }.
% 0.98/1.61 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.98/1.61 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.98/1.61 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.98/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.98/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.98/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.98/1.61 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.98/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.98/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.98/1.61 ) ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.98/1.61 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.98/1.61 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.98/1.61 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.98/1.61 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.98/1.61 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.98/1.61 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.98/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.98/1.61 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.98/1.61 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.98/1.61 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.61 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.61 ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.98/1.61 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), Y ) }.
% 0.98/1.61 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.98/1.61 ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.98/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.98/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.98/1.61 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.98/1.61 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.98/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.98/1.61 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.98/1.61 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.61 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.98/1.61 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.98/1.61 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.98/1.61 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.61 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.98/1.61 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.98/1.61 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.98/1.61 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.98/1.61 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.98/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.98/1.61 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.98/1.61 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.98/1.61 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.98/1.61 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.98/1.61 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.98/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.98/1.61 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.98/1.61 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.98/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.61 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.98/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 0.98/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.61 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.61 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.98/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.61 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.61 ) }.
% 0.98/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.61 ), ! U = T }.
% 0.98/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.98/1.61 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.98/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.98/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.98/1.61 ), ! Z = Y }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.98/1.61 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.98/1.61 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.98/1.61 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.98/1.61 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.28/1.61 ) ), Z ) }.
% 1.28/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.61 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.28/1.61 ), U = Z, T = Y }.
% 1.28/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.61 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.28/1.61 ) }.
% 1.28/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.61 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.61 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.28/1.61 ) }.
% 1.28/1.61 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.28/1.61 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.28/1.61 ( X ) }.
% 1.28/1.61 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.61 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.61 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.61 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.61 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.61 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 1.28/1.61 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 1.28/1.61 ( t_a ), ! skol7 = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.28/1.61 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 1.28/1.61 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 1.28/1.61 ( t_a ), ! v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly(
% 1.28/1.61 t_a ) ), c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If(
% 1.28/1.61 tc_Nat_Onat, c_fequal( skol20, c_Groups_Ozero__class_Ozero(
% 1.28/1.61 tc_Polynomial_Opoly( t_a ) ) ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.28/1.61 ), c_Nat_OSuc( c_Polynomial_Odegree( t_a, skol20 ) ) ), skol18 ) ) =
% 1.28/1.61 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.61 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 1.28/1.61 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 1.28/1.61 ( t_a ), v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a
% 1.28/1.61 ) ), c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If(
% 1.28/1.61 tc_Nat_Onat, c_fequal( skol20, c_Groups_Ozero__class_Ozero(
% 1.28/1.61 tc_Polynomial_Opoly( t_a ) ) ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.28/1.61 ), c_Nat_OSuc( c_Polynomial_Odegree( t_a, skol20 ) ) ), skol18 ) ) =
% 1.28/1.61 c_Nat_OSuc( c_Polynomial_Odegree( t_a, v_cs____ ) ) }.
% 1.28/1.61 { ! class_Rings_Oidom( t_a ), X = c_Groups_Ozero__class_Ozero( t_a ), hAPP
% 1.28/1.61 ( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = c_Groups_Ozero__class_Ozero
% 1.28/1.61 ( t_a ), hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), Y ) = hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( t_a ), Y ), skol18 ) ), hAPP(
% 1.28/1.61 c_Polynomial_Opoly( t_a, c_Polynomial_OpCons( t_a, skol7, skol20 ) ), Y )
% 1.28/1.61 ) }.
% 1.28/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.61 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.61 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.61 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.28/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.61 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.61 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.61 tc_Nat_Onat ), X ), Y ) }.
% 1.28/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.28/1.61 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.28/1.61 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.61 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.61 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.61 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.28/1.61 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.28/1.61 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.61 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.28/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.28/1.61 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.28/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.61 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.28/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.61 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.28/1.61 ) ) }.
% 1.28/1.61 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.61 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.61 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.61 ) ) }.
% 1.28/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.61 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.28/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.61 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.61 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.61 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.61 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.61 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.61 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.61 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.61 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.61 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.61 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.28/1.61 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.61 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.28/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.28/1.61 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.61 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.61 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.28/1.61 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.28/1.61 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.28/1.61 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.61 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.61 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.28/1.61 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.28/1.61 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.61 X, Y, Z ) }.
% 1.28/1.61 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.61 Y, T ), Z = Y }.
% 1.28/1.61 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.61 T, Y ), Z = Y }.
% 1.28/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.61 T, Y ), Z = Y }.
% 1.28/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.61 Y, Z ), T = Y }.
% 1.28/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.61 Y, Z ) }.
% 1.28/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.61 T, Y ), Z = Y }.
% 1.28/1.61 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.61 T, Y ) }.
% 1.28/1.61 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.61 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.61 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.28/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.28/1.61 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.61 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.61 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.28/1.61 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.61 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.61 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.61 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.61 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.61 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.62 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.62 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.62 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.62 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.62 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.28/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.28/1.62 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.28/1.62 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, Z, Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.28/1.62 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, Z, Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.62 , T ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.62 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.62 , T, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.62 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.62 , Y, T ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.28/1.62 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, Z, Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.62 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.62 , T, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.28/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, T, Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.62 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.62 , Y, Z ) ) }.
% 1.28/1.62 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.62 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.28/1.62 ) ), T ), Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.28/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.28/1.62 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.28/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.28/1.62 .
% 1.28/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.28/1.62 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( X ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.28/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.28/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( X ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.62 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( X ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha4( X, Y, Z, T ),
% 1.28/1.62 alpha27( X, Y, Z, T ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z, T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha27( X, Y, Z, T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.62 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! alpha27( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha27( X, Y, Z, T ) }.
% 1.28/1.62 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.28/1.62 { ! alpha4( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.28/1.62 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha4( X, Y, Z, T ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha5( X, Y, Z, T ),
% 1.28/1.62 alpha28( X, Y, Z, T ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z, T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha28( X, Y, Z, T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! alpha28( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! alpha28( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha28( X, Y, Z, T ) }.
% 1.28/1.62 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.62 { ! alpha5( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.62 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha5( X, Y, Z, T ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.62 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.62 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.62 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.62 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.28/1.62 }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.62 , alpha45( X, Y, Z, T ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha45( X, Y, Z, T ),
% 1.28/1.62 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.28/1.62 { ! alpha45( X, Y, Z, T ), alpha6( X, Z, T ) }.
% 1.28/1.62 { ! alpha45( X, Y, Z, T ), alpha29( X, Y, T ) }.
% 1.28/1.62 { ! alpha6( X, Z, T ), ! alpha29( X, Y, T ), alpha45( X, Y, Z, T ) }.
% 1.28/1.62 { ! alpha29( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), alpha46( X, Y, Z ) }.
% 1.28/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha29( X
% 1.28/1.62 , Y, Z ) }.
% 1.28/1.62 { ! alpha46( X, Y, Z ), alpha29( X, Y, Z ) }.
% 1.28/1.62 { ! alpha46( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.62 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.28/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha46( X
% 1.28/1.62 , Y, Z ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.28/1.62 ), c_Polynomial_Odegree( X, Z ) ), alpha46( X, Y, Z ) }.
% 1.28/1.62 { ! alpha6( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha6( X, Y
% 1.28/1.62 , Z ) }.
% 1.28/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha6( X
% 1.28/1.62 , Y, Z ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.28/1.62 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha7
% 1.28/1.62 ( X, Y, Z ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.62 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__idom( X ), ! alpha7( X, Y, Z ),
% 1.28/1.62 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.28/1.62 { ! alpha7( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 1.28/1.62 ( X ) ) }.
% 1.28/1.62 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.62 alpha7( X, Y, Z ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.28/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.28/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.28/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.28/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.28/1.62 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.28/1.62 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.62 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.62 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.62 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.62 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.62 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.28/1.62 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.28/1.62 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.28/1.62 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 1.28/1.62 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.28/1.62 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.62 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.62 }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.28/1.62 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.28/1.62 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.28/1.62 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.28/1.62 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 1.28/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 1.28/1.62 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 1.28/1.62 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.28/1.62 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.28/1.62 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.28/1.62 .
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.28/1.62 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.28/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.28/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 1.28/1.62 , c_Polynomial_Odegree( X, Y ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.28/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.28/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.28/1.62 ( tc_Int_Oint ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Int_Oint ), X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.28/1.62 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.28/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.62 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.28/1.62 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.28/1.62 .
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.28/1.62 .
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Int_Oint ) ), X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.28/1.62 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.28/1.62 }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Int_Oint ) ), X ) }.
% 1.28/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.28/1.62 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.28/1.62 = X }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Int_Oint ) ) ) }.
% 1.28/1.62 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Int_Oint ) ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.28/1.62 }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Int_Oint ) ) ) }.
% 1.28/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.28/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Int_Oint ) ) = X }.
% 1.28/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Int_Oint ), X ) = X }.
% 1.28/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.28/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.28/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.28/1.62 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.28/1.62 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.62 = Y }.
% 1.28/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.62 = Y }.
% 1.28/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.28/1.62 = Y }.
% 1.28/1.62 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.28/1.62 = Y }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.28/1.62 = Y }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.62 = Y }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.62 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.62 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.62 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.62 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.62 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.62 = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.28/1.62 ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.28/1.62 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.28/1.62 }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.28/1.62 c_Nat_OSuc( X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.28/1.62 ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.62 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.28/1.62 , c_Nat_OSuc( X ) ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.28/1.62 .
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol8( X, Y ) ) }.
% 1.28/1.62 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Nat_Onat ) ) = Y }.
% 1.28/1.62 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Nat_Onat ) ) = Y }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.28/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Nat_Onat ) }.
% 1.28/1.62 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Nat_Onat ) }.
% 1.28/1.62 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.28/1.62 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.62 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.62 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.62 , Y ), X ) }.
% 1.28/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.62 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.28/1.62 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.28/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.28/1.62 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.28/1.62 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.28/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.28/1.62 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.62 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 1.28/1.62 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 1.28/1.62 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.62 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.28/1.62 ), Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.28/1.62 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.28/1.62 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.28/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( X ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( X ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( X ) ), alpha8( X, Y, Z ), alpha30( X, Y, Z ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( X ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha30( X, Y, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( X ) ) }.
% 1.28/1.62 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( X ), Y ), alpha30( X, Y, Z ) }.
% 1.28/1.62 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.62 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ), alpha8( X, Y, Z ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha9( X, Y
% 1.28/1.62 , Z ), alpha31( X, Y, Z ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha31( X, Y, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ), alpha31( X, Y, Z ) }.
% 1.28/1.62 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.62 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), alpha9( X, Y, Z ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.62 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 Z, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 Y, Z ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.28/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.62 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.28/1.62 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.28/1.62 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.62 , Y, T ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.28/1.62 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.28/1.62 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.62 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.28/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.62 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.62 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.62 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.62 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.28/1.62 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.28/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.28/1.62 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 1.28/1.62 }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.28/1.62 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 1.28/1.62 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 1.28/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 1.28/1.62 , Y ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.28/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 1.28/1.62 Y ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.28/1.62 .
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.28/1.62 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.28/1.62 ), X ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.62 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.28/1.62 , Y ) ) }.
% 1.28/1.62 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.28/1.62 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.28/1.62 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.28/1.62 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 1.28/1.62 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.62 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.28/1.62 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Groups_Ocomm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.28/1.62 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.62 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.62 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.62 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.62 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.62 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.62 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.62 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.62 ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.62 ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.62 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.62 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.62 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.28/1.62 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.62 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.62 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), Y ), Z = Y }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.62 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.62 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.62 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.28/1.62 c_Polynomial_Odegree( X, Y ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.28/1.62 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.28/1.62 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.28/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.28/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.28/1.62 ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.28/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.28/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.28/1.62 ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.28/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.28/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.28/1.62 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 1.28/1.62 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.28/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 1.28/1.62 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.62 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.62 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 1.28/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.62 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.28/1.62 c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.62 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.62 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.28/1.62 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.28/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.28/1.62 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.28/1.62 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.28/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 1.28/1.62 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.28/1.62 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.28/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.62 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.28/1.62 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.28/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.62 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.28/1.62 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.28/1.62 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.62 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.28/1.62 ( tc_Int_Oint ), Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.62 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, X, Y ) ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Int_Oint ) ) }.
% 1.28/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Int_Oint ) ) }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.28/1.62 , Y ) }.
% 1.28/1.62 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.28/1.62 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.28/1.62 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.28/1.62 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 1.28/1.62 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.62 ) ) }.
% 1.28/1.62 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 1.28/1.62 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.28/1.62 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.28/1.62 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.28/1.62 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.62 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.62 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.62 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.28/1.62 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.28/1.62 c_Polynomial_Odegree( X, Y ) }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.62 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.28/1.62 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.28/1.62 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.28/1.62 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.28/1.62 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.62 Y ) ) = Y }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 Z, Y ) ) = Y }.
% 1.28/1.62 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Y ) ) }.
% 1.28/1.62 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.62 ) ), Y ) }.
% 1.28/1.62 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.28/1.62 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Y ) ) }.
% 1.28/1.62 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.28/1.62 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.62 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.28/1.62 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.62 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.62 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.62 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.62 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.28/1.62 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Y ), Z ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.62 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Z ), Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.28/1.62 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.28/1.62 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 = Y }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( X ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Y ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.62 = Y }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Y ), Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.62 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.62 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.62 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.62 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.62 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.62 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.62 , Y ) }.
% 1.28/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.62 , Y ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.28/1.62 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Z ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.28/1.62 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Y ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.28/1.62 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.62 Z ) = Y }.
% 1.28/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.62 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.28/1.62 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.62 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.62 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.28/1.62 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.62 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.62 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.62 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.28/1.62 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.62 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.62 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.28/1.62 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.62 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.28/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.28/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.28/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.28/1.62 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.62 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.28/1.62 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.28/1.62 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.28/1.62 ) ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.28/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.28/1.62 hAPP( Y, U ) ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.28/1.62 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.28/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.28/1.62 hAPP( Y, U ) ) }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.28/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.28/1.62 hAPP( Y, U ) ) }.
% 1.28/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.28/1.62 ( Z, skol9( X, Y, Z ) ), hAPP( Y, skol9( X, Y, Z ) ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.62 Y ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.28/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.62 Y ), ! Z = Y }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.62 Z ), ! Z = Y }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.62 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.62 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.28/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.62 , ! Z = Y }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.62 , ! Z = Y }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.62 , ! Y = Z }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.28/1.62 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.28/1.62 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.28/1.62 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.62 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.62 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.62 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.62 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.62 , ! Z = Y }.
% 1.28/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.62 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.62 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.28/1.62 Y ) ) ), Y ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.28/1.62 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 1.28/1.62 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.62 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.28/1.62 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.28/1.62 Y ) ) ), Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) }.
% 1.28/1.62 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.28/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.28/1.62 , Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.28/1.62 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 1.28/1.62 , Z, Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.28/1.62 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.28/1.62 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.28/1.62 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.28/1.62 }.
% 1.28/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.28/1.62 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.28/1.62 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.28/1.62 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.62 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.62 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.62 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.62 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.62 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.28/1.62 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.62 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.62 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.28/1.62 Z, T ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.62 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.28/1.62 }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.62 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.28/1.62 }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.62 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.28/1.62 }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.62 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.28/1.62 }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.28/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.62 ), T ), U ), Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.62 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.62 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 1.28/1.62 .
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 1.28/1.62 X, T, Z ), Y ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.28/1.62 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.28/1.62 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha10( X
% 1.28/1.62 , Y, T ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha32( X
% 1.28/1.62 , Y, Z, T ) }.
% 1.28/1.62 { ! class_Fields_Ofield( X ), ! alpha10( X, Y, T ), ! alpha32( X, Y, Z, T )
% 1.28/1.62 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 1.28/1.62 ( X, T, Z ), Y ) }.
% 1.28/1.62 { ! alpha32( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.28/1.62 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha32( X, Y, Z, T ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha32( X
% 1.28/1.62 , Y, Z, T ) }.
% 1.28/1.62 { ! alpha10( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { Z = c_Groups_Ozero__class_Ozero( X ), alpha10( X, Y, Z ) }.
% 1.28/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha10( X
% 1.28/1.62 , Y, Z ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.28/1.62 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 1.28/1.62 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 1.28/1.62 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.28/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.28/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.28/1.62 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.28/1.62 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.28/1.62 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.28/1.62 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 1.28/1.62 ) ) }.
% 1.28/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Y ), Z = Y }.
% 1.28/1.62 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( X, Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.62 ( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.28/1.62 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.28/1.62 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 1.28/1.62 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.28/1.62 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.28/1.62 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.28/1.62 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 1.28/1.62 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.28/1.62 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 1.28/1.62 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.62 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.28/1.62 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.28/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.62 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.28/1.62 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.28/1.62 hAPP( Z, skol11( U, W, Z ) ) ) }.
% 1.28/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.28/1.62 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol11( X
% 1.28/1.62 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.28/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.28/1.62 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol19( X,
% 1.28/1.62 Y, Z ) ) ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.28/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.28/1.62 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.28/1.62 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.28/1.62 X, Z ), Y ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.28/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.28/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 1.28/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 1.28/1.62 c_Polynomial_OpCons( X, T,
% 1.28/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.28/1.62 .
% 1.28/1.62 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.28/1.62 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 1.28/1.62 .
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.62 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.28/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 1.28/1.62 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 1.28/1.62 ) ) }.
% 1.28/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.28/1.62 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.28/1.62 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Int_Oint, Y, X ), X = Y }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.28/1.62 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Int_Oint, Y, X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.28/1.62 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.28/1.62 , Z ), X ) ), T ) ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, U, T ) ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.62 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.28/1.62 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.62 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.62 X ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.28/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), !
% 1.28/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Polynomial_Opoly( X ) ),
% 1.28/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.28/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 1.28/1.62 c_Polynomial_Odegree( X, Z ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.28/1.62 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.28/1.62 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 1.28/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.28/1.62 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.28/1.62 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.28/1.62 ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.28/1.62 ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.28/1.62 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.62 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.62 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.28/1.62 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.28/1.62 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.28/1.62 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.28/1.62 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.28/1.62 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 1.28/1.62 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.62 , Y ) ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.28/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.28/1.62 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Nat_Onat, Z, X ) }.
% 1.28/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.28/1.62 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.28/1.62 ) }.
% 1.28/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.62 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.28/1.62 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.28/1.62 ) }.
% 1.28/1.62 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Nat_Onat, Y, Z ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.28/1.62 , Z ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.28/1.62 Z, Y ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.62 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Nat_Onat, Y, Z ) }.
% 1.28/1.62 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Nat_Onat, Y, Z ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.62 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.62 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.62 { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! alpha11( X, Y ), ! Y = X }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha11( X, Y ) }
% 1.28/1.62 .
% 1.28/1.62 { ! alpha11( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! alpha11( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), alpha11( X, Y ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha12( X, Y ), Y = X }
% 1.28/1.62 .
% 1.28/1.62 { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! alpha12( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! alpha12( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.28/1.62 ( tc_Nat_Onat, X, Y ), alpha12( X, Y ) }.
% 1.28/1.62 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.62 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Nat_Onat ) ) }.
% 1.28/1.62 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.28/1.62 tc_Nat_Onat ), X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Nat_Onat ), Y ) }.
% 1.28/1.62 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Int_Oint, Z, X ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol12( Z, Y ) ) ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.28/1.62 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Int_Oint, skol12( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.62 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.28/1.62 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 1.28/1.62 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 1.28/1.62 ) ) }.
% 1.28/1.62 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.28/1.62 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol13( Z, Y
% 1.28/1.62 ), Y ) }.
% 1.28/1.62 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.28/1.62 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.28/1.62 skol13( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.28/1.62 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.28/1.62 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.28/1.62 , skol13( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.62 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.62 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 1.28/1.62 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 1.28/1.62 , Y ) }.
% 1.28/1.62 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.62 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.28/1.62 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.62 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.28/1.62 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.28/1.62 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.28/1.62 ) ) }.
% 1.28/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.28/1.62 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.28/1.62 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.28/1.62 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.28/1.62 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.28/1.62 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.28/1.62 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.62 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.28/1.62 ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.62 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.28/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.28/1.62 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.28/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.28/1.62 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.62 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( X ) ) }.
% 1.28/1.62 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.62 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.28/1.62 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.62 , Z, Y ) }.
% 1.28/1.62 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.62 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.62 Z ) ), Y ) ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.62 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.62 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.62 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.28/1.62 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.28/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.62 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.62 W ) ), U ), Y ) }.
% 1.28/1.62 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.62 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.62 ( X ), Z ), U ), Y ) }.
% 1.28/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.62 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.28/1.62 Z ) ), U ), T ) = Y }.
% 1.28/1.62 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.28/1.62 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.62 ( X ), Z ), U ), Y ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.28/1.62 X, Y ) }.
% 1.28/1.62 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.28/1.62 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.28/1.62 X, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.28/1.62 X, Z, Y ) }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.28/1.62 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.62 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.28/1.62 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.62 , Y ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.62 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.28/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.62 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.28/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.28/1.62 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.28/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.28/1.62 ) }.
% 1.28/1.62 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.28/1.62 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.28/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.62 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.62 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.28/1.62 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.28/1.62 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.28/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.28/1.62 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.62 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.28/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.62 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.28/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.62 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.28/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.28/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.28/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.28/1.62 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.28/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.62 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.28/1.62 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.62 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.28/1.62 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.62 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.28/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.28/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.28/1.63 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.28/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.28/1.63 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 1.28/1.63 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.28/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.28/1.63 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.28/1.63 c_Polynomial_Ocoeff( X, Y ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.28/1.63 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol14( X
% 1.28/1.63 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol14( X, Y, Z ) ), Z =
% 1.28/1.63 Y }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.28/1.63 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.28/1.63 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.28/1.63 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.28/1.63 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 1.28/1.63 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 1.28/1.63 hAPP( Z, Y ) ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.28/1.63 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 1.28/1.63 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 1.28/1.63 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.28/1.63 ), Y ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ) ) = Z }.
% 1.28/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.28/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, Z, Y ), X ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, Z, X ), Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.28/1.63 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, Z, X ), Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.28/1.63 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.28/1.63 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.28/1.63 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.28/1.63 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.28/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.28/1.63 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 1.28/1.63 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.28/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 1.28/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 1.28/1.63 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.28/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.28/1.63 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.63 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.63 X, W, Z ) ), U ), T ), Y ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), Z ), U ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( X, Z, W ) ), U ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.63 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.28/1.63 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.28/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.28/1.63 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.28/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.28/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.28/1.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.28/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.28/1.63 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.28/1.63 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.28/1.63 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.28/1.63 }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.28/1.63 ) ) = X }.
% 1.28/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.28/1.63 , alpha13( X, Y, Z ) }.
% 1.28/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.28/1.63 , alpha33( X, Y, Z ) }.
% 1.28/1.63 { ! alpha13( X, Y, Z ), ! alpha33( X, Y, Z ), hBOOL( hAPP( Z,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.28/1.63 { ! alpha33( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.28/1.63 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.28/1.63 { ! hBOOL( hAPP( Z, skol15( T, U, Z ) ) ), alpha33( X, Y, Z ) }.
% 1.28/1.63 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol15( X, Y, Z ) ),
% 1.28/1.63 alpha33( X, Y, Z ) }.
% 1.28/1.63 { ! alpha13( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.28/1.63 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha13( X, Y, Z ) }
% 1.28/1.63 .
% 1.28/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13
% 1.28/1.63 ( X, Y, Z ) }.
% 1.28/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.28/1.63 , ! alpha14( X, Y, Z ) }.
% 1.28/1.63 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.28/1.63 , ! alpha34( X, Y, Z ) }.
% 1.28/1.63 { alpha14( X, Y, Z ), alpha34( X, Y, Z ), hBOOL( hAPP( Z,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.28/1.63 { ! alpha34( X, Y, Z ), ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ) }.
% 1.28/1.63 { ! alpha34( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.28/1.63 skol16( X, Y, Z ) ) }.
% 1.28/1.63 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.28/1.63 ) ), alpha34( X, Y, Z ) }.
% 1.28/1.63 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.28/1.63 }.
% 1.28/1.63 { ! alpha14( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ) ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha14( X, Y, Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.63 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.28/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.63 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.28/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.28/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.28/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.28/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.28/1.63 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.28/1.63 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 1.28/1.63 tc_Nat_Onat ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.28/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.28/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.28/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.28/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.28/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.63 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.28/1.63 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.28/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.28/1.63 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.28/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.28/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.63 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.28/1.63 ( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.28/1.63 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.28/1.63 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.28/1.63 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.28/1.63 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.28/1.63 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.28/1.63 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.63 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.28/1.63 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.28/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.28/1.63 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.28/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.28/1.63 ( X ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.28/1.63 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.28/1.63 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.28/1.63 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.28/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.63 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.63 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.63 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.63 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), Y ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.28/1.63 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.63 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.28/1.63 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.28/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.63 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.28/1.63 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.63 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.28/1.63 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.28/1.63 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 1.28/1.63 }.
% 1.28/1.63 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Ominus__class_Ominus
% 1.28/1.63 ( tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X )
% 1.28/1.63 , c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.28/1.63 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.28/1.63 .
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.28/1.63 ( tc_Int_Oint ) ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.28/1.63 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 1.28/1.63 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 1.28/1.63 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 1.28/1.63 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 1.28/1.63 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.63 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.28/1.63 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.63 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.63 ), Y ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.63 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.28/1.63 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.28/1.63 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 1.28/1.63 ( X ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.63 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.63 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.63 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.28/1.63 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 1.28/1.63 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.63 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 1.28/1.63 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 1.28/1.63 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.28/1.63 tc_Nat_Onat, Z, T ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Z, Y ) ), alpha35( X, Y, Z, T ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Z, Y ) ), alpha47( X, Y, Z, T ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha35( X, Y, Z
% 1.28/1.63 , T ), ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), alpha51( X, Y, Z, T ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.63 , alpha47( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha51( X, Y, Z, T ), alpha47( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha51( X, Y, Z, T ), alpha55( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha51( X, Y, Z, T ), alpha15( X, Y, T ) }.
% 1.28/1.63 { ! alpha55( X, Y, Z, T ), ! alpha15( X, Y, T ), alpha51( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha55( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.63 alpha55( X, Y, Z, T ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha55( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha35( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.63 alpha35( X, Y, Z, T ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha35( X, Y, Z, T )
% 1.28/1.63 }.
% 1.28/1.63 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.63 , alpha15( X, Y, Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) ), alpha15( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , T, Z ), Y ), alpha36( X, Y, Z, T ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , T, Z ), Y ), alpha48( X, Y, Z, T ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 1.28/1.63 , T ), ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.28/1.63 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), alpha52( X, Y, Z, T ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.63 , alpha48( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha52( X, Y, Z, T ), alpha48( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha52( X, Y, Z, T ), alpha56( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha52( X, Y, Z, T ), alpha16( X, Y, Z ) }.
% 1.28/1.63 { ! alpha56( X, Y, Z, T ), ! alpha16( X, Y, Z ), alpha52( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha56( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.63 alpha56( X, Y, Z, T ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha56( X, Y, Z, T )
% 1.28/1.63 }.
% 1.28/1.63 { ! alpha36( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.63 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.63 alpha36( X, Y, Z, T ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha36( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.63 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.63 , alpha16( X, Y, Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , Y ), alpha16( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 1.28/1.63 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.63 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.63 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha17( X, Y, Z ), alpha37
% 1.28/1.63 ( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha17( X, Y, Z
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), alpha37( X, Y, Z ) }.
% 1.28/1.63 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.63 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), alpha17( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha18( X, Y, Z ), alpha38
% 1.28/1.63 ( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha18( X, Y, Z
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( X ), Y ), alpha38( X, Y, Z ) }.
% 1.28/1.63 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.63 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), alpha18( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha19( X, Y, Z ), alpha39
% 1.28/1.63 ( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha19( X, Y, Z
% 1.28/1.63 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 1.28/1.63 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! alpha39( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.63 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), alpha39( X, Y, Z ) }.
% 1.28/1.63 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.63 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.63 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), alpha19( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 1.28/1.63 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha20( X, Y, Z ), alpha40( X,
% 1.28/1.63 Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha20( X, Y, Z
% 1.28/1.63 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha40( X, Y, Z
% 1.28/1.63 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! alpha40( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.63 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), alpha40( X, Y, Z ) }.
% 1.28/1.63 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.63 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.63 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), alpha20( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , Y, Z ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , Y, Z ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 1.28/1.63 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha41( X, Y, Z, T ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha21( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha41( X, Y, Z, T ), !
% 1.28/1.63 alpha21( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 1.28/1.63 { ! alpha41( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.28/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.28/1.63 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha41( X, Y, Z, T ) }.
% 1.28/1.63 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha41(
% 1.28/1.63 X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha21( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { Z = c_Groups_Ozero__class_Ozero( X ), alpha21( X, Y, Z ) }.
% 1.28/1.63 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha21( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha42( X, Y, Z, T ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha22( X, Y, T ) }.
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha42( X, Y, Z, T ), !
% 1.28/1.63 alpha22( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.63 { ! alpha42( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.28/1.63 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.28/1.63 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha42( X, Y, Z, T ) }.
% 1.28/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha42(
% 1.28/1.63 X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha22( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { Y = c_Groups_Ozero__class_Ozero( X ), alpha22( X, Y, Z ) }.
% 1.28/1.63 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha22( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.63 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.63 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.63 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.63 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.63 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.28/1.63 X ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.28/1.63 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 Z, Y ) ), alpha43( X, Y, Z, T ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 Z, Y ) ), alpha49( X, Y, Z, T ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha43( X, Y, Z
% 1.28/1.63 , T ), ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.63 { ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), alpha53( X, Y, Z, T ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.63 , alpha49( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha53( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha53( X, Y, Z, T ), alpha57( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha53( X, Y, Z, T ), alpha23( X, Y, T ) }.
% 1.28/1.63 { ! alpha57( X, Y, Z, T ), ! alpha23( X, Y, T ), alpha53( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha57( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.63 alpha57( X, Y, Z, T ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha57( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha43( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.63 alpha43( X, Y, Z, T ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha43( X, Y, Z, T )
% 1.28/1.63 }.
% 1.28/1.63 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.63 , alpha23( X, Y, Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.63 , alpha23( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.63 Z ), Y ), alpha44( X, Y, Z, T ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.63 Z ), Y ), alpha50( X, Y, Z, T ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha44( X, Y, Z
% 1.28/1.63 , T ), ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.28/1.63 { ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), alpha54( X, Y, Z, T ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.63 , alpha50( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha54( X, Y, Z, T ), alpha50( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha54( X, Y, Z, T ), alpha58( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha54( X, Y, Z, T ), alpha24( X, Y, Z ) }.
% 1.28/1.63 { ! alpha58( X, Y, Z, T ), ! alpha24( X, Y, Z ), alpha54( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha58( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.63 alpha58( X, Y, Z, T ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha58( X, Y, Z, T )
% 1.28/1.63 }.
% 1.28/1.63 { ! alpha44( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.63 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.63 alpha44( X, Y, Z, T ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha44( X, Y, Z, T ) }.
% 1.28/1.63 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.63 , alpha24( X, Y, Z ) }.
% 1.28/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.63 , alpha24( X, Y, Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 Z, Y ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.63 Y ), Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.63 Y ), Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 Z, Y ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 Z, Y ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.63 Y ), Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.63 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.63 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.63 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 1.28/1.63 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.63 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.28/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.28/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.63 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.28/1.63 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.63 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.28/1.63 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.63 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , T, Y ), Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , T, Y ), Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , T, Y ), Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.63 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.63 ( X, Z, Y ) ) }.
% 1.28/1.63 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 1.28/1.63 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.63 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.63 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T, Z ), Y ) =
% 1.28/1.63 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.28/1.63 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 1.28/1.63 tc_Polynomial_Opoly( X ), Z, Y ) ), c_Polynomial_Osmult( X,
% 1.28/1.63 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 1.28/1.63 c_Polynomial_OpCons( X, T, c_Divides_Odiv__class_Omod(
% 1.28/1.63 tc_Polynomial_Opoly( X ), Z, Y ) ) ), c_Polynomial_Odegree( X, Y ) ),
% 1.28/1.63 hAPP( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.28/1.63 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 1.28/1.63 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.28/1.63 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 1.28/1.63 ( X ), Z, Y ) ) }.
% 1.28/1.63 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.63 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 1.28/1.63 , Y ) ), Y ) }.
% 1.28/1.63 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.28/1.63 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 1.28/1.63 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.63 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 1.28/1.63 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 1.28/1.63 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.28/1.63 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.28/1.63 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.63 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 1.28/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.63 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.63 ( X, Z, Y ) }.
% 1.28/1.63 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 1.28/1.63 ( X, Y, Z ) }.
% 1.28/1.63 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.63 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 1.28/1.63 , Y ) ), Y ) }.
% 1.28/1.63 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.28/1.63 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.28/1.63 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.28/1.63 ), Z ), Y ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ),
% 1.28/1.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct( X
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__ab__semigroup__add( X ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors( X ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__semigroup__add( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__mult( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__mult( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Oab__semigroup__add( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Ocomm__monoid__add( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__1( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring__0( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__semiring( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Oab__group__add( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ozero__neq__one( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__mult( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring__1( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Omonoid__add( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Osemiring__0( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Ogroup__add( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Omult__zero( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ocomm__ring( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Osemiring( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Ouminus( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__1( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Ominus( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Power_Opower( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Ozero( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Oone( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Odvd( X ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Groups_Ocancel__comm__monoid__add( X ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.28/1.63 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.63 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.28/1.63 ( tc_fun( Y, X ) ) }.
% 1.28/1.63 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.28/1.63 ) ) }.
% 1.28/1.63 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.28/1.63 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.28/1.63 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.28/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.63 tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.28/1.63 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.28/1.63 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.28/1.63 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.28/1.63 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.28/1.63 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.28/1.63 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.28/1.63 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.28/1.63 { class_Power_Opower( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.28/1.63 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.28/1.63 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.28/1.63 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.63 tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.28/1.63 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.28/1.63 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.28/1.63 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.28/1.63 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.28/1.63 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.28/1.63 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ),
% 1.28/1.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.28/1.63 ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.28/1.63 X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.28/1.63 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ),
% 1.28/1.63 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.28/1.63 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.28/1.63 ( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.28/1.63 ( tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.28/1.63 ( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.28/1.63 }.
% 1.28/1.63 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.28/1.63 ) ) }.
% 1.28/1.63 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.28/1.63 .
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.28/1.63 tc_Polynomial_Opoly( X ) ) }.
% 1.28/1.63 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.28/1.63 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.28/1.63 { ! v_z = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.28/1.63 { ! c_Groups_Oplus__class_Oplus( t_a, v_a, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( t_a ), v_z ), hAPP( c_Polynomial_Opoly(
% 1.28/1.63 t_a, v_q ), v_z ) ) ) = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.28/1.63 { ! v_a = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.28/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_If( tc_Nat_Onat, c_fequal(
% 1.28/1.63 v_q, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) ),
% 1.28/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Nat_OSuc(
% 1.28/1.63 c_Polynomial_Odegree( t_a, v_q ) ) ), v_k ) = c_Polynomial_Odegree( t_a,
% 1.28/1.63 v_cs____ ) }.
% 1.28/1.63 { hAPP( c_Polynomial_Opoly( t_a, v_cs____ ), X ) = hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( t_a ), hAPP( hAPP(
% 1.28/1.63 c_Power_Opower__class_Opower( t_a ), X ), v_k ) ),
% 1.28/1.63 c_Groups_Oplus__class_Oplus( t_a, v_a, hAPP( hAPP(
% 1.28/1.63 c_Groups_Otimes__class_Otimes( t_a ), X ), hAPP( c_Polynomial_Opoly( t_a
% 1.28/1.63 , v_q ), X ) ) ) ) }.
% 1.28/1.63 { ! v_cs____ = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) }
% 1.28/1.63 .
% 1.28/1.63 { alpha60, ! v_q = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a )
% 1.28/1.63 ) }.
% 1.28/1.63 { alpha60, ! c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.63 c_Polynomial_Odegree( t_a, v_q ), v_k ) ) = c_Polynomial_Odegree( t_a,
% 1.28/1.63 v_cs____ ) }.
% 1.28/1.63 { ! alpha60, v_q = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a )
% 1.28/1.63 ) }.
% 1.28/1.63 { ! alpha60, alpha62 }.
% 1.28/1.63 { ! v_q = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ), !
% 1.28/1.63 alpha62, alpha60 }.
% 1.28/1.63 { ! alpha62, ! v_k = c_Polynomial_Odegree( t_a, v_cs____ ), alpha63 }.
% 1.28/1.63 { v_k = c_Polynomial_Odegree( t_a, v_cs____ ), alpha62 }.
% 1.28/1.63 { ! alpha63, alpha62 }.
% 1.28/1.63 { ! alpha63, alpha64( skol17 ) }.
% 1.28/1.63 { ! alpha63, ! hAPP( c_Polynomial_Opoly( t_a, v_q ), skol17 ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.28/1.63 { ! alpha64( X ), hAPP( c_Polynomial_Opoly( t_a, v_q ), X ) =
% 1.28/1.63 c_Groups_Ozero__class_Ozero( t_a ), alpha63 }.
% 1.28/1.63 { ! alpha64( X ), alpha65( X ) }.
% 1.28/1.63 { ! alpha64( X ), ! X = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.28/1.63 { ! alpha65( X ), X = c_Groups_Ozero__class_Ozero( t_a ), alpha64( X ) }.
% 1.28/1.63 { ! alpha65( X ), ! X = c_Groups_Ozero__class_Ozero( t_a ) }.
% 1.28/1.63 { ! alpha65( X ), ! X = c_Groups_Ozero__class_Ozero( t_a ), !
% 1.28/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.63 tc_Nat_Onat ), v_k ) }.
% 1.28/1.63 { X = c_Groups_Ozero__class_Ozero( t_a ), X = c_Groups_Ozero__class_Ozero(
% 1.28/1.63 t_a ), alpha65( X ) }.
% 1.28/1.63 { X = c_Groups_Ozero__class_Ozero( t_a ), c_Orderings_Oord__class_Oless(
% 1.28/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), v_k ), alpha65(
% 1.28/1.63 X ) }.
% 1.28/1.63 { class_Rings_Oidom( t_a ) }.
% 1.28/1.63
% 1.28/1.63 *** allocated 15000 integers for clauses
% 1.28/1.63 *** allocated 22500 integers for clauses
% 1.28/1.63 *** allocated 33750 integers for clauses
% 1.28/1.63 *** allocated 50625 integers for clauses
% 1.28/1.63 *** allocated 75937 integers for clauses
% 1.28/1.63 percentage equality = 0.254395, percentage horn = 0.889598
% 1.28/1.63 This is a problem with some equality
% 1.28/1.63
% 1.28/1.63
% 1.28/1.63
% 1.28/1.63 Options Used:
% 1.28/1.63
% 1.28/1.63 useres = 1
% 1.28/1.63 useparamod = 1
% 1.28/1.63 useeqrefl = 1
% 1.28/1.63 useeqfact = 1
% 1.28/1.63 usefactor = 1
% 1.28/1.63 usesimpsplitting = 0
% 1.28/1.63 usesimpdemod = 5
% 1.28/1.63 usesimpres = 3
% 1.28/1.63
% 1.28/1.63 resimpinuse = 1000
% 1.28/1.63 resimpclauses = 20000
% 1.28/1.63 substype = eqrewr
% 1.28/1.63 backwardsubs = 1
% 1.28/1.63 selectoldest = 5
% 1.28/1.63
% 1.28/1.63 litorderings [0] = split
% 1.28/1.63 litorderings [1] = extend the termordering, first sorting on arguments
% 1.28/1.63
% 1.28/1.63 termordering = kbo
% 1.28/1.63
% 1.28/1.63 litapriori = 0
% 1.28/1.63 termapriori = 1
% 1.28/1.63 litaposteriori = 0
% 1.28/1.63 termaposteriori = 0
% 1.28/1.63 demodaposteriori = 0
% 1.28/1.63 ordereqreflfact = 0
% 1.28/1.63
% 1.28/1.63 litselect = negord
% 1.28/1.63
% 1.28/1.63 maxweight = 15
% 1.28/1.63 maxdepth = 30000
% 1.28/1.63 maxlength = 115
% 1.28/1.63 maxnrvars = 195
% 1.28/1.63 excuselevel = 1
% 1.28/1.63 increasemaxweight = 1
% 1.28/1.63
% 1.28/1.63 maxselected = 10000000
% 1.28/1.63 maxnrclauses = 10000000
% 1.28/1.63
% 1.28/1.63 showgenerated = 0
% 1.28/1.63 showkept = 0
% 1.28/1.63 showselected = 0
% 1.28/1.63 showdeleted = 0
% 1.28/1.63 showresimp = 1
% 1.28/1.63 showstatus = 2000
% 1.28/1.63
% 1.28/1.63 prologoutput = 0
% 1.28/1.63 nrgoals = 5000000
% 1.28/1.63 totalproof = 1
% 1.28/1.63
% 1.28/1.63 Symbols occurring in the translation:
% 1.28/1.63
% 1.28/1.63 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.28/1.63 . [1, 2] (w:1, o:205, a:1, s:1, b:0),
% 1.28/1.63 ! [4, 1] (w:0, o:119, a:1, s:1, b:0),
% 1.28/1.63 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.28/1.63 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.28/1.63 hAPP [38, 2] (w:1, o:229, a:1, s:1, b:0),
% 1.28/1.63 t_a [39, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Oidom [40, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.28/1.63 v_c____ [41, 0] (w:1, o:18, a:1, s:1, b:0),
% 1.28/1.63 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.28/1.63 v_p [44, 0] (w:1, o:20, a:1, s:1, b:0),
% 1.28/1.63 c_Polynomial_Opoly [45, 2] (w:1, o:230, a:1, s:1, b:0),
% 1.28/1.63 tc_Nat_Onat [47, 0] (w:1, o:28, a:1, s:1, b:0),
% 1.28/1.63 c_Nat_OSuc [48, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.28/1.63 c_Orderings_Oord__class_Oless [49, 3] (w:1, o:253, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Olinordered__ring [54, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.28/1.63 c_Groups_Otimes__class_Otimes [55, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.28/1.63 c_Groups_Oplus__class_Oplus [56, 3] (w:1, o:255, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Olinordered__ring__strict [60, 1] (w:1, o:129, a:1, s:1
% 1.28/1.63 , b:0),
% 1.28/1.63 class_Groups_Ozero [62, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.28/1.63 tc_Polynomial_Opoly [63, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.28/1.63 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [64, 2] (w:1, o:231
% 1.28/1.63 , a:1, s:1, b:0),
% 1.28/1.63 c_Polynomial_Odegree [65, 2] (w:1, o:233, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Ocomm__semiring__0 [66, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.28/1.63 class_Groups_Ocomm__monoid__add [73, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.28/1.63
% 1.28/1.63 hBOOL [79, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.28/1.63 class_Int_Oring__char__0 [85, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Ocomm__semiring__1 [89, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.28/1.63 c_Power_Opower__class_Opower [90, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.28/1.63 v_cs____ [93, 0] (w:1, o:78, a:1, s:1, b:0),
% 1.28/1.63 c_Polynomial_OpCons [94, 3] (w:1, o:258, a:1, s:1, b:0),
% 1.28/1.63 class_Groups_Omonoid__mult [96, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.28/1.63 class_Power_Opower [97, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Osemiring__0 [98, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Omult__zero [100, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Ono__zero__divisors [101, 1] (w:1, o:165, a:1, s:1, b:0)
% 1.28/1.63 ,
% 1.28/1.63 class_Rings_Ozero__neq__one [102, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Olinordered__semidom [103, 1] (w:1, o:157, a:1, s:1, b:0)
% 1.28/1.63 ,
% 1.28/1.63 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.28/1.63 113, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Oring__1__no__zero__divisors [118, 1] (w:1, o:152, a:1
% 1.28/1.63 , s:1, b:0),
% 1.28/1.63 class_Groups_Ocomm__monoid__mult [119, 1] (w:1, o:180, a:1, s:1, b:0)
% 1.28/1.63 ,
% 1.28/1.63 c_fequal [122, 2] (w:1, o:234, a:1, s:1, b:0),
% 1.28/1.63 c_If [123, 4] (w:1, o:303, a:1, s:1, b:0),
% 1.28/1.63 c_Polynomial_Opcompose [124, 3] (w:1, o:259, a:1, s:1, b:0),
% 1.28/1.63 class_Groups_Olinordered__ab__group__add [125, 1] (w:1, o:145, a:1
% 1.28/1.63 , s:1, b:0),
% 1.28/1.63 class_Rings_Olinordered__idom [126, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.28/1.63 class_Groups_Oordered__comm__monoid__add [127, 1] (w:1, o:181, a:1
% 1.28/1.63 , s:1, b:0),
% 1.28/1.63 class_Groups_Oab__semigroup__mult [128, 1] (w:1, o:182, a:1, s:1, b:0
% 1.28/1.63 ),
% 1.28/1.63 class_Groups_Ocancel__semigroup__add [129, 1] (w:1, o:183, a:1, s:1
% 1.28/1.63 , b:0),
% 1.28/1.63 class_Groups_Ocancel__ab__semigroup__add [130, 1] (w:1, o:184, a:1
% 1.28/1.63 , s:1, b:0),
% 1.28/1.63 class_Groups_Oab__semigroup__add [131, 1] (w:1, o:185, a:1, s:1, b:0)
% 1.28/1.63 ,
% 1.28/1.63 tc_Int_Oint [132, 0] (w:1, o:93, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Oring__no__zero__divisors [133, 1] (w:1, o:153, a:1, s:1
% 1.28/1.63 , b:0),
% 1.28/1.63 class_Groups_Omonoid__add [134, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.28/1.63 class_Groups_Oordered__ab__semigroup__add__imp__le [135, 1] (w:1, o:
% 1.28/1.63 187, a:1, s:1, b:0),
% 1.28/1.63 class_Groups_Oordered__cancel__ab__semigroup__add [136, 1] (w:1, o:
% 1.28/1.63 188, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Osemiring [138, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Ocomm__semiring [139, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Olinordered__comm__semiring__strict [141, 1] (w:1, o:159
% 1.28/1.63 , a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Olinordered__semiring__strict [142, 1] (w:1, o:160, a:1
% 1.28/1.63 , s:1, b:0),
% 1.28/1.63 c_Polynomial_Oorder [143, 3] (w:1, o:257, a:1, s:1, b:0),
% 1.28/1.63 class_Fields_Ofield [145, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.28/1.63 c_Polynomial_Opdivmod__rel [146, 5] (w:1, o:328, a:1, s:1, b:0),
% 1.28/1.63 c_Polynomial_Opos__poly [147, 2] (w:1, o:235, a:1, s:1, b:0),
% 1.28/1.63 class_RealVector_Oreal__normed__algebra [149, 1] (w:1, o:169, a:1, s:
% 1.28/1.63 1, b:0),
% 1.28/1.63 c_Polynomial_Opoly__rec [164, 5] (w:1, o:329, a:1, s:1, b:0),
% 1.28/1.63 c_Polynomial_Osynthetic__div [165, 3] (w:1, o:260, a:1, s:1, b:0),
% 1.28/1.63 c_Orderings_Oord__class_Oless__eq [166, 3] (w:1, o:256, a:1, s:1, b:0
% 1.28/1.63 ),
% 1.28/1.63 c_Groups_Oone__class_Oone [167, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.28/1.63 c_Nat_Onat_Onat__size [169, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.28/1.63 c_Polynomial_Osmult [170, 3] (w:1, o:261, a:1, s:1, b:0),
% 1.28/1.63 class_Groups_Oone [172, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.28/1.63 class_Groups_Oordered__ab__semigroup__add [175, 1] (w:1, o:192, a:1
% 1.28/1.63 , s:1, b:0),
% 1.28/1.63 class_Rings_Olinordered__semiring__1 [177, 1] (w:1, o:161, a:1, s:1
% 1.28/1.63 , b:0),
% 1.28/1.63 class_Rings_Olinordered__semiring__1__strict [178, 1] (w:1, o:162, a:
% 1.28/1.63 1, s:1, b:0),
% 1.28/1.63 class_Rings_Oordered__cancel__semiring [179, 1] (w:1, o:170, a:1, s:1
% 1.28/1.63 , b:0),
% 1.28/1.63 class_Rings_Oordered__ring [180, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Oordered__semiring [181, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.28/1.63
% 1.28/1.63 class_Rings_Oordered__comm__semiring [182, 1] (w:1, o:173, a:1, s:1
% 1.28/1.63 , b:0),
% 1.28/1.63 class_Rings_Olinordered__semiring [183, 1] (w:1, o:163, a:1, s:1, b:0
% 1.28/1.63 ),
% 1.28/1.63 class_Orderings_Opreorder [184, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.28/1.63 c_Power_Opower_Opower [185, 3] (w:1, o:262, a:1, s:1, b:0),
% 1.28/1.63 class_Rings_Ocomm__ring__1 [186, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.28/1.63 c_Groups_Ouminus__class_Ouminus [187, 2] (w:1, o:236, a:1, s:1, b:0)
% 2.04/2.41 ,
% 2.04/2.41 c_Nat_Osize__class_Osize [188, 2] (w:1, o:237, a:1, s:1, b:0),
% 2.04/2.41 class_Rings_Ocomm__ring [189, 1] (w:1, o:138, a:1, s:1, b:0),
% 2.04/2.41 class_Groups_Oab__group__add [190, 1] (w:1, o:193, a:1, s:1, b:0),
% 2.04/2.41 class_Groups_Ogroup__add [191, 1] (w:1, o:194, a:1, s:1, b:0),
% 2.04/2.41 class_Rings_Oring [192, 1] (w:1, o:154, a:1, s:1, b:0),
% 2.04/2.41 class_Groups_Oordered__ab__group__add [193, 1] (w:1, o:195, a:1, s:1
% 2.04/2.41 , b:0),
% 2.04/2.41 class_Rings_Oring__1 [194, 1] (w:1, o:155, a:1, s:1, b:0),
% 2.04/2.41 class_Orderings_Olinorder [197, 1] (w:1, o:150, a:1, s:1, b:0),
% 2.04/2.41 class_Orderings_Oord [198, 1] (w:1, o:147, a:1, s:1, b:0),
% 2.04/2.41 tc_fun [199, 2] (w:1, o:245, a:1, s:1, b:0),
% 2.04/2.41 class_Orderings_Oorder [200, 1] (w:1, o:148, a:1, s:1, b:0),
% 2.04/2.41 c_Rings_Odvd__class_Odvd [201, 3] (w:1, o:263, a:1, s:1, b:0),
% 2.04/2.41 class_Lattices_Oboolean__algebra [204, 1] (w:1, o:197, a:1, s:1, b:0)
% 2.04/2.41 ,
% 2.04/2.41 class_Rings_Odvd [205, 1] (w:1, o:174, a:1, s:1, b:0),
% 2.04/2.41 class_Lattices_Oab__semigroup__idem__mult [206, 1] (w:1, o:196, a:1
% 2.04/2.41 , s:1, b:0),
% 2.04/2.41 class_Groups_Ouminus [208, 1] (w:1, o:198, a:1, s:1, b:0),
% 2.04/2.41 c_Polynomial_Omonom [209, 3] (w:1, o:264, a:1, s:1, b:0),
% 2.04/2.41 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [211, 3] (w:
% 2.04/2.41 1, o:254, a:1, s:1, b:0),
% 2.04/2.41 c_Polynomial_Ocoeff [215, 2] (w:1, o:232, a:1, s:1, b:0),
% 2.04/2.41 c_Groups_Ominus__class_Ominus [216, 3] (w:1, o:265, a:1, s:1, b:0),
% 2.04/2.41 class_Groups_Ominus [219, 1] (w:1, o:199, a:1, s:1, b:0),
% 2.04/2.41 c_Rings_Oinverse__class_Odivide [225, 3] (w:1, o:266, a:1, s:1, b:0)
% 2.04/2.41 ,
% 2.04/2.41 class_RealVector_Oreal__normed__field [226, 1] (w:1, o:175, a:1, s:1
% 2.04/2.41 , b:0),
% 2.04/2.41 class_Rings_Odivision__ring [227, 1] (w:1, o:176, a:1, s:1, b:0),
% 2.04/2.41 class_Rings_Odivision__ring__inverse__zero [228, 1] (w:1, o:177, a:1
% 2.04/2.41 , s:1, b:0),
% 2.04/2.41 class_Fields_Ofield__inverse__zero [229, 1] (w:1, o:131, a:1, s:1, b:
% 2.04/2.41 0),
% 2.04/2.41 class_Fields_Olinordered__field__inverse__zero [230, 1] (w:1, o:132
% 2.04/2.41 , a:1, s:1, b:0),
% 2.04/2.41 class_Fields_Olinordered__field [231, 1] (w:1, o:133, a:1, s:1, b:0)
% 2.04/2.41 ,
% 2.04/2.41 class_RealVector_Oreal__field [232, 1] (w:1, o:178, a:1, s:1, b:0),
% 2.04/2.41 c_Divides_Odiv__class_Omod [233, 3] (w:1, o:267, a:1, s:1, b:0),
% 2.04/2.41 class_Divides_Oring__div [234, 1] (w:1, o:200, a:1, s:1, b:0),
% 2.04/2.41 class_Divides_Osemiring__div [235, 1] (w:1, o:201, a:1, s:1, b:0),
% 2.04/2.41 class_Groups_Ocancel__comm__monoid__add [237, 1] (w:1, o:202, a:1, s:
% 2.04/2.41 1, b:0),
% 2.04/2.41 tc_HOL_Obool [240, 0] (w:1, o:92, a:1, s:1, b:0),
% 2.04/2.41 v_z [241, 0] (w:1, o:112, a:1, s:1, b:0),
% 2.04/2.41 v_a [242, 0] (w:1, o:113, a:1, s:1, b:0),
% 2.04/2.41 v_q [243, 0] (w:1, o:114, a:1, s:1, b:0),
% 2.04/2.41 v_k [244, 0] (w:1, o:115, a:1, s:1, b:0),
% 2.04/2.41 alpha1 [245, 2] (w:1, o:246, a:1, s:1, b:1),
% 2.04/2.41 alpha2 [246, 2] (w:1, o:249, a:1, s:1, b:1),
% 2.04/2.41 alpha3 [247, 2] (w:1, o:252, a:1, s:1, b:1),
% 2.04/2.41 alpha4 [248, 4] (w:1, o:307, a:1, s:1, b:1),
% 2.04/2.41 alpha5 [249, 4] (w:1, o:316, a:1, s:1, b:1),
% 2.04/2.41 alpha6 [250, 3] (w:1, o:269, a:1, s:1, b:1),
% 2.04/2.41 alpha7 [251, 3] (w:1, o:271, a:1, s:1, b:1),
% 2.04/2.41 alpha8 [252, 3] (w:1, o:272, a:1, s:1, b:1),
% 2.04/2.41 alpha9 [253, 3] (w:1, o:273, a:1, s:1, b:1),
% 2.04/2.41 alpha10 [254, 3] (w:1, o:274, a:1, s:1, b:1),
% 2.04/2.41 alpha11 [255, 2] (w:1, o:247, a:1, s:1, b:1),
% 2.04/2.41 alpha12 [256, 2] (w:1, o:248, a:1, s:1, b:1),
% 2.04/2.41 alpha13 [257, 3] (w:1, o:275, a:1, s:1, b:1),
% 2.04/2.41 alpha14 [258, 3] (w:1, o:276, a:1, s:1, b:1),
% 2.04/2.41 alpha15 [259, 3] (w:1, o:277, a:1, s:1, b:1),
% 2.04/2.41 alpha16 [260, 3] (w:1, o:278, a:1, s:1, b:1),
% 2.04/2.41 alpha17 [261, 3] (w:1, o:279, a:1, s:1, b:1),
% 2.04/2.41 alpha18 [262, 3] (w:1, o:280, a:1, s:1, b:1),
% 2.04/2.41 alpha19 [263, 3] (w:1, o:281, a:1, s:1, b:1),
% 2.04/2.41 alpha20 [264, 3] (w:1, o:282, a:1, s:1, b:1),
% 2.04/2.41 alpha21 [265, 3] (w:1, o:283, a:1, s:1, b:1),
% 2.04/2.41 alpha22 [266, 3] (w:1, o:284, a:1, s:1, b:1),
% 2.04/2.41 alpha23 [267, 3] (w:1, o:285, a:1, s:1, b:1),
% 2.04/2.41 alpha24 [268, 3] (w:1, o:286, a:1, s:1, b:1),
% 2.04/2.41 alpha25 [269, 2] (w:1, o:250, a:1, s:1, b:1),
% 2.04/2.41 alpha26 [270, 2] (w:1, o:251, a:1, s:1, b:1),
% 17.58/17.95 alpha27 [271, 4] (w:1, o:317, a:1, s:1, b:1),
% 17.58/17.95 alpha28 [272, 4] (w:1, o:318, a:1, s:1, b:1),
% 17.58/17.95 alpha29 [273, 3] (w:1, o:287, a:1, s:1, b:1),
% 17.58/17.95 alpha30 [274, 3] (w:1, o:288, a:1, s:1, b:1),
% 17.58/17.95 alpha31 [275, 3] (w:1, o:289, a:1, s:1, b:1),
% 17.58/17.95 alpha32 [276, 4] (w:1, o:304, a:1, s:1, b:1),
% 17.58/17.95 alpha33 [277, 3] (w:1, o:290, a:1, s:1, b:1),
% 17.58/17.95 alpha34 [278, 3] (w:1, o:291, a:1, s:1, b:1),
% 17.58/17.95 alpha35 [279, 4] (w:1, o:305, a:1, s:1, b:1),
% 17.58/17.95 alpha36 [280, 4] (w:1, o:306, a:1, s:1, b:1),
% 17.58/17.95 alpha37 [281, 3] (w:1, o:292, a:1, s:1, b:1),
% 17.58/17.95 alpha38 [282, 3] (w:1, o:293, a:1, s:1, b:1),
% 17.58/17.95 alpha39 [283, 3] (w:1, o:294, a:1, s:1, b:1),
% 17.58/17.95 alpha40 [284, 3] (w:1, o:295, a:1, s:1, b:1),
% 17.58/17.95 alpha41 [285, 4] (w:1, o:308, a:1, s:1, b:1),
% 17.58/17.95 alpha42 [286, 4] (w:1, o:309, a:1, s:1, b:1),
% 17.58/17.95 alpha43 [287, 4] (w:1, o:310, a:1, s:1, b:1),
% 17.58/17.95 alpha44 [288, 4] (w:1, o:311, a:1, s:1, b:1),
% 17.58/17.95 alpha45 [289, 4] (w:1, o:312, a:1, s:1, b:1),
% 17.58/17.95 alpha46 [290, 3] (w:1, o:296, a:1, s:1, b:1),
% 17.58/17.95 alpha47 [291, 4] (w:1, o:313, a:1, s:1, b:1),
% 17.58/17.95 alpha48 [292, 4] (w:1, o:314, a:1, s:1, b:1),
% 17.58/17.95 alpha49 [293, 4] (w:1, o:315, a:1, s:1, b:1),
% 17.58/17.95 alpha50 [294, 4] (w:1, o:319, a:1, s:1, b:1),
% 17.58/17.95 alpha51 [295, 4] (w:1, o:320, a:1, s:1, b:1),
% 17.58/17.95 alpha52 [296, 4] (w:1, o:321, a:1, s:1, b:1),
% 17.58/17.95 alpha53 [297, 4] (w:1, o:322, a:1, s:1, b:1),
% 17.58/17.95 alpha54 [298, 4] (w:1, o:323, a:1, s:1, b:1),
% 17.58/17.95 alpha55 [299, 4] (w:1, o:324, a:1, s:1, b:1),
% 17.58/17.95 alpha56 [300, 4] (w:1, o:325, a:1, s:1, b:1),
% 17.58/17.95 alpha57 [301, 4] (w:1, o:326, a:1, s:1, b:1),
% 17.58/17.95 alpha58 [302, 4] (w:1, o:327, a:1, s:1, b:1),
% 17.58/17.95 alpha59 [303, 3] (w:1, o:268, a:1, s:1, b:1),
% 17.58/17.95 alpha60 [304, 0] (w:1, o:116, a:1, s:1, b:1),
% 17.58/17.95 alpha61 [305, 3] (w:1, o:270, a:1, s:1, b:1),
% 17.58/17.95 alpha62 [306, 0] (w:1, o:117, a:1, s:1, b:1),
% 17.58/17.95 alpha63 [307, 0] (w:1, o:118, a:1, s:1, b:1),
% 17.58/17.95 alpha64 [308, 1] (w:1, o:203, a:1, s:1, b:1),
% 17.58/17.95 alpha65 [309, 1] (w:1, o:204, a:1, s:1, b:1),
% 17.58/17.95 skol1 [310, 2] (w:1, o:238, a:1, s:1, b:1),
% 17.58/17.95 skol2 [311, 0] (w:1, o:13, a:1, s:1, b:1),
% 17.58/17.95 skol3 [312, 2] (w:1, o:239, a:1, s:1, b:1),
% 17.58/17.95 skol4 [313, 2] (w:1, o:240, a:1, s:1, b:1),
% 17.58/17.95 skol5 [314, 1] (w:1, o:135, a:1, s:1, b:1),
% 17.58/17.95 skol6 [315, 0] (w:1, o:14, a:1, s:1, b:1),
% 17.58/17.95 skol7 [316, 0] (w:1, o:15, a:1, s:1, b:1),
% 17.58/17.95 skol8 [317, 2] (w:1, o:241, a:1, s:1, b:1),
% 17.58/17.95 skol9 [318, 3] (w:1, o:297, a:1, s:1, b:1),
% 17.58/17.95 skol10 [319, 2] (w:1, o:242, a:1, s:1, b:1),
% 17.58/17.95 skol11 [320, 3] (w:1, o:298, a:1, s:1, b:1),
% 17.58/17.95 skol12 [321, 2] (w:1, o:243, a:1, s:1, b:1),
% 17.58/17.95 skol13 [322, 2] (w:1, o:244, a:1, s:1, b:1),
% 17.58/17.95 skol14 [323, 3] (w:1, o:299, a:1, s:1, b:1),
% 17.58/17.95 skol15 [324, 3] (w:1, o:300, a:1, s:1, b:1),
% 17.58/17.95 skol16 [325, 3] (w:1, o:301, a:1, s:1, b:1),
% 17.58/17.95 skol17 [326, 0] (w:1, o:11, a:1, s:1, b:1),
% 17.58/17.95 skol18 [327, 0] (w:1, o:12, a:1, s:1, b:1),
% 17.58/17.95 skol19 [328, 3] (w:1, o:302, a:1, s:1, b:1),
% 17.58/17.95 skol20 [329, 0] (w:1, o:16, a:1, s:1, b:1).
% 17.58/17.95
% 17.58/17.95
% 17.58/17.95 Starting Search:
% 17.58/17.95
% 17.58/17.95 *** allocated 113905 integers for clauses
% 17.58/17.95 *** allocated 170857 integers for clauses
% 17.58/17.95 Resimplifying inuse:
% 17.58/17.95 Done
% 17.58/17.95
% 17.58/17.95
% 17.58/17.95 Intermediate Status:
% 17.58/17.95 Generated: 3008
% 17.58/17.95 Kept: 2061
% 17.58/17.95 Inuse: 52
% 17.58/17.95 Deleted: 4
% 17.58/17.95 Deletedinuse: 0
% 17.58/17.95
% 17.58/17.95 *** allocated 256285 integers for clauses
% 17.58/17.95 *** allocated 170857 integers for termspace/termends
% 17.58/17.95 Resimplifying inuse:
% 17.58/17.95 Done
% 17.58/17.95
% 17.58/17.95 Resimplifying inuse:
% 17.58/17.95 Done
% 17.58/17.95
% 17.58/17.95
% 17.58/17.95 Intermediate Status:
% 17.58/17.95 Generated: 12601
% 17.58/17.95 Kept: 4071
% 17.58/17.95 Inuse: 137
% 17.58/17.95 Deleted: 8
% 17.58/17.95 Deletedinuse: 0
% 17.58/17.95
% 17.58/17.95 *** allocated 384427 integers for clauses
% 17.58/17.95 *** allocated 256285 integers for termspace/termends
% 17.58/17.95 Resimplifying inuse:
% 17.58/17.95 Done
% 17.58/17.95
% 17.58/17.95 Resimplifying inuse:
% 17.58/17.95 Done
% 17.58/17.95
% 17.58/17.95
% 17.58/17.95 Intermediate Status:
% 17.58/17.95 Generated: 20714
% 17.58/17.95 Kept: 6103
% 17.58/17.95 Inuse: 252
% 17.58/17.95 Deleted: 15
% 17.58/17.95 Deletedinuse: 1
% 17.58/17.95
% 17.58/17.95 *** allocated 576640 integers for clauses
% 17.58/17.95 *** allocated 384427 integers for termspace/termends
% 17.58/17.95 Resimplifying inuse:
% 17.58/17.95 Done
% 17.58/17.95
% 17.58/17.95
% 17.58/17.95 Intermediate Status:
% 17.58/17.95 Generated: 32481
% 17.58/17.95 Kept: 8923
% 17.58/17.95 Inuse: 304
% 17.58/17.95 Deleted: 18
% 17.58/17.95 Deletedinuse: 1
% 17.58/17.95
% 17.58/17.95 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 40690
% 39.70/40.12 Kept: 10925
% 39.70/40.12 Inuse: 353
% 39.70/40.12 Deleted: 23
% 39.70/40.12 Deletedinuse: 5
% 39.70/40.12
% 39.70/40.12 *** allocated 864960 integers for clauses
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 49556
% 39.70/40.12 Kept: 12943
% 39.70/40.12 Inuse: 383
% 39.70/40.12 Deleted: 23
% 39.70/40.12 Deletedinuse: 5
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 *** allocated 576640 integers for termspace/termends
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 56978
% 39.70/40.12 Kept: 15979
% 39.70/40.12 Inuse: 413
% 39.70/40.12 Deleted: 24
% 39.70/40.12 Deletedinuse: 6
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 *** allocated 1297440 integers for clauses
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 62577
% 39.70/40.12 Kept: 18245
% 39.70/40.12 Inuse: 448
% 39.70/40.12 Deleted: 24
% 39.70/40.12 Deletedinuse: 6
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying clauses:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 67435
% 39.70/40.12 Kept: 20756
% 39.70/40.12 Inuse: 459
% 39.70/40.12 Deleted: 393
% 39.70/40.12 Deletedinuse: 6
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 73527
% 39.70/40.12 Kept: 22767
% 39.70/40.12 Inuse: 523
% 39.70/40.12 Deleted: 394
% 39.70/40.12 Deletedinuse: 7
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 *** allocated 864960 integers for termspace/termends
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 79496
% 39.70/40.12 Kept: 25008
% 39.70/40.12 Inuse: 543
% 39.70/40.12 Deleted: 394
% 39.70/40.12 Deletedinuse: 7
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 86013
% 39.70/40.12 Kept: 27151
% 39.70/40.12 Inuse: 558
% 39.70/40.12 Deleted: 394
% 39.70/40.12 Deletedinuse: 7
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 *** allocated 1946160 integers for clauses
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 91303
% 39.70/40.12 Kept: 29472
% 39.70/40.12 Inuse: 598
% 39.70/40.12 Deleted: 395
% 39.70/40.12 Deletedinuse: 8
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 95129
% 39.70/40.12 Kept: 31652
% 39.70/40.12 Inuse: 608
% 39.70/40.12 Deleted: 395
% 39.70/40.12 Deletedinuse: 8
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 99493
% 39.70/40.12 Kept: 33691
% 39.70/40.12 Inuse: 628
% 39.70/40.12 Deleted: 395
% 39.70/40.12 Deletedinuse: 8
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 108262
% 39.70/40.12 Kept: 35746
% 39.70/40.12 Inuse: 648
% 39.70/40.12 Deleted: 395
% 39.70/40.12 Deletedinuse: 8
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 *** allocated 1297440 integers for termspace/termends
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 113138
% 39.70/40.12 Kept: 37821
% 39.70/40.12 Inuse: 666
% 39.70/40.12 Deleted: 397
% 39.70/40.12 Deletedinuse: 8
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 122210
% 39.70/40.12 Kept: 40252
% 39.70/40.12 Inuse: 676
% 39.70/40.12 Deleted: 397
% 39.70/40.12 Deletedinuse: 8
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying clauses:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 130719
% 39.70/40.12 Kept: 43259
% 39.70/40.12 Inuse: 701
% 39.70/40.12 Deleted: 655
% 39.70/40.12 Deletedinuse: 9
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 *** allocated 2919240 integers for clauses
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 138429
% 39.70/40.12 Kept: 45281
% 39.70/40.12 Inuse: 727
% 39.70/40.12 Deleted: 656
% 39.70/40.12 Deletedinuse: 10
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 149049
% 39.70/40.12 Kept: 47715
% 39.70/40.12 Inuse: 771
% 39.70/40.12 Deleted: 656
% 39.70/40.12 Deletedinuse: 10
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 155290
% 39.70/40.12 Kept: 50389
% 39.70/40.12 Inuse: 801
% 39.70/40.12 Deleted: 656
% 39.70/40.12 Deletedinuse: 10
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 *** allocated 1946160 integers for termspace/termends
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 180711
% 39.70/40.12 Kept: 53143
% 39.70/40.12 Inuse: 816
% 39.70/40.12 Deleted: 656
% 39.70/40.12 Deletedinuse: 10
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 190830
% 39.70/40.12 Kept: 55731
% 39.70/40.12 Inuse: 836
% 39.70/40.12 Deleted: 656
% 39.70/40.12 Deletedinuse: 10
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 216224
% 39.70/40.12 Kept: 58307
% 39.70/40.12 Inuse: 851
% 39.70/40.12 Deleted: 656
% 39.70/40.12 Deletedinuse: 10
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12
% 39.70/40.12 Intermediate Status:
% 39.70/40.12 Generated: 223256
% 39.70/40.12 Kept: 60317
% 39.70/40.12 Inuse: 881
% 39.70/40.12 Deleted: 656
% 39.70/40.12 Deletedinuse: 10
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying clauses:
% 39.70/40.12 Done
% 39.70/40.12
% 39.70/40.12 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 235638
% 82.09/82.44 Kept: 63452
% 82.09/82.44 Inuse: 911
% 82.09/82.44 Deleted: 731
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 244114
% 82.09/82.44 Kept: 65484
% 82.09/82.44 Inuse: 922
% 82.09/82.44 Deleted: 731
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 *** allocated 4378860 integers for clauses
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 257619
% 82.09/82.44 Kept: 68640
% 82.09/82.44 Inuse: 931
% 82.09/82.44 Deleted: 731
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 266279
% 82.09/82.44 Kept: 70740
% 82.09/82.44 Inuse: 956
% 82.09/82.44 Deleted: 731
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 282298
% 82.09/82.44 Kept: 72773
% 82.09/82.44 Inuse: 965
% 82.09/82.44 Deleted: 731
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 299111
% 82.09/82.44 Kept: 74815
% 82.09/82.44 Inuse: 971
% 82.09/82.44 Deleted: 731
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 *** allocated 2919240 integers for termspace/termends
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 308294
% 82.09/82.44 Kept: 77446
% 82.09/82.44 Inuse: 991
% 82.09/82.44 Deleted: 731
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 315766
% 82.09/82.44 Kept: 79509
% 82.09/82.44 Inuse: 1027
% 82.09/82.44 Deleted: 731
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying clauses:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 320926
% 82.09/82.44 Kept: 81625
% 82.09/82.44 Inuse: 1051
% 82.09/82.44 Deleted: 767
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 327119
% 82.09/82.44 Kept: 83640
% 82.09/82.44 Inuse: 1066
% 82.09/82.44 Deleted: 767
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 334156
% 82.09/82.44 Kept: 85939
% 82.09/82.44 Inuse: 1081
% 82.09/82.44 Deleted: 767
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 340632
% 82.09/82.44 Kept: 88003
% 82.09/82.44 Inuse: 1096
% 82.09/82.44 Deleted: 767
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 346224
% 82.09/82.44 Kept: 90057
% 82.09/82.44 Inuse: 1112
% 82.09/82.44 Deleted: 767
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 351992
% 82.09/82.44 Kept: 92074
% 82.09/82.44 Inuse: 1128
% 82.09/82.44 Deleted: 767
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 357920
% 82.09/82.44 Kept: 94364
% 82.09/82.44 Inuse: 1146
% 82.09/82.44 Deleted: 767
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 362587
% 82.09/82.44 Kept: 96423
% 82.09/82.44 Inuse: 1174
% 82.09/82.44 Deleted: 767
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 367614
% 82.09/82.44 Kept: 98651
% 82.09/82.44 Inuse: 1191
% 82.09/82.44 Deleted: 767
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 Resimplifying clauses:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 373240
% 82.09/82.44 Kept: 100693
% 82.09/82.44 Inuse: 1226
% 82.09/82.44 Deleted: 962
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 *** allocated 6568290 integers for clauses
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 381503
% 82.09/82.44 Kept: 102831
% 82.09/82.44 Inuse: 1241
% 82.09/82.44 Deleted: 962
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 389881
% 82.09/82.44 Kept: 105087
% 82.09/82.44 Inuse: 1261
% 82.09/82.44 Deleted: 962
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 396030
% 82.09/82.44 Kept: 107721
% 82.09/82.44 Inuse: 1281
% 82.09/82.44 Deleted: 962
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 403020
% 82.09/82.44 Kept: 109723
% 82.09/82.44 Inuse: 1296
% 82.09/82.44 Deleted: 962
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44 *** allocated 4378860 integers for termspace/termends
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 412195
% 82.09/82.44 Kept: 113763
% 82.09/82.44 Inuse: 1311
% 82.09/82.44 Deleted: 962
% 82.09/82.44 Deletedinuse: 10
% 82.09/82.44
% 82.09/82.44 Resimplifying inuse:
% 82.09/82.44 Done
% 82.09/82.44
% 82.09/82.44
% 82.09/82.44 Intermediate Status:
% 82.09/82.44 Generated: 416875
% 82.09/82.44 Kept: 116404
% 82.09/82.44 Inuse: 1316
% 82.09/82.44 Deleted: 962
% 82.09/82.44 Deletedinuse: 10
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 424772
% 168.38/168.88 Kept: 120122
% 168.38/168.88 Inuse: 1341
% 168.38/168.88 Deleted: 962
% 168.38/168.88 Deletedinuse: 10
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying clauses:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 432607
% 168.38/168.88 Kept: 122403
% 168.38/168.88 Inuse: 1366
% 168.38/168.88 Deleted: 979
% 168.38/168.88 Deletedinuse: 10
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 441156
% 168.38/168.88 Kept: 124646
% 168.38/168.88 Inuse: 1386
% 168.38/168.88 Deleted: 979
% 168.38/168.88 Deletedinuse: 10
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 457148
% 168.38/168.88 Kept: 126970
% 168.38/168.88 Inuse: 1396
% 168.38/168.88 Deleted: 979
% 168.38/168.88 Deletedinuse: 10
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 467502
% 168.38/168.88 Kept: 130278
% 168.38/168.88 Inuse: 1406
% 168.38/168.88 Deleted: 979
% 168.38/168.88 Deletedinuse: 10
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 474904
% 168.38/168.88 Kept: 132401
% 168.38/168.88 Inuse: 1416
% 168.38/168.88 Deleted: 979
% 168.38/168.88 Deletedinuse: 10
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 484037
% 168.38/168.88 Kept: 137592
% 168.38/168.88 Inuse: 1421
% 168.38/168.88 Deleted: 979
% 168.38/168.88 Deletedinuse: 10
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 491245
% 168.38/168.88 Kept: 139632
% 168.38/168.88 Inuse: 1450
% 168.38/168.88 Deleted: 979
% 168.38/168.88 Deletedinuse: 10
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying clauses:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 498331
% 168.38/168.88 Kept: 141668
% 168.38/168.88 Inuse: 1470
% 168.38/168.88 Deleted: 992
% 168.38/168.88 Deletedinuse: 10
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 506439
% 168.38/168.88 Kept: 144181
% 168.38/168.88 Inuse: 1486
% 168.38/168.88 Deleted: 992
% 168.38/168.88 Deletedinuse: 10
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 514287
% 168.38/168.88 Kept: 146525
% 168.38/168.88 Inuse: 1506
% 168.38/168.88 Deleted: 993
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 520694
% 168.38/168.88 Kept: 148528
% 168.38/168.88 Inuse: 1525
% 168.38/168.88 Deleted: 993
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 526101
% 168.38/168.88 Kept: 150571
% 168.38/168.88 Inuse: 1546
% 168.38/168.88 Deleted: 993
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 532352
% 168.38/168.88 Kept: 152587
% 168.38/168.88 Inuse: 1574
% 168.38/168.88 Deleted: 993
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 *** allocated 9852435 integers for clauses
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 542745
% 168.38/168.88 Kept: 158606
% 168.38/168.88 Inuse: 1581
% 168.38/168.88 Deleted: 993
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 554416
% 168.38/168.88 Kept: 161680
% 168.38/168.88 Inuse: 1586
% 168.38/168.88 Deleted: 993
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying clauses:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 561101
% 168.38/168.88 Kept: 163735
% 168.38/168.88 Inuse: 1610
% 168.38/168.88 Deleted: 1082
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 568215
% 168.38/168.88 Kept: 165786
% 168.38/168.88 Inuse: 1630
% 168.38/168.88 Deleted: 1083
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 580623
% 168.38/168.88 Kept: 169028
% 168.38/168.88 Inuse: 1640
% 168.38/168.88 Deleted: 1083
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 *** allocated 6568290 integers for termspace/termends
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 586955
% 168.38/168.88 Kept: 171040
% 168.38/168.88 Inuse: 1660
% 168.38/168.88 Deleted: 1083
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 595372
% 168.38/168.88 Kept: 173266
% 168.38/168.88 Inuse: 1685
% 168.38/168.88 Deleted: 1083
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 602702
% 168.38/168.88 Kept: 175489
% 168.38/168.88 Inuse: 1710
% 168.38/168.88 Deleted: 1083
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 609361
% 168.38/168.88 Kept: 177502
% 168.38/168.88 Inuse: 1732
% 168.38/168.88 Deleted: 1083
% 168.38/168.88 Deletedinuse: 11
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88 Resimplifying inuse:
% 168.38/168.88 Done
% 168.38/168.88
% 168.38/168.88
% 168.38/168.88 Intermediate Status:
% 168.38/168.88 Generated: 615186
% 168.38/168.88 Kept: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------