TSTP Solution File: SWW186+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW186+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:07 EDT 2022
% Result : Timeout 300.07s 300.55s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW186+1 : TPTP v8.1.0. Released v5.2.0.
% 0.08/0.14 % Command : bliksem %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % DateTime : Sun Jun 5 15:58:19 EDT 2022
% 0.15/0.36 % CPUTime :
% 1.02/1.64 *** allocated 10000 integers for termspace/termends
% 1.02/1.64 *** allocated 10000 integers for clauses
% 1.02/1.64 *** allocated 10000 integers for justifications
% 1.02/1.64 *** allocated 15000 integers for termspace/termends
% 1.02/1.64 *** allocated 22500 integers for termspace/termends
% 1.02/1.64 *** allocated 33750 integers for termspace/termends
% 1.02/1.64 Bliksem 1.12
% 1.02/1.64
% 1.02/1.64
% 1.02/1.64 Automatic Strategy Selection
% 1.02/1.64
% 1.02/1.64 *** allocated 50625 integers for termspace/termends
% 1.02/1.64 *** allocated 75937 integers for termspace/termends
% 1.02/1.64 *** allocated 113905 integers for termspace/termends
% 1.02/1.64
% 1.02/1.64 Clauses:
% 1.02/1.64
% 1.02/1.64 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.02/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.02/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.02/1.64 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.02/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.02/1.64 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 1.02/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 1.02/1.64 c_Polynomial_OpCons( X, T,
% 1.02/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.64 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.02/1.64 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.02/1.64 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.02/1.64 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 Y, T ), Z = Y }.
% 1.02/1.64 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 T, Y ), Z = Y }.
% 1.02/1.64 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 T, Y ), Z = Y }.
% 1.02/1.64 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 Y, Z ), T = Y }.
% 1.02/1.64 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 Y, Z ) }.
% 1.02/1.64 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 T, Y ), Z = Y }.
% 1.02/1.64 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 T, Y ) }.
% 1.02/1.64 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.02/1.64 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.02/1.64 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.64 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.64 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.64 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.02/1.64 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.64 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.64 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.64 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.02/1.64 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 1.02/1.64 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 1.02/1.64 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 1.02/1.64 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.64 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 1.02/1.64 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.02/1.64 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.64 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.02/1.64 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.64 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.64 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.64 ), ! U = T }.
% 1.02/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.64 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.64 ), ! Z = Y }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.64 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.02/1.64 ) ), Z ) }.
% 1.02/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.64 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.64 ), U = Z, T = Y }.
% 1.02/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.64 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.64 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.64 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.64 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.64 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.02/1.64 ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 1.02/1.64 Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.64 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.02/1.64 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.02/1.64 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.64 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.64 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.64 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.64 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.64 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.02/1.64 ) ), T ), Y ) }.
% 1.02/1.64 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.02/1.64 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.64 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.02/1.64 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.02/1.64 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.02/1.64 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.64 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha1( X
% 1.02/1.64 , Y, T ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha13( X
% 1.02/1.64 , Y, Z, T ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! alpha1( X, Y, T ), ! alpha13( X, Y, Z, T )
% 1.02/1.64 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 1.02/1.64 ( X, T, Z ), Y ) }.
% 1.02/1.64 { ! alpha13( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.64 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha13( X, Y, Z, T ) }.
% 1.02/1.64 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha13( X
% 1.02/1.64 , Y, Z, T ) }.
% 1.02/1.64 { ! alpha1( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { Z = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 1.02/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha1( X
% 1.02/1.64 , Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.64 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.64 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.64 Z, T ) }.
% 1.02/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.64 , Y, T ) ) }.
% 1.02/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.02/1.64 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.02/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.02/1.64 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.02/1.64 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.02/1.64 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.64 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.64 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.64 ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.64 ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.64 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.64 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.02/1.64 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.64 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.64 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.64 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.64 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.64 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, T, Y ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.64 , Y, Z ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, Z, Y ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.64 , T, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.64 , Y, T ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.64 , T, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.64 , T ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, Z, Y ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, Z, Y ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.64 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.64 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.64 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.64 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.64 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.64 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.64 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.64 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.64 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.64 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.02/1.64 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.64 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 1.02/1.64 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.64 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.64 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.64 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.64 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.02/1.64 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.02/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.02/1.64 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 1.02/1.64 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.02/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.02/1.64 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 1.02/1.64 X, T, Z ), Y ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.64 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.02/1.64 tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha2( X, Y, Z, T ),
% 1.02/1.64 alpha14( X, Y, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha14( X, Y, Z, T ) }.
% 1.02/1.64 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.64 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.64 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha2( X, Y, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha3( X, Y, Z, T ),
% 1.02/1.64 alpha15( X, Y, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! alpha15( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha15( X, Y, Z, T ) }.
% 1.02/1.64 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.02/1.64 { ! alpha3( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.02/1.64 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha3( X, Y, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) ) }.
% 1.02/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.64 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.02/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.64 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.64 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha4( X, Y
% 1.02/1.64 , Z ), alpha16( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), alpha16( X, Y, Z ) }.
% 1.02/1.64 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.64 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ), alpha4( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ), alpha5( X, Y, Z ), alpha17( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ), Y ), alpha17( X, Y, Z ) }.
% 1.02/1.64 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.64 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), alpha5( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.64 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.02/1.64 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.02/1.64 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 Y, Z ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 Z, Y ) ) }.
% 1.02/1.64 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.64 ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.02/1.64 , Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.02/1.64 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.02/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.02/1.64 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.02/1.64 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 1.02/1.64 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.64 , Y ) ) }.
% 1.02/1.64 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.02/1.64 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.02/1.64 hAPP( Z, skol2( U, W, Z ) ) ) }.
% 1.02/1.64 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.02/1.64 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol2( X
% 1.02/1.64 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.02/1.64 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.02/1.64 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.02/1.64 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol18( X,
% 1.02/1.64 Y, Z ) ) ) ) }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.02/1.64 , Y ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 1.02/1.64 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 1.02/1.64 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 1.02/1.64 , Y ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.02/1.64 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.02/1.64 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.64 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ), alpha6
% 1.02/1.64 ( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.64 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! alpha6( X, Y, Z ),
% 1.02/1.64 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.02/1.64 { ! alpha6( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly
% 1.02/1.64 ( X ) ) }.
% 1.02/1.64 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.64 alpha6( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.64 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.64 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.64 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.64 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.64 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.02/1.64 hAPP( Y, U ) ) }.
% 1.02/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.02/1.64 ( Z, skol3( X, Y, Z ) ), hAPP( Y, skol3( X, Y, Z ) ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.02/1.64 ( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.02/1.64 ( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.64 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.02/1.64 hAPP( Y, U ) ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.64 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.02/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.02/1.64 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.64 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.02/1.64 hAPP( Y, U ) ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.64 Y ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.64 Y ), ! Z = Y }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.64 Z ), ! Z = Y }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.64 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.64 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.64 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.64 , ! Z = Y }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.64 , ! Z = Y }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.64 , ! Y = Z }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.64 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.02/1.64 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.02/1.64 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.02/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.02/1.64 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.64 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.64 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.64 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.64 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.02/1.64 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.02/1.64 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.02/1.64 ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.64 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.64 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.64 , ! Z = Y }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.64 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.64 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.64 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.02/1.64 ( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.64 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.64 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.64 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.64 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.64 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.64 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.02/1.64 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.64 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.64 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.64 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.02/1.64 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.02/1.64 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.64 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.64 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.64 , alpha21( X, Y, Z, T ) }.
% 1.02/1.64 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha21( X, Y, Z, T ),
% 1.02/1.64 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.02/1.64 { ! alpha21( X, Y, Z, T ), alpha7( X, Z, T ) }.
% 1.02/1.64 { ! alpha21( X, Y, Z, T ), alpha18( X, Y, T ) }.
% 1.02/1.64 { ! alpha7( X, Z, T ), ! alpha18( X, Y, T ), alpha21( X, Y, Z, T ) }.
% 1.02/1.64 { ! alpha18( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), alpha22( X, Y, Z ) }.
% 1.02/1.64 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha18( X
% 1.02/1.64 , Y, Z ) }.
% 1.02/1.64 { ! alpha22( X, Y, Z ), alpha18( X, Y, Z ) }.
% 1.02/1.64 { ! alpha22( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.64 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.02/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha22( X
% 1.02/1.64 , Y, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.02/1.64 ), c_Polynomial_Odegree( X, Z ) ), alpha22( X, Y, Z ) }.
% 1.02/1.64 { ! alpha7( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.64 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.64 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha7( X, Y
% 1.02/1.64 , Z ) }.
% 1.02/1.64 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha7( X
% 1.02/1.64 , Y, Z ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.02/1.64 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.64 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.64 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.64 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.64 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.02/1.64 ), Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.02/1.64 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.64 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.02/1.64 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.64 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.02/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.02/1.64 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.02/1.64 .
% 1.02/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.02/1.64 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.02/1.64 }.
% 1.02/1.64 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.64 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.02/1.64 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.64 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.02/1.64 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.02/1.64 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.64 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.64 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.64 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.02/1.64 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.64 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.02/1.64 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.02/1.64 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.02/1.64 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.02/1.64 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.02/1.64 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.02/1.64 { alpha23( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.02/1.64 ( X, Y ), Z ) ) }.
% 1.02/1.64 { ! alpha23( X, Y, Z ), alpha25( X, Y, Z ), Z = Y }.
% 1.02/1.64 { ! alpha23( X, Y, Z ), alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.02/1.64 ) ) }.
% 1.02/1.64 { ! alpha25( X, Y, Z ), alpha23( X, Y, Z ) }.
% 1.02/1.64 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha23( X, Y, Z ) }.
% 1.02/1.64 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.02/1.64 }.
% 1.02/1.64 { ! alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.02/1.64 X, Y ), Z ) ), alpha25( X, Y, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.02/1.64 , X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.64 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.02/1.64 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.64 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.64 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.02/1.64 .
% 1.02/1.64 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol4( X, Y ) ) }.
% 1.02/1.64 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.64 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.64 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.02/1.64 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.64 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.64 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.65 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 1.02/1.65 , c_Polynomial_Odegree( X, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.02/1.65 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.02/1.65 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.02/1.65 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.02/1.65 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.65 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 1.02/1.65 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 1.02/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.65 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.65 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.65 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 1.02/1.65 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 1.02/1.65 c_Polynomial_Odegree( X, Z ) ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.65 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.65 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.02/1.65 c_Polynomial_Odegree( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.02/1.65 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.65 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.02/1.65 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.02/1.65 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 1.02/1.65 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.02/1.65 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.02/1.65 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.02/1.65 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.65 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.02/1.65 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.02/1.65 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.65 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.02/1.65 .
% 1.02/1.65 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.02/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.02/1.65 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.65 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.02/1.65 .
% 1.02/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), X ) = X }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ) ) = X }.
% 1.02/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), X ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.02/1.65 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.02/1.65 .
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.02/1.65 ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.02/1.65 ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.02/1.65 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Z ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.02/1.65 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.65 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.65 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.65 Y ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.02/1.65 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.65 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Nat_Onat, Y, Z ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.02/1.65 , Z ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.02/1.65 Z, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.65 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Nat_Onat, Y, Z ) }.
% 1.02/1.65 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Nat_Onat, Y, Z ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.65 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.65 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.65 { ! alpha8( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! alpha8( X, Y ), ! Y = X }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha8( X, Y ) }
% 1.02/1.65 .
% 1.02/1.65 { ! alpha8( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! alpha8( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), alpha8( X, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha9( X, Y ), Y = X }
% 1.02/1.65 .
% 1.02/1.65 { ! alpha9( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! alpha9( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! alpha9( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), alpha9( X, Y ) }.
% 1.02/1.65 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.65 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.02/1.65 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Nat_Onat ), X ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Nat_Onat ) }.
% 1.02/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Nat_Onat ) }.
% 1.02/1.65 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.02/1.65 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.65 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.65 , Y ), X ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.02/1.65 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.02/1.65 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.02/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.02/1.65 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ), Z = Y }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.02/1.65 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.02/1.65 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.02/1.65 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.65 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.65 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.65 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.65 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( X ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.02/1.65 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ), Z ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Z ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.65 ) ), Y ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.65 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.65 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.65 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.65 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.65 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.02/1.65 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 Z, Y ) ) = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.65 Y ) ) = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.02/1.65 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 1.02/1.65 , Z, Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.65 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.65 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.02/1.65 c_Polynomial_Odegree( X, Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.02/1.65 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 Z ) = Y }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Y ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.65 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.65 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.65 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.65 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.65 X ) ) }.
% 1.02/1.65 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.02/1.65 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.02/1.65 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.65 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.02/1.65 .
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.65 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 1.02/1.65 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.65 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.65 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 1.02/1.65 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( X, Z ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) }.
% 1.02/1.65 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.02/1.65 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 1.02/1.65 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.65 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.02/1.65 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.02/1.65 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.02/1.65 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol6( Z, Y )
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.02/1.65 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.65 skol6( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.02/1.65 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.02/1.65 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.02/1.65 , skol6( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.02/1.65 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 1.02/1.65 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Nat_Onat ) ) = Y }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.02/1.65 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.02/1.65 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.02/1.65 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.02/1.65 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol7( X
% 1.02/1.65 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol7( X, Y, Z ) ), Z = Y
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.02/1.65 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.02/1.65 c_Polynomial_Ocoeff( X, Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.02/1.65 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.02/1.65 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.65 ( X ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.65 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ) ) = Z }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.65 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.02/1.65 ), Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 1.02/1.65 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.65 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.65 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.02/1.65 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.65 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.65 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.65 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.65 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.65 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.65 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.65 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.02/1.65 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.02/1.65 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.02/1.65 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.02/1.65 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.02/1.65 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.65 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.02/1.65 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.65 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.65 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.02/1.65 ( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.02/1.65 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.02/1.65 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.02/1.65 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Int_Oint, Z, X ) }.
% 1.02/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.02/1.65 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.02/1.65 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.02/1.65 ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.02/1.65 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.02/1.65 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Nat_Onat, Z, X ) }.
% 1.02/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.02/1.65 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( X ) }.
% 1.02/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.65 = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.02/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.02/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Nat_Onat ) ) = Y }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.02/1.65 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.65 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.65 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.65 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.65 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ) }.
% 1.02/1.65 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.65 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.65 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.02/1.65 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.65 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.02/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.65 ), T ), U ), Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.65 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.65 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.65 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.02/1.65 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.02/1.65 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.65 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.02/1.65 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.02/1.65 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.02/1.65 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.02/1.65 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.65 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 1.02/1.65 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.65 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.02/1.65 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.02/1.65 Y ) ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.02/1.65 Y ) ) ), Y ) }.
% 1.02/1.65 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.02/1.65 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.02/1.65 X ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.02/1.65 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.02/1.65 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.02/1.65 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.02/1.65 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.02/1.65 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.02/1.65 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Int_Oint, Y, X ), X = Y }.
% 1.02/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.02/1.65 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.65 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.02/1.65 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.65 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.65 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.02/1.65 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.65 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Int_Oint, Y, X ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.02/1.65 , Z ), X ) ), T ) ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, U, T ) ) }.
% 1.02/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 1.02/1.65 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 1.02/1.65 ) ) }.
% 1.02/1.65 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.02/1.65 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.02/1.65 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.02/1.65 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.02/1.65 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.02/1.65 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.02/1.65 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.02/1.65 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.02/1.65 .
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.02/1.65 .
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.02/1.65 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.02/1.65 X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.02/1.65 }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.02/1.65 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.02/1.65 }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.02/1.65 c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.02/1.65 , c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.02/1.65 .
% 1.02/1.65 { ! X = c_Nat_OSuc( X ) }.
% 1.02/1.65 { ! c_Nat_OSuc( X ) = X }.
% 1.02/1.65 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.02/1.65 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.02/1.65 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 1.02/1.65 .
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.02/1.65 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.65 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.02/1.65 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.65 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.65 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol8( X ) ) }.
% 1.02/1.65 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 1.02/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.65 c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { ! alpha10( X, Y ), Y = c_Nat_OSuc( skol9( Z, Y ) ) }.
% 1.02/1.65 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol9( X,
% 1.02/1.65 Y ), X ) }.
% 1.02/1.65 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.02/1.65 ), alpha10( X, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha11( X, Y ), alpha19( X
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! alpha11( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! alpha19( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! alpha19( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! alpha19( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha19( X, Y ) }.
% 1.02/1.65 { ! alpha11( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! alpha11( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha11( X, Y ) }.
% 1.02/1.65 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha12( X, Y ),
% 1.02/1.65 alpha20( X, Y ) }.
% 1.02/1.65 { ! alpha12( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.65 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! alpha20( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.65 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! alpha20( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 1.02/1.65 { ! alpha12( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! alpha12( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha12( X, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.02/1.65 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.02/1.65 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.02/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) ) }.
% 1.02/1.65 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.02/1.65 .
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.65 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.65 ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.02/1.65 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.02/1.65 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.65 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.65 ), X ) ) }.
% 1.02/1.65 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.02/1.65 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.65 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 1.02/1.65 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ), Y ), Z = Y }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.65 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.65 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.02/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.65 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.02/1.65 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.02/1.65 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.02/1.65 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 1.02/1.65 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.02/1.65 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.02/1.65 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.02/1.65 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.02/1.65 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.02/1.65 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.02/1.65 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), Y ) }.
% 1.02/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.02/1.65 ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.02/1.65 , skol11( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Polynomial_Odegree( X, Y ), Z ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol11( X
% 1.02/1.65 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.02/1.65 Y ), Z ) }.
% 1.02/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.02/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), X ) = X }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ) ) = X }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.02/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.02/1.65 }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.02/1.65 = X }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ) ) }.
% 1.02/1.65 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.02/1.65 }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ) ) }.
% 1.02/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.02/1.65 ( tc_Int_Oint ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.02/1.65 ( tc_Int_Oint ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.65 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.65 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.65 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.02/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.65 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.02/1.65 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.02/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.65 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.02/1.65 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.02/1.65 tc_Int_Oint ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.02/1.65 .
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol12( Z, Y ) ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.02/1.65 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Int_Oint, skol12( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.65 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.02/1.65 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 1.02/1.65 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.65 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.65 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, Y ), alpha26( X, Y, Z, T ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, Y ), alpha26( X, Y, Z, T ), ! hAPP(
% 1.02/1.65 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 1.02/1.65 .
% 1.02/1.65 { ! alpha26( X, Y, Z, T ), alpha27( X, Y, Z, T ), alpha24( X, Y, T ) }.
% 1.02/1.65 { ! alpha26( X, Y, Z, T ), alpha27( X, Y, Z, T ), ! hAPP(
% 1.02/1.65 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! alpha27( X, Y, Z, T ), alpha26( X, Y, Z, T ) }.
% 1.02/1.65 { ! alpha24( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.02/1.65 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 alpha26( X, Y, Z, T ) }.
% 1.02/1.65 { ! alpha27( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.65 ( X ), Z, T ), alpha28( X, Y, Z, T ) }.
% 1.02/1.65 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha27( X, Y
% 1.02/1.65 , Z, T ) }.
% 1.02/1.65 { ! alpha28( X, Y, Z, T ), alpha27( X, Y, Z, T ) }.
% 1.02/1.65 { ! alpha28( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.02/1.65 ), skol13( X, Y, U, W ), Y ) }.
% 1.02/1.65 { ! alpha28( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.02/1.65 ), skol13( X, Y, U, T ), T ) }.
% 1.02/1.65 { ! alpha28( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.02/1.65 ( X ), skol13( X, Y, Z, T ), Z ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha28( X, Y
% 1.02/1.65 , Z, T ) }.
% 1.02/1.65 { ! alpha24( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! alpha24( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha24( X, Y, Z
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.65 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 1.02/1.65 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 1.02/1.65 ) ), Y ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.02/1.65 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.02/1.65 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.65 , Y ) ) = Y }.
% 1.02/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.65 ) ), Z ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.65 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 1.02/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 1.02/1.65 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.65 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.65 = Y }.
% 1.02/1.65 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.65 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( X ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.65 X, Y ) ) = Y }.
% 1.02/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.65 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.02/1.65 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 1.02/1.65 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.65 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.65 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.65 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.65 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.65 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 1.02/1.65 , Y = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.02/1.65 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 1.02/1.65 = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.65 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.65 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.65 , Y ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.65 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( X ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.65 .
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.65 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.65 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.65 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.65 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.65 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.02/1.65 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 1.02/1.65 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.65 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.65 ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.65 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.65 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.65 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 1.02/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.02/1.65 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 1.02/1.65 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 1.02/1.65 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 skol14( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, skol14( X, T, U ),
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.65 , Y ) }.
% 1.02/1.65 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), skol14( X, Y, Z ) ), Z ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.65 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.65 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.65 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 X ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 1.02/1.65 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.02/1.65 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 1.02/1.65 , Y ) ), Y ) }.
% 1.02/1.65 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.02/1.65 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 1.02/1.65 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 1.02/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.02/1.65 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.02/1.65 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.02/1.65 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 1.02/1.65 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 1.02/1.65 ), Z ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 1.02/1.65 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 T, Y ), Z ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 1.02/1.65 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 T, Z ), Y ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.02/1.65 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.02/1.65 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.02/1.65 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.02/1.65 ), Z ), Y ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.02/1.65 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 1.02/1.65 , Y ) ), Y ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 1.02/1.65 ( X, Y, Z ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 1.02/1.65 ( X, Z, Y ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 1.02/1.65 X, Z, Y ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 1.02/1.65 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.65 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.65 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 1.02/1.65 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 1.02/1.65 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.02/1.65 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.65 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 1.02/1.65 , Y ) ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.02/1.65 ), Z ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.02/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 1.02/1.65 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.02/1.65 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.02/1.65 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.02/1.65 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.02/1.65 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 1.02/1.65 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.02/1.65 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 1.02/1.65 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 1.02/1.65 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 1.02/1.65 ( X ), Z, Y ) ) }.
% 1.02/1.65 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.02/1.65 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 1.02/1.65 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 Z, c_Polynomial_Odegree( X, Y ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 tc_Nat_Onat, Z, skol15( T, U, Z ) ) }.
% 1.02/1.65 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 Z, c_Polynomial_Odegree( X, Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.65 skol15( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.65 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.02/1.65 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.02/1.65 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.02/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.02/1.65 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol16( X, Y ) ) }.
% 1.02/1.65 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 1.02/1.65 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.65 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 1.02/1.65 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 1.02/1.65 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol17( X, Y ) ) }.
% 1.02/1.65 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 1.02/1.65 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 1.02/1.65 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 1.02/1.65 .
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 1.02/1.65 ( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( tc_Int_Oint, Y ), X ) }.
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 1.02/1.65 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.65 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.02/1.65 tc_Int_Oint, X, Y ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.65 tc_Nat_Onat, X, Y ), Y ) }.
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.65 tc_Nat_Onat, Y, X ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.65 tc_Nat_Onat, Y, X ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.02/1.65 ( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.02/1.65 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.02/1.65 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 1.02/1.65 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 1.02/1.65 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 1.02/1.65 , U ), Z ) }.
% 1.02/1.65 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 1.02/1.65 Y ) ), Y ) }.
% 1.02/1.65 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 1.02/1.65 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.65 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 1.02/1.65 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.02/1.65 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.02/1.65 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.65 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.65 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.65 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.02/1.65 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 1.02/1.65 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 1.02/1.65 }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.65 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.65 ) }.
% 1.02/1.65 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.02/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.02/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.02/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.65 ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.65 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.02/1.65 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.02/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.65 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.02/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.65 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.65 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( X ) ) }.
% 1.02/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.65 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.65 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.65 , Z, Y ) }.
% 1.02/1.65 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.65 Z ) ), U ), T ) = Y }.
% 1.02/1.65 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.65 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), Z ), U ), Y ) }.
% 1.02/1.65 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.65 W ) ), U ), Y ) }.
% 1.02/1.65 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.65 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), Z ), U ), Y ) }.
% 1.02/1.65 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.65 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.65 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.02/1.65 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.02/1.65 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.65 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.02/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.65 Z ) ), Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 X, Y ) }.
% 1.02/1.65 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.65 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.02/1.65 X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.65 X, Z, Y ) }.
% 1.02/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.65 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.02/1.65 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.65 , Y ) ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.65 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.02/1.65 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.65 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.65 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.65 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.02/1.65 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.02/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.65 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.65 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.02/1.66 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.66 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.02/1.66 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.66 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.66 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.02/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.66 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.02/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.66 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.02/1.66 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 1.02/1.66 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.02/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 1.02/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.02/1.66 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 1.02/1.66 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.02/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.66 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.66 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.02/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.02/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.02/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.66 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.66 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.02/1.66 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.66 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.66 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.02/1.66 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.66 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.02/1.66 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.02/1.66 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.02/1.66 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.02/1.66 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 1.02/1.66 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 1.02/1.66 hAPP( Z, Y ) ) }.
% 1.02/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.66 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.66 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.02/1.66 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.02/1.66 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.66 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 1.02/1.66 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.02/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.66 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.66 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.66 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.02/1.66 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.02/1.66 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.66 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.02/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.66 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.66 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.66 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.66 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.02/1.66 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.66 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.02/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.02/1.66 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.66 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.66 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.02/1.66 ( X, Z, W ) ), U ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.02/1.66 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.66 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.66 X, W, Z ) ), U ), T ), Y ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.02/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), Z ), U ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.02/1.66 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.02/1.66 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.02/1.66 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.02/1.66 .
% 1.02/1.66 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.66 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.02/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.02/1.66 }.
% 1.02/1.66 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.02/1.66 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.02/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.02/1.66 }.
% 1.02/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.66 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.66 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.66 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 1.02/1.66 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.66 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.02/1.66 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 1.02/1.66 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.02/1.66 ( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.66 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.02/1.66 ( X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__add(
% 1.02/1.66 X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ocomm__monoid__add( X
% 1.02/1.66 ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring( X ) }
% 1.02/1.66 .
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Omonoid__add( X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0( X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero( X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring( X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oplus( X ) }.
% 1.02/1.66 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.66 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.66 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.02/1.66 ( tc_fun( Y, X ) ) }.
% 1.02/1.66 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.02/1.66 ) ) }.
% 1.02/1.66 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.02/1.66 .
% 1.02/1.66 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.02/1.66 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.02/1.66 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.02/1.66 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.66 tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.02/1.66 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.02/1.66 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.02/1.66 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.02/1.66 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.02/1.66 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.02/1.66 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.02/1.66 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.02/1.66 { class_Power_Opower( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Oplus( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.02/1.66 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.02/1.66 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.02/1.66 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.66 tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Oplus( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.02/1.66 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.02/1.66 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.02/1.66 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.02/1.66 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.02/1.66 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.02/1.66 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ),
% 1.02/1.66 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.02/1.66 ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.02/1.66 X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.02/1.66 }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.66 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.66 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.66 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.02/1.66 ( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.02/1.66 ( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.02/1.66 ( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.02/1.66 }.
% 1.02/1.66 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.02/1.66 ) ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.02/1.66 .
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.02/1.66 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.02/1.66 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a, v_p, v_h
% 1.02/1.66 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ), v_p =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) }.
% 1.02/1.66 { c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( t_a ),
% 1.02/1.66 c_Polynomial_Osmult( t_a, v_h,
% 1.02/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a, v_p, v_h )
% 1.02/1.66 ), c_Polynomial_OpCons( t_a, v_a,
% 1.02/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a, v_p, v_h )
% 1.02/1.66 ) ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) }.
% 1.02/1.66 { ! v_a = c_Groups_Ozero__class_Ozero( t_a ), ! v_p =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ) }.
% 1.02/1.66 { class_Rings_Ocomm__semiring__0( t_a ) }.
% 1.02/1.66
% 1.02/1.66 *** allocated 15000 integers for clauses
% 1.02/1.66 *** allocated 22500 integers for clauses
% 1.02/1.66 *** allocated 33750 integers for clauses
% 1.02/1.66 *** allocated 50625 integers for clauses
% 1.02/1.66 *** allocated 75937 integers for clauses
% 1.02/1.66 percentage equality = 0.273930, percentage horn = 0.904830
% 1.02/1.66 This is a problem with some equality
% 1.02/1.66
% 1.02/1.66
% 1.02/1.66
% 1.02/1.66 Options Used:
% 1.02/1.66
% 1.02/1.66 useres = 1
% 1.02/1.66 useparamod = 1
% 1.02/1.66 useeqrefl = 1
% 1.02/1.66 useeqfact = 1
% 1.02/1.66 usefactor = 1
% 1.02/1.66 usesimpsplitting = 0
% 1.02/1.66 usesimpdemod = 5
% 1.02/1.66 usesimpres = 3
% 1.02/1.66
% 1.02/1.66 resimpinuse = 1000
% 1.02/1.66 resimpclauses = 20000
% 1.02/1.66 substype = eqrewr
% 1.02/1.66 backwardsubs = 1
% 1.02/1.66 selectoldest = 5
% 1.02/1.66
% 1.02/1.66 litorderings [0] = split
% 1.02/1.66 litorderings [1] = extend the termordering, first sorting on arguments
% 1.02/1.66
% 1.02/1.66 termordering = kbo
% 1.02/1.66
% 1.02/1.66 litapriori = 0
% 1.02/1.66 termapriori = 1
% 1.02/1.66 litaposteriori = 0
% 1.02/1.66 termaposteriori = 0
% 1.02/1.66 demodaposteriori = 0
% 1.02/1.66 ordereqreflfact = 0
% 1.02/1.66
% 1.02/1.66 litselect = negord
% 1.02/1.66
% 1.02/1.66 maxweight = 15
% 1.02/1.66 maxdepth = 30000
% 1.02/1.66 maxlength = 115
% 1.02/1.66 maxnrvars = 195
% 1.02/1.66 excuselevel = 1
% 1.02/1.66 increasemaxweight = 1
% 1.02/1.66
% 1.02/1.66 maxselected = 10000000
% 1.02/1.66 maxnrclauses = 10000000
% 1.02/1.66
% 1.02/1.66 showgenerated = 0
% 1.02/1.66 showkept = 0
% 1.02/1.66 showselected = 0
% 1.02/1.66 showdeleted = 0
% 1.02/1.66 showresimp = 1
% 1.02/1.66 showstatus = 2000
% 1.02/1.66
% 1.02/1.66 prologoutput = 0
% 1.02/1.66 nrgoals = 5000000
% 1.02/1.66 totalproof = 1
% 1.02/1.66
% 1.02/1.66 Symbols occurring in the translation:
% 1.02/1.66
% 1.02/1.66 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.02/1.66 . [1, 2] (w:1, o:184, a:1, s:1, b:0),
% 1.02/1.66 ! [4, 1] (w:0, o:102, a:1, s:1, b:0),
% 1.02/1.66 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.66 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.66 hAPP [38, 2] (w:1, o:208, a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Ocomm__semiring__0 [41, 1] (w:1, o:109, a:1, s:1, b:0),
% 1.02/1.66 tc_Polynomial_Opoly [42, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.02/1.66 c_Groups_Ozero__class_Ozero [43, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.02/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [44, 3] (w:1
% 1.02/1.66 , o:233, a:1, s:1, b:0),
% 1.02/1.66 c_Polynomial_OpCons [46, 3] (w:1, o:237, a:1, s:1, b:0),
% 1.02/1.66 c_Polynomial_Osmult [48, 3] (w:1, o:238, a:1, s:1, b:0),
% 1.02/1.66 c_Groups_Oplus__class_Oplus [49, 3] (w:1, o:239, a:1, s:1, b:0),
% 1.02/1.66 class_Groups_Ocomm__monoid__add [53, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.02/1.66
% 1.02/1.66 class_Rings_Oidom [57, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.02/1.66 class_Groups_Ozero [58, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.02/1.66 class_Groups_Omonoid__add [59, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.02/1.66 class_Groups_Ocancel__semigroup__add [61, 1] (w:1, o:122, a:1, s:1
% 1.02/1.66 , b:0),
% 1.02/1.66 class_Groups_Ocancel__ab__semigroup__add [62, 1] (w:1, o:123, a:1, s:
% 1.02/1.66 1, b:0),
% 1.02/1.66 class_Groups_Oab__semigroup__add [65, 1] (w:1, o:124, a:1, s:1, b:0)
% 1.02/1.66 ,
% 1.02/1.66 class_Groups_Olinordered__ab__group__add [67, 1] (w:1, o:120, a:1, s:
% 1.02/1.66 1, b:0),
% 1.02/1.66 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [68
% 1.02/1.66 , 1] (w:1, o:153, a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Ocomm__semiring__1 [69, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.02/1.66 c_Polynomial_Opoly__rec [72, 5] (w:1, o:278, a:1, s:1, b:0),
% 1.02/1.66 c_fequal [73, 2] (w:1, o:209, a:1, s:1, b:0),
% 1.02/1.66 c_If [74, 4] (w:1, o:267, a:1, s:1, b:0),
% 1.02/1.66 c_Groups_Otimes__class_Otimes [75, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.02/1.66 class_Groups_Oab__semigroup__mult [77, 1] (w:1, o:155, a:1, s:1, b:0)
% 1.02/1.66 ,
% 1.02/1.66 c_Polynomial_Opcompose [90, 3] (w:1, o:240, a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Olinordered__ring__strict [91, 1] (w:1, o:126, a:1, s:1
% 1.02/1.66 , b:0),
% 1.02/1.66 class_RealVector_Oreal__normed__algebra [93, 1] (w:1, o:127, a:1, s:1
% 1.02/1.66 , b:0),
% 1.02/1.66 class_Rings_Ocomm__semiring [95, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Osemiring [99, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Omult__zero [100, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Ono__zero__divisors [101, 1] (w:1, o:143, a:1, s:1, b:0)
% 1.02/1.66 ,
% 1.02/1.66 class_Rings_Oring__no__zero__divisors [102, 1] (w:1, o:129, a:1, s:1
% 1.02/1.66 , b:0),
% 1.02/1.66 c_Polynomial_Opoly [103, 2] (w:1, o:210, a:1, s:1, b:0),
% 1.02/1.66 class_Fields_Ofield [106, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.02/1.66 c_Polynomial_Opdivmod__rel [107, 5] (w:1, o:279, a:1, s:1, b:0),
% 1.02/1.66 class_Lattices_Oab__semigroup__idem__mult [108, 1] (w:1, o:156, a:1
% 1.02/1.66 , s:1, b:0),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq [109, 3] (w:1, o:234, a:1, s:1, b:0
% 1.02/1.66 ),
% 1.02/1.66 class_Rings_Olinordered__ring [110, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.02/1.66 c_Rings_Odvd__class_Odvd [111, 3] (w:1, o:241, a:1, s:1, b:0),
% 1.02/1.66 c_Orderings_Oord__class_Oless [112, 3] (w:1, o:235, a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Olinordered__idom [113, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.02/1.66 class_Groups_Oordered__cancel__ab__semigroup__add [114, 1] (w:1, o:
% 1.02/1.66 157, a:1, s:1, b:0),
% 1.02/1.66 class_Int_Oring__char__0 [115, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Olinordered__semiring__strict [120, 1] (w:1, o:136, a:1
% 1.02/1.66 , s:1, b:0),
% 1.02/1.66 class_Rings_Olinordered__semiring [121, 1] (w:1, o:137, a:1, s:1, b:0
% 1.02/1.66 ),
% 1.02/1.66 class_Groups_Oordered__comm__monoid__add [122, 1] (w:1, o:159, a:1
% 1.02/1.66 , s:1, b:0),
% 1.02/1.66 class_Rings_Odvd [124, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.02/1.66 class_Groups_Oordered__ab__semigroup__add__imp__le [125, 1] (w:1, o:
% 1.02/1.66 160, a:1, s:1, b:0),
% 1.02/1.66 class_Groups_Oordered__ab__semigroup__add [126, 1] (w:1, o:161, a:1
% 1.02/1.66 , s:1, b:0),
% 1.02/1.66 class_Rings_Olinordered__comm__semiring__strict [128, 1] (w:1, o:138
% 1.02/1.66 , a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Olinordered__semidom [129, 1] (w:1, o:139, a:1, s:1, b:0)
% 1.02/1.66 ,
% 1.02/1.66 class_Rings_Oordered__cancel__semiring [130, 1] (w:1, o:145, a:1, s:1
% 1.02/1.66 , b:0),
% 1.02/1.66 class_Rings_Oordered__ring [131, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Oordered__semiring [132, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.02/1.66
% 1.02/1.66 class_Rings_Oordered__comm__semiring [133, 1] (w:1, o:148, a:1, s:1
% 1.02/1.66 , b:0),
% 1.02/1.66 class_Rings_Osemiring__0 [136, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.02/1.66 hBOOL [137, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.02/1.66 class_Orderings_Opreorder [138, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.02/1.66 c_Polynomial_Osynthetic__div [139, 3] (w:1, o:242, a:1, s:1, b:0),
% 1.02/1.66 c_Polynomial_Opos__poly [140, 2] (w:1, o:211, a:1, s:1, b:0),
% 1.02/1.66 c_Polynomial_Oorder [141, 3] (w:1, o:236, a:1, s:1, b:0),
% 1.02/1.66 tc_Nat_Onat [142, 0] (w:1, o:68, a:1, s:1, b:0),
% 1.02/1.66 class_Orderings_Oorder [143, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.02/1.66 class_Orderings_Oord [144, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.02/1.66 tc_fun [145, 2] (w:1, o:221, a:1, s:1, b:0),
% 1.02/1.66 class_Orderings_Olinorder [146, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Olinordered__semiring__1__strict [150, 1] (w:1, o:140, a:
% 1.02/1.66 1, s:1, b:0),
% 1.02/1.66 c_Groups_Oone__class_Oone [151, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.02/1.66 c_Polynomial_Odegree [152, 2] (w:1, o:223, a:1, s:1, b:0),
% 1.02/1.66 c_Polynomial_Omonom [153, 3] (w:1, o:243, a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Olinordered__semiring__1 [154, 1] (w:1, o:141, a:1, s:1
% 1.02/1.66 , b:0),
% 1.02/1.66 class_Groups_Oone [157, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.02/1.66 class_Rings_Ozero__neq__one [165, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.02/1.66 class_Groups_Omonoid__mult [166, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.02/1.66 class_Groups_Ocomm__monoid__mult [167, 1] (w:1, o:170, a:1, s:1, b:0)
% 1.02/1.66 ,
% 1.02/1.66 class_Rings_Ocomm__ring__1 [168, 1] (w:1, o:107, a:1, s:1, b:0),
% 5.15/5.50 c_Groups_Ouminus__class_Ouminus [169, 2] (w:1, o:224, a:1, s:1, b:0)
% 5.15/5.50 ,
% 5.15/5.50 class_Groups_Oab__group__add [170, 1] (w:1, o:171, a:1, s:1, b:0),
% 5.15/5.50 class_Lattices_Oboolean__algebra [171, 1] (w:1, o:172, a:1, s:1, b:0)
% 5.15/5.50 ,
% 5.15/5.50 class_Groups_Ouminus [173, 1] (w:1, o:173, a:1, s:1, b:0),
% 5.15/5.50 class_Rings_Ocomm__ring [174, 1] (w:1, o:108, a:1, s:1, b:0),
% 5.15/5.50 class_Groups_Ogroup__add [175, 1] (w:1, o:174, a:1, s:1, b:0),
% 5.15/5.50 class_Groups_Oordered__ab__group__add [176, 1] (w:1, o:175, a:1, s:1
% 5.15/5.50 , b:0),
% 5.15/5.50 class_Rings_Oring [177, 1] (w:1, o:130, a:1, s:1, b:0),
% 5.15/5.50 class_Rings_Oring__1__no__zero__divisors [178, 1] (w:1, o:131, a:1
% 5.15/5.50 , s:1, b:0),
% 5.15/5.50 c_Power_Opower__class_Opower [180, 1] (w:1, o:176, a:1, s:1, b:0),
% 5.15/5.50 c_Polynomial_Ocoeff [182, 2] (w:1, o:222, a:1, s:1, b:0),
% 5.15/5.50 tc_Int_Oint [183, 0] (w:1, o:85, a:1, s:1, b:0),
% 5.15/5.50 class_Power_Opower [184, 1] (w:1, o:177, a:1, s:1, b:0),
% 5.15/5.50 class_Rings_Oring__1 [185, 1] (w:1, o:132, a:1, s:1, b:0),
% 5.15/5.50 c_Nat_OSuc [187, 1] (w:1, o:178, a:1, s:1, b:0),
% 5.15/5.50 c_Power_Opower_Opower [188, 3] (w:1, o:244, a:1, s:1, b:0),
% 5.15/5.50 c_Polynomial_Opoly__gcd [204, 3] (w:1, o:245, a:1, s:1, b:0),
% 5.15/5.50 c_Rings_Oinverse__class_Oinverse [205, 2] (w:1, o:225, a:1, s:1, b:0)
% 5.15/5.50 ,
% 5.15/5.50 class_Rings_Odivision__ring__inverse__zero [206, 1] (w:1, o:151, a:1
% 5.15/5.50 , s:1, b:0),
% 5.15/5.50 class_Rings_Odivision__ring [207, 1] (w:1, o:152, a:1, s:1, b:0),
% 5.15/5.50 class_Fields_Olinordered__field [208, 1] (w:1, o:114, a:1, s:1, b:0)
% 5.15/5.50 ,
% 5.15/5.50 class_Fields_Olinordered__field__inverse__zero [209, 1] (w:1, o:115
% 5.15/5.50 , a:1, s:1, b:0),
% 5.15/5.50 class_Fields_Ofield__inverse__zero [210, 1] (w:1, o:116, a:1, s:1, b:
% 5.15/5.50 0),
% 5.15/5.50 c_Divides_Odiv__class_Omod [211, 3] (w:1, o:246, a:1, s:1, b:0),
% 5.15/5.50 class_Divides_Osemiring__div [213, 1] (w:1, o:180, a:1, s:1, b:0),
% 5.15/5.50 class_Divides_Oring__div [214, 1] (w:1, o:179, a:1, s:1, b:0),
% 5.15/5.50 c_Groups_Ominus__class_Ominus [215, 3] (w:1, o:247, a:1, s:1, b:0),
% 5.15/5.50 class_Groups_Ominus [222, 1] (w:1, o:181, a:1, s:1, b:0),
% 5.15/5.50 class_Groups_Oplus [225, 1] (w:1, o:182, a:1, s:1, b:0),
% 5.15/5.50 class_Groups_Ocancel__comm__monoid__add [227, 1] (w:1, o:183, a:1, s:
% 5.15/5.50 1, b:0),
% 5.15/5.50 tc_HOL_Obool [229, 0] (w:1, o:84, a:1, s:1, b:0),
% 5.15/5.50 t_a [230, 0] (w:1, o:98, a:1, s:1, b:0),
% 5.15/5.50 v_p [231, 0] (w:1, o:99, a:1, s:1, b:0),
% 5.15/5.50 v_h [232, 0] (w:1, o:100, a:1, s:1, b:0),
% 5.15/5.50 v_a [233, 0] (w:1, o:101, a:1, s:1, b:0),
% 5.15/5.50 alpha1 [234, 3] (w:1, o:248, a:1, s:1, b:1),
% 5.15/5.50 alpha2 [235, 4] (w:1, o:271, a:1, s:1, b:1),
% 5.15/5.50 alpha3 [236, 4] (w:1, o:276, a:1, s:1, b:1),
% 5.15/5.50 alpha4 [237, 3] (w:1, o:249, a:1, s:1, b:1),
% 5.15/5.50 alpha5 [238, 3] (w:1, o:250, a:1, s:1, b:1),
% 5.15/5.50 alpha6 [239, 3] (w:1, o:251, a:1, s:1, b:1),
% 5.15/5.50 alpha7 [240, 3] (w:1, o:252, a:1, s:1, b:1),
% 5.15/5.50 alpha8 [241, 2] (w:1, o:226, a:1, s:1, b:1),
% 5.15/5.50 alpha9 [242, 2] (w:1, o:227, a:1, s:1, b:1),
% 5.15/5.50 alpha10 [243, 2] (w:1, o:228, a:1, s:1, b:1),
% 5.15/5.50 alpha11 [244, 2] (w:1, o:229, a:1, s:1, b:1),
% 5.15/5.50 alpha12 [245, 2] (w:1, o:230, a:1, s:1, b:1),
% 5.15/5.50 alpha13 [246, 4] (w:1, o:268, a:1, s:1, b:1),
% 5.15/5.50 alpha14 [247, 4] (w:1, o:269, a:1, s:1, b:1),
% 5.15/5.50 alpha15 [248, 4] (w:1, o:270, a:1, s:1, b:1),
% 5.15/5.50 alpha16 [249, 3] (w:1, o:253, a:1, s:1, b:1),
% 5.15/5.50 alpha17 [250, 3] (w:1, o:254, a:1, s:1, b:1),
% 5.15/5.50 alpha18 [251, 3] (w:1, o:255, a:1, s:1, b:1),
% 5.15/5.50 alpha19 [252, 2] (w:1, o:231, a:1, s:1, b:1),
% 5.15/5.50 alpha20 [253, 2] (w:1, o:232, a:1, s:1, b:1),
% 5.15/5.50 alpha21 [254, 4] (w:1, o:272, a:1, s:1, b:1),
% 5.15/5.50 alpha22 [255, 3] (w:1, o:256, a:1, s:1, b:1),
% 5.15/5.50 alpha23 [256, 3] (w:1, o:257, a:1, s:1, b:1),
% 5.15/5.50 alpha24 [257, 3] (w:1, o:258, a:1, s:1, b:1),
% 5.15/5.50 alpha25 [258, 3] (w:1, o:259, a:1, s:1, b:1),
% 5.15/5.50 alpha26 [259, 4] (w:1, o:273, a:1, s:1, b:1),
% 5.15/5.50 alpha27 [260, 4] (w:1, o:274, a:1, s:1, b:1),
% 5.15/5.50 alpha28 [261, 4] (w:1, o:275, a:1, s:1, b:1),
% 5.15/5.50 skol1 [262, 2] (w:1, o:212, a:1, s:1, b:1),
% 5.15/5.50 skol2 [263, 3] (w:1, o:264, a:1, s:1, b:1),
% 5.15/5.50 skol3 [264, 3] (w:1, o:265, a:1, s:1, b:1),
% 5.15/5.50 skol4 [265, 2] (w:1, o:213, a:1, s:1, b:1),
% 19.18/19.55 skol5 [266, 2] (w:1, o:214, a:1, s:1, b:1),
% 19.18/19.55 skol6 [267, 2] (w:1, o:215, a:1, s:1, b:1),
% 19.18/19.55 skol7 [268, 3] (w:1, o:266, a:1, s:1, b:1),
% 19.18/19.55 skol8 [269, 1] (w:1, o:110, a:1, s:1, b:1),
% 19.18/19.55 skol9 [270, 2] (w:1, o:216, a:1, s:1, b:1),
% 19.18/19.55 skol10 [271, 2] (w:1, o:217, a:1, s:1, b:1),
% 19.18/19.55 skol11 [272, 3] (w:1, o:260, a:1, s:1, b:1),
% 19.18/19.55 skol12 [273, 2] (w:1, o:218, a:1, s:1, b:1),
% 19.18/19.55 skol13 [274, 4] (w:1, o:277, a:1, s:1, b:1),
% 19.18/19.55 skol14 [275, 3] (w:1, o:261, a:1, s:1, b:1),
% 19.18/19.55 skol15 [276, 3] (w:1, o:262, a:1, s:1, b:1),
% 19.18/19.55 skol16 [277, 2] (w:1, o:219, a:1, s:1, b:1),
% 19.18/19.55 skol17 [278, 2] (w:1, o:220, a:1, s:1, b:1),
% 19.18/19.55 skol18 [279, 3] (w:1, o:263, a:1, s:1, b:1).
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Starting Search:
% 19.18/19.55
% 19.18/19.55 *** allocated 113905 integers for clauses
% 19.18/19.55 *** allocated 170857 integers for clauses
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 4027
% 19.18/19.55 Kept: 2138
% 19.18/19.55 Inuse: 51
% 19.18/19.55 Deleted: 0
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 *** allocated 256285 integers for clauses
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 *** allocated 170857 integers for termspace/termends
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 9797
% 19.18/19.55 Kept: 4252
% 19.18/19.55 Inuse: 145
% 19.18/19.55 Deleted: 1
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 *** allocated 384427 integers for clauses
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 *** allocated 256285 integers for termspace/termends
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 15236
% 19.18/19.55 Kept: 6336
% 19.18/19.55 Inuse: 205
% 19.18/19.55 Deleted: 1
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 *** allocated 576640 integers for clauses
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 20541
% 19.18/19.55 Kept: 8340
% 19.18/19.55 Inuse: 269
% 19.18/19.55 Deleted: 5
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 *** allocated 384427 integers for termspace/termends
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 33397
% 19.18/19.55 Kept: 10457
% 19.18/19.55 Inuse: 301
% 19.18/19.55 Deleted: 5
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 *** allocated 864960 integers for clauses
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 *** allocated 576640 integers for termspace/termends
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 49164
% 19.18/19.55 Kept: 12818
% 19.18/19.55 Inuse: 340
% 19.18/19.55 Deleted: 6
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 58338
% 19.18/19.55 Kept: 15276
% 19.18/19.55 Inuse: 375
% 19.18/19.55 Deleted: 6
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 *** allocated 1297440 integers for clauses
% 19.18/19.55 *** allocated 864960 integers for termspace/termends
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 73541
% 19.18/19.55 Kept: 18308
% 19.18/19.55 Inuse: 420
% 19.18/19.55 Deleted: 6
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 Resimplifying clauses:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 85310
% 19.18/19.55 Kept: 20336
% 19.18/19.55 Inuse: 443
% 19.18/19.55 Deleted: 195
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 94739
% 19.18/19.55 Kept: 22975
% 19.18/19.55 Inuse: 470
% 19.18/19.55 Deleted: 195
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 100845
% 19.18/19.55 Kept: 25030
% 19.18/19.55 Inuse: 500
% 19.18/19.55 Deleted: 195
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 *** allocated 1946160 integers for clauses
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 105836
% 19.18/19.55 Kept: 27179
% 19.18/19.55 Inuse: 510
% 19.18/19.55 Deleted: 195
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 *** allocated 1297440 integers for termspace/termends
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 112814
% 19.18/19.55 Kept: 29584
% 19.18/19.55 Inuse: 525
% 19.18/19.55 Deleted: 195
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 123763
% 19.18/19.55 Kept: 32240
% 19.18/19.55 Inuse: 550
% 19.18/19.55 Deleted: 195
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 133573
% 19.18/19.55 Kept: 34261
% 19.18/19.55 Inuse: 579
% 19.18/19.55 Deleted: 195
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 146378
% 19.18/19.55 Kept: 36498
% 19.18/19.55 Inuse: 600
% 19.18/19.55 Deleted: 195
% 19.18/19.55 Deletedinuse: 0
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55 Resimplifying inuse:
% 19.18/19.55 Done
% 19.18/19.55
% 19.18/19.55
% 19.18/19.55 Intermediate Status:
% 19.18/19.55 Generated: 155009
% 60.65/61.02 Kept: 38626
% 60.65/61.02 Inuse: 625
% 60.65/61.02 Deleted: 195
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying clauses:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 160647
% 60.65/61.02 Kept: 40677
% 60.65/61.02 Inuse: 650
% 60.65/61.02 Deleted: 255
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 *** allocated 1946160 integers for termspace/termends
% 60.65/61.02 *** allocated 2919240 integers for clauses
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 168663
% 60.65/61.02 Kept: 43696
% 60.65/61.02 Inuse: 680
% 60.65/61.02 Deleted: 255
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 177459
% 60.65/61.02 Kept: 45819
% 60.65/61.02 Inuse: 735
% 60.65/61.02 Deleted: 255
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 185100
% 60.65/61.02 Kept: 47826
% 60.65/61.02 Inuse: 784
% 60.65/61.02 Deleted: 255
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 194622
% 60.65/61.02 Kept: 50015
% 60.65/61.02 Inuse: 810
% 60.65/61.02 Deleted: 255
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 205570
% 60.65/61.02 Kept: 52686
% 60.65/61.02 Inuse: 825
% 60.65/61.02 Deleted: 255
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 212532
% 60.65/61.02 Kept: 56118
% 60.65/61.02 Inuse: 830
% 60.65/61.02 Deleted: 255
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 224641
% 60.65/61.02 Kept: 58298
% 60.65/61.02 Inuse: 855
% 60.65/61.02 Deleted: 255
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 234067
% 60.65/61.02 Kept: 60332
% 60.65/61.02 Inuse: 870
% 60.65/61.02 Deleted: 255
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying clauses:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 244885
% 60.65/61.02 Kept: 62451
% 60.65/61.02 Inuse: 890
% 60.65/61.02 Deleted: 311
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 *** allocated 2919240 integers for termspace/termends
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 255559
% 60.65/61.02 Kept: 64772
% 60.65/61.02 Inuse: 900
% 60.65/61.02 Deleted: 311
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 260512
% 60.65/61.02 Kept: 66813
% 60.65/61.02 Inuse: 939
% 60.65/61.02 Deleted: 312
% 60.65/61.02 Deletedinuse: 0
% 60.65/61.02
% 60.65/61.02 *** allocated 4378860 integers for clauses
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 264978
% 60.65/61.02 Kept: 68839
% 60.65/61.02 Inuse: 994
% 60.65/61.02 Deleted: 315
% 60.65/61.02 Deletedinuse: 3
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 271121
% 60.65/61.02 Kept: 71024
% 60.65/61.02 Inuse: 1014
% 60.65/61.02 Deleted: 319
% 60.65/61.02 Deletedinuse: 7
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 279140
% 60.65/61.02 Kept: 73331
% 60.65/61.02 Inuse: 1044
% 60.65/61.02 Deleted: 319
% 60.65/61.02 Deletedinuse: 7
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 286512
% 60.65/61.02 Kept: 75369
% 60.65/61.02 Inuse: 1069
% 60.65/61.02 Deleted: 319
% 60.65/61.02 Deletedinuse: 7
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02 Resimplifying inuse:
% 60.65/61.02 Done
% 60.65/61.02
% 60.65/61.02
% 60.65/61.02 Intermediate Status:
% 60.65/61.02 Generated: 294550
% 60.65/61.02 Kept: 77579
% 60.65/61.02 Inuse: 1109
% 60.65/61.03 Deleted: 319
% 60.65/61.03 Deletedinuse: 7
% 60.65/61.03
% 60.65/61.03 Resimplifying inuse:
% 60.65/61.03 Done
% 60.65/61.03
% 60.65/61.03 Resimplifying inuse:
% 60.65/61.03 Done
% 60.65/61.03
% 60.65/61.03
% 60.65/61.03 Intermediate Status:
% 60.65/61.03 Generated: 301036
% 60.65/61.03 Kept: 79591
% 60.65/61.03 Inuse: 1157
% 60.65/61.03 Deleted: 319
% 60.65/61.03 Deletedinuse: 7
% 60.65/61.03
% 60.65/61.03
% 60.65/61.03 Intermediate Status:
% 60.65/61.03 Generated: 305448
% 60.65/61.03 Kept: 81989
% 60.65/61.03 Inuse: 1166
% 60.65/61.03 Deleted: 319
% 60.65/61.03 Deletedinuse: 7
% 60.65/61.03
% 60.65/61.03 Resimplifying inuse:
% 60.65/61.03 Done
% 60.65/61.03
% 60.65/61.03 Resimplifying clauses:
% 60.65/61.03 Done
% 60.65/61.03
% 60.65/61.03
% 60.65/61.03 Intermediate Status:
% 60.65/61.03 Generated: 313874
% 60.65/61.03 Kept: 84217
% 60.65/61.03 Inuse: 1170
% 60.65/61.03 Deleted: 569
% 60.65/61.03 Deletedinuse: 7
% 60.65/61.03
% 60.65/61.03 Resimplifying inuse:
% 60.65/61.03 Done
% 60.65/61.03
% 60.65/61.03 Resimplifying inuse:
% 60.65/61.03 Done
% 60.65/61.03
% 60.65/61.03
% 60.65/61.03 Intermediate Status:
% 60.65/61.03 Generated: 322260
% 60.65/61.03 Kept: 86474
% 60.65/61.03 Inuse: 1219
% 60.65/61.03 Deleted: 570
% 60.65/61.03 Deletedinuse: 8
% 60.65/61.03
% 60.65/61.03 Resimplifying inuse:
% 60.65/61.03 Done
% 60.65/61.03
% 60.65/61.03 Resimplifying inuse:
% 60.65/61.03 Done
% 60.65/61.03
% 60.65/61.03
% 60.65/61.03 Intermediate Status:
% 60.65/61.03 Generated: 329814
% 60.65/61.03 Kept: 88549
% 60.65/61.03 Inuse: 1244
% 60.65/61.03 Deleted: 570
% 60.65/61.03 Deletedinuse: 8
% 60.65/61.03
% 60.65/61.03 Resimplifying inuse:
% 60.65/61.03 Done
% 60.65/61.03
% 60.65/61.03 Resimplifying inuse:
% 60.65/61.03 Done
% 60.65/61.03
% 60.65/61.03
% 60.65/61.03 Intermediate Status:
% 60.65/61.03 Generated: 341913
% 60.65/61.03 Kept: 90606
% 60.65/61.03 Inuse: 1269
% 60.65/61.03 Deleted: 570
% 60.65/61.03 Deletedinuse: 8
% 60.65/61.03
% 60.65/61.03 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 352067
% 163.64/164.08 Kept: 92804
% 163.64/164.08 Inuse: 1289
% 163.64/164.08 Deleted: 570
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 *** allocated 4378860 integers for termspace/termends
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 363630
% 163.64/164.08 Kept: 94981
% 163.64/164.08 Inuse: 1304
% 163.64/164.08 Deleted: 570
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 373004
% 163.64/164.08 Kept: 97022
% 163.64/164.08 Inuse: 1344
% 163.64/164.08 Deleted: 570
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 383107
% 163.64/164.08 Kept: 99744
% 163.64/164.08 Inuse: 1364
% 163.64/164.08 Deleted: 570
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 *** allocated 6568290 integers for clauses
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 396872
% 163.64/164.08 Kept: 104959
% 163.64/164.08 Inuse: 1389
% 163.64/164.08 Deleted: 570
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying clauses:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 405419
% 163.64/164.08 Kept: 107202
% 163.64/164.08 Inuse: 1404
% 163.64/164.08 Deleted: 3002
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 416047
% 163.64/164.08 Kept: 109301
% 163.64/164.08 Inuse: 1449
% 163.64/164.08 Deleted: 3002
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 432965
% 163.64/164.08 Kept: 112587
% 163.64/164.08 Inuse: 1479
% 163.64/164.08 Deleted: 3002
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 453086
% 163.64/164.08 Kept: 116250
% 163.64/164.08 Inuse: 1519
% 163.64/164.08 Deleted: 3002
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 463705
% 163.64/164.08 Kept: 118288
% 163.64/164.08 Inuse: 1569
% 163.64/164.08 Deleted: 3002
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 479667
% 163.64/164.08 Kept: 123211
% 163.64/164.08 Inuse: 1599
% 163.64/164.08 Deleted: 3002
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 493112
% 163.64/164.08 Kept: 127470
% 163.64/164.08 Inuse: 1619
% 163.64/164.08 Deleted: 3002
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying clauses:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 504930
% 163.64/164.08 Kept: 130128
% 163.64/164.08 Inuse: 1634
% 163.64/164.08 Deleted: 3086
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 515619
% 163.64/164.08 Kept: 133018
% 163.64/164.08 Inuse: 1664
% 163.64/164.08 Deleted: 3086
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 524375
% 163.64/164.08 Kept: 135107
% 163.64/164.08 Inuse: 1679
% 163.64/164.08 Deleted: 3086
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 535555
% 163.64/164.08 Kept: 138557
% 163.64/164.08 Inuse: 1694
% 163.64/164.08 Deleted: 3086
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 *** allocated 6568290 integers for termspace/termends
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 542331
% 163.64/164.08 Kept: 142670
% 163.64/164.08 Inuse: 1699
% 163.64/164.08 Deleted: 3086
% 163.64/164.08 Deletedinuse: 8
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 560124
% 163.64/164.08 Kept: 145867
% 163.64/164.08 Inuse: 1719
% 163.64/164.08 Deleted: 3088
% 163.64/164.08 Deletedinuse: 10
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 569325
% 163.64/164.08 Kept: 148117
% 163.64/164.08 Inuse: 1729
% 163.64/164.08 Deleted: 3088
% 163.64/164.08 Deletedinuse: 10
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying clauses:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 584974
% 163.64/164.08 Kept: 151882
% 163.64/164.08 Inuse: 1754
% 163.64/164.08 Deleted: 3636
% 163.64/164.08 Deletedinuse: 10
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 606631
% 163.64/164.08 Kept: 155130
% 163.64/164.08 Inuse: 1764
% 163.64/164.08 Deleted: 3636
% 163.64/164.08 Deletedinuse: 10
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 619858
% 163.64/164.08 Kept: 157329
% 163.64/164.08 Inuse: 1774
% 163.64/164.08 Deleted: 3636
% 163.64/164.08 Deletedinuse: 10
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08 *** allocated 9852435 integers for clauses
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 636380
% 163.64/164.08 Kept: 160909
% 163.64/164.08 Inuse: 1784
% 163.64/164.08 Deleted: 3636
% 163.64/164.08 Deletedinuse: 10
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 163.64/164.08
% 163.64/164.08
% 163.64/164.08 Intermediate Status:
% 163.64/164.08 Generated: 652559
% 163.64/164.08 Kept: 167574
% 163.64/164.08 Inuse: 1799
% 163.64/164.08 Deleted: 3636
% 163.64/164.08 Deletedinuse: 10
% 163.64/164.08
% 163.64/164.08 Resimplifying inuse:
% 163.64/164.08 Done
% 300.07/300.55 Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------