TSTP Solution File: SWW187+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW187+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n029.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 300.02s 300.44s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW187+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon Jun 6 01:28:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.63/1.98 *** allocated 10000 integers for termspace/termends
% 1.63/1.98 *** allocated 10000 integers for clauses
% 1.63/1.98 *** allocated 10000 integers for justifications
% 1.63/1.98 *** allocated 15000 integers for termspace/termends
% 1.63/1.98 *** allocated 22500 integers for termspace/termends
% 1.63/1.98 *** allocated 33750 integers for termspace/termends
% 1.63/1.98 Bliksem 1.12
% 1.63/1.98
% 1.63/1.98
% 1.63/1.98 Automatic Strategy Selection
% 1.63/1.98
% 1.63/1.98 *** allocated 50625 integers for termspace/termends
% 1.63/1.98 *** allocated 75937 integers for termspace/termends
% 1.63/1.98 *** allocated 113905 integers for termspace/termends
% 1.63/1.98
% 1.63/1.98 Clauses:
% 1.63/1.98
% 1.63/1.98 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.63/1.98 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.63/1.98 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.63/1.98 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.63/1.98 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.63/1.98 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.63/1.98 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__semiring__0( X ), !
% 1.63/1.98 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 1.63/1.98 ( tc_Polynomial_Opoly( X ) ),
% 1.63/1.98 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.63/1.98 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.63/1.98 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.63/1.98 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 1.63/1.98 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 1.63/1.98 c_Polynomial_OpCons( X, T,
% 1.63/1.98 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.63/1.98 .
% 1.63/1.98 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 1.63/1.98 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), Y = c_Polynomial_OpCons( X, skol2( X, Y ),
% 1.63/1.98 skol19( X, Y ) ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.63/1.98 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.63/1.98 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 1.63/1.98 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.63/1.98 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 1.63/1.98 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.63/1.98 , Y ) ) }.
% 1.63/1.98 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 1.63/1.98 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.63/1.98 c_Polynomial_Odegree( X, Y ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), !
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ), c_Polynomial_OpCons
% 1.63/1.98 ( X, U, T ), c_Polynomial_OpCons( X, Z, Y ) ), c_HOL_Oequal__class_Oequal
% 1.63/1.98 ( X, U, Z ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), !
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ), c_Polynomial_OpCons
% 1.63/1.98 ( X, U, T ), c_Polynomial_OpCons( X, Z, Y ) ), c_HOL_Oequal__class_Oequal
% 1.63/1.98 ( tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), !
% 1.63/1.98 c_HOL_Oequal__class_Oequal( X, U, Z ), ! c_HOL_Oequal__class_Oequal(
% 1.63/1.98 tc_Polynomial_Opoly( X ), T, Y ), c_HOL_Oequal__class_Oequal(
% 1.63/1.98 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.63/1.98 c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.98 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.63/1.98 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.63/1.98 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 1.63/1.98 , c_Polynomial_Odegree( X, Y ) ) }.
% 1.63/1.98 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.63/1.98 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.63/1.98 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.63/1.98 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.63/1.98 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.63/1.98 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.63/1.98 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.63/1.98 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.63/1.98 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.98 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.98 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.98 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.63/1.98 c_Polynomial_Odegree( X, Y ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.63/1.98 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ),
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ),
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.63/1.98 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.63/1.98 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), !
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ),
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.63/1.98 c_Polynomial_OpCons( X, Z, Y ) ), c_HOL_Oequal__class_Oequal( X,
% 1.63/1.98 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), !
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ),
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.63/1.98 c_Polynomial_OpCons( X, Z, Y ) ), c_HOL_Oequal__class_Oequal(
% 1.63/1.98 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), !
% 1.63/1.98 c_HOL_Oequal__class_Oequal( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ),
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ),
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ),
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.63/1.98 c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.63/1.98 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), !
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), ! Z = Y,
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 1.63/1.98 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.63/1.98 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.63/1.98 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.63/1.98 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.63/1.98 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.63/1.98 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.63/1.98 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.63/1.98 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.63/1.98 ) }.
% 1.63/1.98 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.63/1.98 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 1.63/1.98 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.63/1.98 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.63/1.98 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.63/1.98 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.63/1.98 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.63/1.98 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.63/1.98 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.63/1.98 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.63/1.98 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.63/1.98 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.98 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.63/1.98 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), !
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ), c_Polynomial_OpCons
% 1.63/1.98 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 1.63/1.98 c_HOL_Oequal__class_Oequal( X, Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), !
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ), c_Polynomial_OpCons
% 1.63/1.98 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ), Y,
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.63/1.98 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), !
% 1.63/1.98 c_HOL_Oequal__class_Oequal( X, Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ), Y,
% 1.63/1.98 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ),
% 1.63/1.98 c_HOL_Oequal__class_Oequal( tc_Polynomial_Opoly( X ), c_Polynomial_OpCons
% 1.63/1.98 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }
% 1.63/1.98 .
% 1.63/1.98 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.63/1.98 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.63/1.99 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.63/1.99 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.63/1.99 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.63/1.99 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Ocomm__monoid__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.63/1.99 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/1.99 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 1.63/1.99 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 1.63/1.99 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.63/1.99 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.99 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.63/1.99 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.63/1.99 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 1.63/1.99 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.63/1.99 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Y ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.63/1.99 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Z ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.63/1.99 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.63/1.99 Z ) = Y }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Y ), Y ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.63/1.99 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 Y, T ), Z = Y }.
% 1.63/1.99 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 T, Y ), Z = Y }.
% 1.63/1.99 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 T, Y ), Z = Y }.
% 1.63/1.99 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 Y, Z ), T = Y }.
% 1.63/1.99 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 Y, Z ) }.
% 1.63/1.99 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 T, Y ), Z = Y }.
% 1.63/1.99 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 T, Y ) }.
% 1.63/1.99 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.63/1.99 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.63/1.99 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.63/1.99 ( tc_Nat_Onat ) ) = X }.
% 1.63/1.99 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ), X ) = X }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.63/1.99 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.63/1.99 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.63/1.99 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.63/1.99 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.63/1.99 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.63/1.99 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.63/1.99 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.63/1.99 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.63/1.99 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.63/1.99 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.63/1.99 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.63/1.99 { ! c_Nat_OSuc( X ) = X }.
% 1.63/1.99 { ! X = c_Nat_OSuc( X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.63/1.99 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.63/1.99 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol3( X, Y ) ) }.
% 1.63/1.99 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.63/1.99 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.63/1.99 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.63/1.99 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.63/1.99 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.63/1.99 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.63/1.99 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.63/1.99 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.63/1.99 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.63/1.99 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.63/1.99 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.63/1.99 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.63/1.99 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.63/1.99 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.63/1.99 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.63/1.99 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.63/1.99 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.63/1.99 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.63/1.99 = Y }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.63/1.99 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.63/1.99 ( X ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Y ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 = Y }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 Z, Y ) ) = Y }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.63/1.99 Y ) ) = Y }.
% 1.63/1.99 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.63/1.99 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.63/1.99 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.63/1.99 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.63/1.99 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.63/1.99 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha1( X, Y ), alpha13( X
% 1.63/1.99 , Y ) }.
% 1.63/1.99 { ! alpha1( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.63/1.99 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/1.99 { ! alpha13( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.63/1.99 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/1.99 { ! alpha13( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! alpha13( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ) ) }.
% 1.63/1.99 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha13( X, Y ) }.
% 1.63/1.99 { ! alpha1( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ) ) }.
% 1.63/1.99 { ! alpha1( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha1( X, Y ) }.
% 1.63/1.99 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha2( X, Y ), alpha14
% 1.63/1.99 ( X, Y ) }.
% 1.63/1.99 { ! alpha2( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.63/1.99 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! alpha14( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.63/1.99 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! alpha14( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! alpha14( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ) ) }.
% 1.63/1.99 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha14( X, Y ) }.
% 1.63/1.99 { ! alpha2( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ) ) }.
% 1.63/1.99 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 1.63/1.99 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.63/1.99 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/1.99 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.63/1.99 ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.63/1.99 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.63/1.99 }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.63/1.99 c_Nat_OSuc( X ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.63/1.99 ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.63/1.99 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.63/1.99 , c_Nat_OSuc( X ) ) }.
% 1.63/1.99 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.63/1.99 .
% 1.63/1.99 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 Z, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 Y, Z ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.63/1.99 .
% 1.63/1.99 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.63/1.99 .
% 1.63/1.99 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.63/1.99 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.63/1.99 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.63/1.99 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.63/1.99 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.63/1.99 , Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.63/1.99 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 1.63/1.99 }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.63/1.99 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 1.63/1.99 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 1.63/1.99 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 1.63/1.99 , Y ) ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.63/1.99 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.63/1.99 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.63/1.99 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.63/1.99 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.63/1.99 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.63/1.99 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.63/1.99 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.63/1.99 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.63/1.99 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.63/1.99 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.63/1.99 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.63/1.99 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.63/1.99 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.63/1.99 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.63/1.99 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.63/1.99 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.99 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.63/1.99 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.63/1.99 hAPP( Y, U ) ) }.
% 1.63/1.99 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.63/1.99 ( Z, skol4( X, Y, Z ) ), hAPP( Y, skol4( X, Y, Z ) ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.63/1.99 ( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.63/1.99 ( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.63/1.99 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.63/1.99 hAPP( Y, U ) ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.63/1.99 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.63/1.99 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.63/1.99 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.63/1.99 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.63/1.99 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.63/1.99 hAPP( Y, U ) ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.63/1.99 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.63/1.99 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.63/1.99 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.63/1.99 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.63/1.99 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.63/1.99 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.63/1.99 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.63/1.99 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.63/1.99 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.63/1.99 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.63/1.99 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.63/1.99 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 1.63/1.99 ) ) }.
% 1.63/1.99 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Y ), Z = Y }.
% 1.63/1.99 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.63/1.99 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.63/1.99 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.63/1.99 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.63/1.99 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.63/1.99 }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.63/1.99 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) }.
% 1.63/1.99 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.63/1.99 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.63/1.99 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 1.63/1.99 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.63/1.99 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.63/1.99 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 1.63/1.99 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 1.63/1.99 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 1.63/1.99 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.63/1.99 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 1.63/1.99 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.63/1.99 .
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.63/1.99 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.63/1.99 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.63/1.99 .
% 1.63/1.99 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.63/1.99 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.63/1.99 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.63/1.99 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.63/1.99 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.63/1.99 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.63/1.99 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.63/1.99 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.63/1.99 ), U = Z, T = Y }.
% 1.63/1.99 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.63/1.99 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.63/1.99 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.63/1.99 ) ), Z ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.63/1.99 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.63/1.99 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.63/1.99 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.63/1.99 ), ! U = T }.
% 1.63/1.99 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.63/1.99 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.63/1.99 ), ! Z = Y }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.63/1.99 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.63/1.99 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.63/1.99 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.63/1.99 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.63/1.99 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.63/1.99 .
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.63/1.99 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.63/1.99 ) ) }.
% 1.63/1.99 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.63/1.99 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.63/1.99 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.63/1.99 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.63/1.99 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 1.63/1.99 Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.63/1.99 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.63/1.99 , Y ) ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.63/1.99 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.63/1.99 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.63/1.99 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 1.63/1.99 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 1.63/1.99 c_Polynomial_Odegree( X, Z ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.63/1.99 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.63/1.99 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.63/1.99 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.63/1.99 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.63/1.99 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.63/1.99 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.63/1.99 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.63/1.99 ( X ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__semiring( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__semiring( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/1.99 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.63/1.99 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.63/1.99 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.63/1.99 .
% 1.63/1.99 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.63/1.99 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.63/1.99 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.63/1.99 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.63/1.99 .
% 1.63/1.99 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.63/1.99 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.63/1.99 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.63/1.99 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.63/1.99 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.63/1.99 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.63/1.99 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.63/1.99 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.63/1.99 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.63/1.99 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.63/1.99 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.63/1.99 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 1.63/1.99 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.63/1.99 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.63/1.99 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.63/1.99 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.63/1.99 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/1.99 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.63/1.99 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.63/1.99 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/1.99 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.63/1.99 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/1.99 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.63/1.99 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.63/1.99 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.63/1.99 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.63/1.99 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.63/1.99 ), X ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.63/1.99 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.63/1.99 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.63/1.99 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.63/1.99 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.63/1.99 ) ), T ), Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.63/1.99 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.63/1.99 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.63/1.99 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.63/1.99 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.63/1.99 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.63/1.99 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.63/1.99 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Y ) ) }.
% 1.63/1.99 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.63/1.99 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.63/1.99 ) ), Y ) }.
% 1.63/1.99 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.63/1.99 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Y ) ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.63/1.99 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha3( X, Y
% 1.63/1.99 , Z ), alpha15( X, Y, Z ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha3( X, Y, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha15( X, Y, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ), alpha15( X, Y, Z ) }.
% 1.63/1.99 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.63/1.99 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Y ), alpha3( X, Y, Z ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.63/1.99 ( X ) ), alpha4( X, Y, Z ), alpha16( X, Y, Z ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.63/1.99 ( X ) ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.63/1.99 ( X ) ) }.
% 1.63/1.99 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.63/1.99 ( X ), Y ), alpha16( X, Y, Z ) }.
% 1.63/1.99 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.63/1.99 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ), alpha4( X, Y, Z ) }.
% 1.63/1.99 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.63/1.99 ( X ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__semiring( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.63/1.99 { ! class_Rings_Oordered__semiring( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.63/1.99 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.63/1.99 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.63/1.99 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 1.63/1.99 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.63/1.99 ) ) }.
% 1.63/1.99 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.63/1.99 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.63/1.99 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.63/1.99 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.63/1.99 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.63/1.99 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.63/1.99 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.63/1.99 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.63/1.99 , Y ), X ) }.
% 1.63/1.99 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.63/1.99 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.63/1.99 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.63/1.99 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.63/1.99 tc_Nat_Onat ) }.
% 1.63/1.99 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.63/1.99 tc_Nat_Onat ) }.
% 1.63/1.99 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.63/1.99 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.63/1.99 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.63/1.99 c_Groups_Oone__class_Oone( X ) }.
% 1.63/1.99 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.63/1.99 c_Groups_Oone__class_Oone( X ) }.
% 1.63/1.99 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.63/1.99 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.63/1.99 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.63/1.99 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) ) }.
% 1.63/1.99 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.63/1.99 c_Groups_Oone__class_Oone( X ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.63/1.99 = Y }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.63/1.99 = Y }.
% 1.63/1.99 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.63/1.99 = Y }.
% 1.63/1.99 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.63/1.99 = Y }.
% 1.63/1.99 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.63/1.99 = Y }.
% 1.63/1.99 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.63/1.99 = Y }.
% 1.63/1.99 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.63/1.99 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.63/1.99 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.63/1.99 { ! class_Rings_Olinordered__semidom( X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.99 c_Groups_Oone__class_Oone( X ) ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__semidom( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.63/1.99 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.63/1.99 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.63/1.99 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.63/1.99 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.63/1.99 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.63/1.99 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.63/1.99 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.63/1.99 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.63/1.99 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.63/1.99 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.63/1.99 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.63/1.99 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.63/1.99 c_Groups_Oone__class_Oone( X ) }.
% 1.63/1.99 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/1.99 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.63/1.99 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.63/1.99 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.63/1.99 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.63/1.99 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.63/1.99 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.63/1.99 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.63/1.99 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.63/1.99 ), Y ) }.
% 1.63/1.99 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.63/1.99 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.63/1.99 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.63/1.99 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/1.99 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/1.99 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.63/1.99 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.63/1.99 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.63/1.99 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.63/1.99 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.63/1.99 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.63/1.99 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.63/1.99 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.63/1.99 .
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.63/1.99 ( X ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.63/1.99 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) ) ), Y ), hAPP( c_Polynomial_Opoly( X, Y ),
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ),
% 1.63/1.99 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.63/1.99 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) ) ), Y ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.63/1.99 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.63/1.99 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) ) ), Z ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.63/1.99 ( X ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.63/1.99 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ), Z ), hAPP(
% 1.63/1.99 c_Polynomial_Opoly( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ) }.
% 1.63/1.99 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/1.99 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.63/1.99 Z, T ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.63/1.99 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/1.99 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/1.99 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/1.99 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/1.99 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/1.99 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.63/1.99 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.63/1.99 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.63/1.99 , Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.63/1.99 , c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ), c_Rings_Odvd__class_Odvd( X
% 1.63/1.99 , Z, Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.63/1.99 , c_Rings_Odvd__class_Odvd( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y
% 1.63/1.99 ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.63/1.99 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.63/1.99 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.63/1.99 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.63/1.99 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.63/1.99 }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.63/1.99 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.63/1.99 }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.63/1.99 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.63/1.99 }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.63/1.99 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.63/1.99 }.
% 1.63/1.99 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.63/1.99 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.63/1.99 c_Polynomial_Osmult( X, Y, Z ) ), c_Rings_Odvd__class_Odvd(
% 1.63/1.99 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.63/1.99 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.63/1.99 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T,
% 1.63/1.99 c_Polynomial_Osmult( X, Y, Z ) ) }.
% 1.63/1.99 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.63/1.99 tc_Polynomial_Opoly( X ), Z, Y ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult(
% 1.63/1.99 X, T, Z ), Y ) }.
% 1.63/1.99 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.63/1.99 tc_Polynomial_Opoly( X ), T, c_Polynomial_Osmult( X, Z, Y ) ), Z =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd(
% 1.63/1.99 tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.63/1.99 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.63/1.99 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha5( X
% 1.63/1.99 , Y, T ) }.
% 1.63/1.99 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.63/1.99 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ), alpha17( X
% 1.63/1.99 , Y, Z, T ) }.
% 1.63/1.99 { ! class_Fields_Ofield( X ), ! alpha5( X, Y, T ), ! alpha17( X, Y, Z, T )
% 1.63/1.99 , c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult
% 1.63/1.99 ( X, T, Z ), Y ) }.
% 1.63/1.99 { ! alpha17( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.63/1.99 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha17( X, Y, Z, T ) }.
% 1.63/1.99 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ), alpha17( X
% 1.63/1.99 , Y, Z, T ) }.
% 1.63/1.99 { ! alpha5( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/1.99 { Z = c_Groups_Ozero__class_Ozero( X ), alpha5( X, Y, Z ) }.
% 1.63/1.99 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha5( X
% 1.63/1.99 , Y, Z ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.63/1.99 ( X ), Z, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X )
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree
% 1.63/1.99 ( X, Z ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.63/1.99 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.63/1.99 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.63/1.99 hAPP( Z, skol6( U, W, Z ) ) ) }.
% 1.63/1.99 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.63/1.99 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, skol6( X
% 1.63/1.99 , Y, Z ), c_Groups_Ozero__class_Ozero( X ) ) ) }.
% 1.63/1.99 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), !
% 1.63/1.99 c_Rings_Odvd__class_Odvd( X, Y, c_Groups_Oplus__class_Oplus( X, T,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ) ) ), ! hBOOL( hAPP( Z, T ) ), hBOOL(
% 1.63/1.99 hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), skol20( X,
% 1.63/1.99 Y, Z ) ) ) ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.63/1.99 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.63/1.99 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.63/1.99 Y ) ) ), Y ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.63/1.99 ( X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X )
% 1.63/1.99 ), c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.63/1.99 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.63/1.99 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), ! c_Rings_Odvd__class_Odvd(
% 1.63/1.99 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.63/1.99 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.63/1.99 Y ) ) ), Y ) }.
% 1.63/1.99 { ! class_Rings_Oidom( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.63/1.99 X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) )
% 1.63/1.99 , c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.63/1.99 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ),
% 1.63/1.99 c_Polynomial_Oorder( X, Z, Y ) ), Y ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.63/1.99 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.63/1.99 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.63/1.99 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.63/1.99 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.63/1.99 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.63/1.99 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.63/1.99 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/1.99 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.63/1.99 X ) ) }.
% 1.63/1.99 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.63/1.99 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.63/1.99 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/1.99 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.63/1.99 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/1.99 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.63/1.99 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/1.99 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.63/1.99 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.63/1.99 ) }.
% 1.63/1.99 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/1.99 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.63/1.99 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/1.99 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.63/1.99 X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.63/1.99 Y ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.63/1.99 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.63/1.99 Y ), ! Z = Y }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.63/1.99 Z ), ! Z = Y }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.63/1.99 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.63/1.99 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.63/1.99 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.63/1.99 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.63/1.99 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.63/1.99 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.63/1.99 , ! Z = Y }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.63/1.99 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.63/1.99 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.63/1.99 , ! Z = Y }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.63/1.99 , ! Y = Z }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.63/1.99 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.63/1.99 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.63/1.99 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.63/1.99 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.63/1.99 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.63/1.99 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.63/1.99 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.63/1.99 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.63/1.99 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.63/1.99 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.63/1.99 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.63/1.99 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.63/1.99 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.63/1.99 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.63/1.99 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.63/1.99 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.63/1.99 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol7( X
% 1.63/1.99 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol7( X, Y, Z ) ), Z = Y
% 1.63/1.99 }.
% 1.63/1.99 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.63/1.99 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.63/1.99 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.63/1.99 c_Polynomial_Ocoeff( X, Y ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/1.99 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.63/1.99 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.63/1.99 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.63/1.99 .
% 1.63/1.99 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.63/1.99 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.63/1.99 }.
% 1.63/1.99 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.63/1.99 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.63/1.99 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.63/1.99 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.63/1.99 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.63/1.99 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.63/1.99 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.63/1.99 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.63/1.99 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.63/1.99 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.63/1.99 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.63/1.99 ( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.63/1.99 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.63/1.99 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.63/1.99 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.63/1.99 , ! Z = Y }.
% 1.63/1.99 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/1.99 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.63/1.99 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.63/1.99 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.63/1.99 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/1.99 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.63/1.99 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.63/1.99 ( X, Z, Y ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.63/1.99 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.63/1.99 ( X, Z, Y ) }.
% 1.63/1.99 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.63/1.99 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.63/1.99 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.63/1.99 , T ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.63/1.99 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.63/1.99 , T, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.63/1.99 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.63/1.99 , Y, T ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.63/1.99 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.63/1.99 ( X, Z, Y ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.63/1.99 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.63/1.99 , T, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.63/1.99 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.63/1.99 ( X, T, Y ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.63/1.99 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.63/1.99 , Y, Z ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.63/1.99 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.63/1.99 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.63/1.99 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.63/1.99 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.63/1.99 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.63/1.99 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Y ), Z ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.63/1.99 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.63/1.99 ( X, Z ), Y ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.63/1.99 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.63/1.99 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/1.99 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.63/1.99 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.63/1.99 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.63/1.99 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/1.99 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.63/1.99 tc_Nat_Onat ) ) = Y }.
% 1.63/1.99 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.63/1.99 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/1.99 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/1.99 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.63/1.99 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.63/1.99 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/1.99 tc_Nat_Onat ), X ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.63/1.99 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/1.99 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/2.00 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.63/2.00 .
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.63/2.00 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.63/2.00 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.63/2.00 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.63/2.00 .
% 1.63/2.00 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.63/2.00 .
% 1.63/2.00 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.63/2.00 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.63/2.00 X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.63/2.00 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.63/2.00 }.
% 1.63/2.00 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.63/2.00 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.63/2.00 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.63/2.00 , X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.63/2.00 .
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.63/2.00 .
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.63/2.00 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.63/2.00 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.63/2.00 .
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.63/2.00 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.63/2.00 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.63/2.00 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.63/2.00 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.63/2.00 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.63/2.00 ( X ) }.
% 1.63/2.00 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.63/2.00 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 1.63/2.00 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 1.63/2.00 , Y ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Nat_Onat, Z, Y ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.63/2.00 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.00 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.63/2.00 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( X ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.63/2.00 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.63/2.00 .
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.63/2.00 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.63/2.00 .
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.63/2.00 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( X ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.63/2.00 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( X ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.63/2.00 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.00 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha6( X, Y, Z, T ),
% 1.63/2.00 alpha18( X, Y, Z, T ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z, T ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z, T ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/2.00 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.00 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.63/2.00 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha18( X, Y, Z, T ) }.
% 1.63/2.00 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.63/2.00 { ! alpha6( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.63/2.00 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha6( X, Y, Z, T ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha7( X, Y, Z, T ),
% 1.63/2.00 alpha19( X, Y, Z, T ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z, T ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z, T ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.00 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.63/2.00 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha19( X, Y, Z, T ) }.
% 1.63/2.00 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.63/2.00 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.63/2.00 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha7( X, Y, Z, T ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.00 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.63/2.00 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.63/2.00 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.00 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.63/2.00 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.00 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.63/2.00 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.63/2.00 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.63/2.00 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.00 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.63/2.00 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.00 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.00 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.63/2.00 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.63/2.00 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.00 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.63/2.00 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.63/2.00 ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.63/2.00 ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.63/2.00 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.63/2.00 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.63/2.00 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.63/2.00 , Y, T ) ) }.
% 1.63/2.00 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.63/2.00 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.63/2.00 .
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.63/2.00 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.63/2.00 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.63/2.00 , Y ) }.
% 1.63/2.00 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.63/2.00 , Y ) }.
% 1.63/2.00 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.63/2.00 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.63/2.00 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.63/2.00 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.00 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.00 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.63/2.00 .
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.63/2.00 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.63/2.00 ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X = c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/2.00 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.63/2.00 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.63/2.00 X ) ) }.
% 1.63/2.00 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha8( X, Y ) }.
% 1.63/2.00 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.63/2.00 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.63/2.00 c_Nat_OSuc( X ) ) }.
% 1.63/2.00 { ! alpha8( X, Y ), Y = c_Nat_OSuc( skol8( Z, Y ) ) }.
% 1.63/2.00 { ! alpha8( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol8( X, Y
% 1.63/2.00 ), X ) }.
% 1.63/2.00 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.63/2.00 ), alpha8( X, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/2.00 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol9( X ) ) }.
% 1.63/2.00 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Nat_Onat, Y, X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Nat_Onat, Y, X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) ) }.
% 1.63/2.00 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.63/2.00 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.63/2.00 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.63/2.00 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ) ) = Z }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.63/2.00 .
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.63/2.00 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.63/2.00 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.63/2.00 Y ), X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), Z ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.63/2.00 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.63/2.00 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.63/2.00 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.63/2.00 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.63/2.00 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.63/2.00 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.63/2.00 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.63/2.00 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.63/2.00 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.00 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.63/2.00 tc_Nat_Onat ), X ), Y ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.63/2.00 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.63/2.00 ), Y ) ) }.
% 1.63/2.00 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.63/2.00 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 1.63/2.00 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.63/2.00 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.63/2.00 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.63/2.00 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.63/2.00 ), X ) ) }.
% 1.63/2.00 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.63/2.00 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 1.63/2.00 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.63/2.00 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.63/2.00 ) ) }.
% 1.63/2.00 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.63/2.00 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.63/2.00 c_Polynomial_Odegree( X, Y ) ), ! c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Polynomial_Opoly( X ), Y, Z ), Z = Y }.
% 1.63/2.00 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.00 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.63/2.00 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.63/2.00 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.00 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.63/2.00 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.63/2.00 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.00 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.63/2.00 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.63/2.00 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 1.63/2.00 .
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.63/2.00 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.63/2.00 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.63/2.00 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.63/2.00 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.63/2.00 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.63/2.00 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.63/2.00 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.63/2.00 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.63/2.00 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/2.00 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.63/2.00 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.63/2.00 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.63/2.00 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.63/2.00 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.63/2.00 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.63/2.00 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.63/2.00 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.63/2.00 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.63/2.00 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/2.00 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.63/2.00 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.63/2.00 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.00 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.63/2.00 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.63/2.00 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.00 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/2.00 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.63/2.00 ) ) }.
% 1.63/2.00 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.63/2.00 ) ) }.
% 1.63/2.00 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/2.00 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.63/2.00 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.63/2.00 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.63/2.00 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.00 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.63/2.00 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.63/2.00 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.00 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.00 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.63/2.00 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.63/2.00 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.63/2.00 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/2.00 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.63/2.00 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.63/2.00 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 1.63/2.00 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.63/2.00 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.63/2.00 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.63/2.00 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.63/2.00 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.00 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.63/2.00 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.63/2.00 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.63/2.00 ) }.
% 1.63/2.00 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.63/2.00 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.63/2.00 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.63/2.00 ) }.
% 1.63/2.00 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.63/2.00 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.63/2.00 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.00 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.63/2.00 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.63/2.00 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/2.00 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.63/2.00 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.63/2.00 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.63/2.00 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.63/2.00 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.63/2.00 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.63/2.00 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.63/2.00 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.63/2.00 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.63/2.00 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.63/2.00 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.63/2.00 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.63/2.00 c_Groups_Oone__class_Oone( X ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.63/2.00 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Nat_Onat, Y, Z ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, Z, Y ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.63/2.00 , Z ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.63/2.00 Z, Y ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.63/2.00 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Nat_Onat, Y, Z ) }.
% 1.63/2.00 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, Z, Y ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Nat_Onat, Y, Z ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.63/2.00 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.63/2.00 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.63/2.00 { ! alpha9( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! alpha9( X, Y ), ! Y = X }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha9( X, Y ) }
% 1.63/2.00 .
% 1.63/2.00 { ! alpha9( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! alpha9( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), alpha9( X, Y ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha10( X, Y ), Y = X }
% 1.63/2.00 .
% 1.63/2.00 { ! alpha10( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! alpha10( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! alpha10( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Nat_Onat, X, Y ), alpha10( X, Y ) }.
% 1.63/2.00 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.63/2.00 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.63/2.00 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.63/2.00 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.63/2.00 { alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.63/2.00 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.63/2.00 { alpha23( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.63/2.00 ( X, Y ), Z ) ) }.
% 1.63/2.00 { ! alpha23( X, Y, Z ), alpha25( X, Y, Z ), Z = Y }.
% 1.63/2.00 { ! alpha23( X, Y, Z ), alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.63/2.00 ) ) }.
% 1.63/2.00 { ! alpha25( X, Y, Z ), alpha23( X, Y, Z ) }.
% 1.63/2.00 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha23( X, Y, Z ) }.
% 1.63/2.00 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.63/2.00 }.
% 1.63/2.00 { ! alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.63/2.00 X, Y ), Z ) ), alpha25( X, Y, Z ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.63/2.00 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.63/2.00 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.63/2.00 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.63/2.00 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.63/2.00 ), X ) ) }.
% 1.63/2.00 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.63/2.00 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.63/2.00 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.63/2.00 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/2.00 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.63/2.00 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/2.00 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/2.00 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.63/2.00 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.63/2.00 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.63/2.00 ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.63/2.00 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( X ) }.
% 1.63/2.00 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.63/2.00 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.63/2.00 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.63/2.00 = c_Groups_Oone__class_Oone( X ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/2.00 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.63/2.00 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.63/2.00 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Nat_Onat ) ) = Y }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/2.00 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.63/2.00 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.63/2.00 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.63/2.00 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.63/2.00 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.63/2.00 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.63/2.00 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.63/2.00 .
% 1.63/2.00 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.63/2.00 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.63/2.00 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ) }.
% 1.63/2.00 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.63/2.00 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.63/2.00 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.63/2.00 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.63/2.00 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.63/2.00 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.63/2.00 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.63/2.00 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.63/2.00 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.00 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.00 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.63/2.00 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.63/2.00 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.63/2.00 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.63/2.00 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.63/2.00 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.63/2.00 c_Groups_Oone__class_Oone( X ) }.
% 1.63/2.00 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.63/2.00 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.63/2.00 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.63/2.00 ), T ), U ), Y ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/2.00 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.63/2.00 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 1.63/2.00 .
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.63/2.00 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 1.63/2.00 .
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.63/2.00 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/2.00 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.63/2.00 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.63/2.00 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/2.00 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.63/2.00 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 X ), Y ), Z = Y }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.63/2.00 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.63/2.00 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.63/2.00 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.63/2.00 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.63/2.00 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.63/2.00 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.63/2.00 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.63/2.00 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.63/2.00 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.63/2.00 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.63/2.00 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.63/2.00 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.00 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.63/2.00 ( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.63/2.00 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.63/2.00 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.00 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.63/2.00 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.63/2.00 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.63/2.00 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.63/2.00 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.63/2.00 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.63/2.00 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), Z =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Int_Oint, Y, X ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, U, T ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.63/2.00 , Z ), X ) ), T ) ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, U, T ) ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.63/2.00 , Z ), X ) ) ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) }.
% 1.63/2.00 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X
% 1.63/2.00 ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y
% 1.63/2.00 ) ) }.
% 1.63/2.00 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.63/2.00 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.63/2.00 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.63/2.00 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.63/2.00 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.63/2.00 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.63/2.00 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.63/2.00 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.63/2.00 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.63/2.00 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.63/2.00 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.63/2.00 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.63/2.00 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.63/2.00 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.63/2.00 ) ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ), Y =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Int_Oint, Z, X ) }.
% 1.63/2.00 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.63/2.00 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Int_Oint, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z )
% 1.63/2.00 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X )
% 1.63/2.00 ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.63/2.00 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), Y ) }.
% 1.63/2.00 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.63/2.00 ), X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.63/2.00 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Nat_Onat ) ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ), Y =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Nat_Onat, Z, X ) }.
% 1.63/2.00 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.63/2.00 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z )
% 1.63/2.00 , X ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X )
% 1.63/2.00 ) }.
% 1.63/2.00 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Nat_Onat ), X ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.63/2.00 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.63/2.00 }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.63/2.00 , alpha21( X, Y, Z, T ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha21( X, Y, Z, T ),
% 1.63/2.00 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.63/2.00 { ! alpha21( X, Y, Z, T ), alpha11( X, Z, T ) }.
% 1.63/2.00 { ! alpha21( X, Y, Z, T ), alpha20( X, Y, T ) }.
% 1.63/2.00 { ! alpha11( X, Z, T ), ! alpha20( X, Y, T ), alpha21( X, Y, Z, T ) }.
% 1.63/2.00 { ! alpha20( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), alpha22( X, Y, Z ) }.
% 1.63/2.00 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha20( X
% 1.63/2.00 , Y, Z ) }.
% 1.63/2.00 { ! alpha22( X, Y, Z ), alpha20( X, Y, Z ) }.
% 1.63/2.00 { ! alpha22( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.00 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.63/2.00 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha22( X
% 1.63/2.00 , Y, Z ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.63/2.00 ), c_Polynomial_Odegree( X, Z ) ), alpha22( X, Y, Z ) }.
% 1.63/2.00 { ! alpha11( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X,
% 1.63/2.00 Y, Z ) }.
% 1.63/2.00 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X
% 1.63/2.00 , Y, Z ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.63/2.00 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.63/2.00 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.63/2.00 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.63/2.00 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.63/2.00 alpha12( X, Y, Z ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.63/2.00 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), ! alpha12( X, Y, Z ),
% 1.63/2.00 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.63/2.00 { ! alpha12( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.63/2.00 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.63/2.00 alpha12( X, Y, Z ) }.
% 1.63/2.00 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.63/2.00 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.63/2.00 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.63/2.00 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.63/2.00 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.63/2.00 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.63/2.00 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.63/2.00 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.63/2.00 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.63/2.00 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.63/2.00 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.63/2.00 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.63/2.00 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.63/2.00 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.63/2.00 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Int_Oint ) ) = X }.
% 1.63/2.00 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Int_Oint ), X ) = X }.
% 1.63/2.00 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.63/2.00 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.63/2.00 ( tc_Int_Oint ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.63/2.00 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 1.63/2.00 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.63/2.00 .
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.63/2.00 .
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.63/2.00 .
% 1.63/2.00 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.63/2.00 ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y,
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.63/2.00 ( tc_Int_Oint, Y ), X ), c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ) }
% 1.63/2.00 .
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.63/2.00 ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Int_Oint, X, Y ), ! c_Rings_Odvd__class_Odvd
% 1.63/2.00 ( tc_Int_Oint, Y, X ), X = Y }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Int_Oint ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.63/2.00 }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Int_Oint ) ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.63/2.00 }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Int_Oint ) ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Int_Oint ) ), X ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.63/2.00 = X }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Int_Oint ) ) ) }.
% 1.63/2.00 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Int_Oint ) ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.63/2.00 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.63/2.00 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.63/2.00 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.63/2.00 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.63/2.00 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.63/2.00 .
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.63/2.00 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.63/2.00 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.63/2.00 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 1.63/2.00 ) }.
% 1.63/2.00 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.63/2.00 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.63/2.00 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.63/2.00 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.63/2.00 ( tc_Int_Oint ), Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.63/2.00 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.63/2.00 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.63/2.00 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.63/2.00 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.63/2.00 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.63/2.00 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.63/2.00 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.63/2.00 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.63/2.00 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.63/2.00 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.63/2.00 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.63/2.00 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.63/2.00 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.63/2.00 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.63/2.00 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.63/2.00 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Int_Oint ) ) }.
% 1.63/2.00 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.63/2.00 tc_Int_Oint ) ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.63/2.00 tc_Int_Oint, X, Y ) ) }.
% 1.63/2.00 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.63/2.00 , skol11( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.00 c_Polynomial_Odegree( X, Y ), Z ) }.
% 1.63/2.00 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol11( X
% 1.63/2.00 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.63/2.00 Y ), Z ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.63/2.00 }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.63/2.00 .
% 1.63/2.00 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.63/2.00 .
% 1.63/2.00 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.63/2.00 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Z ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.63/2.00 ( X ), c_Polynomial_Opoly__gcd( X, Z, Y ), Y ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.63/2.00 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 1.63/2.00 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), T, Y ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Polynomial_Opoly( X ), T, Z ), ! c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Polynomial_Opoly( X ), T, Y ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Polynomial_Opoly( X ), T, c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Polynomial_Opoly( X ), Z, Y ), ! c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Polynomial_Opoly( X ), Z, T ), c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Opoly__gcd( X, Y, T ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Polynomial_Opoly( X ), Z, Y ), alpha26( X, Y, Z, T ), ! Y =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.63/2.00 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 1.63/2.00 { ! class_Fields_Ofield( X ), ! c_Rings_Odvd__class_Odvd(
% 1.63/2.00 tc_Polynomial_Opoly( X ), Z, Y ), alpha26( X, Y, Z, T ), ! hAPP(
% 1.63/2.00 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.63/2.00 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 1.63/2.00 .
% 1.63/2.00 { ! alpha26( X, Y, Z, T ), alpha27( X, Y, Z, T ), alpha24( X, Y, T ) }.
% 1.63/2.00 { ! alpha26( X, Y, Z, T ), alpha27( X, Y, Z, T ), ! hAPP(
% 1.63/2.00 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.00 { ! alpha27( X, Y, Z, T ), alpha26( X, Y, Z, T ) }.
% 1.63/2.00 { ! alpha24( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.63/2.00 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.00 alpha26( X, Y, Z, T ) }.
% 1.63/2.00 { ! alpha27( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.63/2.00 ( X ), Z, T ), alpha28( X, Y, Z, T ) }.
% 1.63/2.00 { c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, T ), alpha27( X, Y
% 1.63/2.00 , Z, T ) }.
% 1.63/2.00 { ! alpha28( X, Y, Z, T ), alpha27( X, Y, Z, T ) }.
% 1.63/2.00 { ! alpha28( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.63/2.00 ), skol12( X, Y, U, W ), Y ) }.
% 1.63/2.00 { ! alpha28( X, Y, Z, T ), c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.63/2.00 ), skol12( X, Y, U, T ), T ) }.
% 1.63/2.00 { ! alpha28( X, Y, Z, T ), ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly
% 1.63/2.00 ( X ), skol12( X, Y, Z, T ), Z ) }.
% 1.63/2.00 { ! c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Y ), !
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, T ),
% 1.63/2.00 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), U, Z ), alpha28( X, Y
% 1.63/2.00 , Z, T ) }.
% 1.63/2.00 { ! alpha24( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! alpha24( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.63/2.00 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.00 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha24( X, Y, Z
% 1.63/2.00 ) }.
% 1.63/2.00 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.00 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol13( Z, Y ) ) ), !
% 1.63/2.00 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.00 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.63/2.01 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 1.63/2.01 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 1.63/2.01 tc_Int_Oint, skol13( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.63/2.01 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.63/2.01 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 1.63/2.01 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 1.63/2.01 ) ) }.
% 1.63/2.01 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.63/2.01 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol14( Z, Y
% 1.63/2.01 ), Y ) }.
% 1.63/2.01 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.63/2.01 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.63/2.01 skol14( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.63/2.01 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.63/2.01 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.63/2.01 , skol14( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.63/2.01 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 1.63/2.01 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 1.63/2.01 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 1.63/2.01 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 1.63/2.01 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.63/2.01 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.63/2.01 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.63/2.01 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.63/2.01 ) ), Z ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.63/2.01 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 1.63/2.01 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.63/2.01 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.63/2.01 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 1.63/2.01 X, Y ) ) = Y }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.63/2.01 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( X ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.63/2.01 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.63/2.01 = Y }.
% 1.63/2.01 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 1.63/2.01 , Y ) ) = Y }.
% 1.63/2.01 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.63/2.01 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.63/2.01 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.63/2.01 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.63/2.01 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 1.63/2.01 ) ), Y ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.63/2.01 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 1.63/2.01 ) }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.63/2.01 c_Groups_Oone__class_Oone( X ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.63/2.01 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 1.63/2.01 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.63/2.01 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.63/2.01 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.63/2.01 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 1.63/2.01 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.63/2.01 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.63/2.01 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.01 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.63/2.01 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.63/2.01 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 1.63/2.01 , Y = c_Groups_Oone__class_Oone( X ) }.
% 1.63/2.01 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.63/2.01 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 1.63/2.01 = c_Groups_Oone__class_Oone( X ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.63/2.01 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.63/2.01 ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/2.01 ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.63/2.01 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.63/2.01 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.63/2.01 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.63/2.01 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.63/2.01 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.63/2.01 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.63/2.01 , Y ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.63/2.01 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.63/2.01 .
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( X ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.63/2.01 .
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.63/2.01 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.63/2.01 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.63/2.01 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.63/2.01 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.63/2.01 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.63/2.01 , Y ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 1.63/2.01 ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.63/2.01 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 1.63/2.01 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.63/2.01 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.63/2.01 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.63/2.01 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.01 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.63/2.01 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.63/2.01 ) ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.63/2.01 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.63/2.01 c_Groups_Oone__class_Oone( X ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.63/2.01 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.63/2.01 }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.63/2.01 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 1.63/2.01 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.63/2.01 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 1.63/2.01 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 1.63/2.01 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 1.63/2.01 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.01 skol15( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, skol15( X, T, U ),
% 1.63/2.01 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.63/2.01 , Y ) }.
% 1.63/2.01 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), skol15( X, Y, Z ) ), Z ), Y ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 1.63/2.01 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 1.63/2.01 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.63/2.01 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 1.63/2.01 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.63/2.01 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 1.63/2.01 ( X ), Z, Y ) ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Polynomial_Opoly( X ), Z, c_Groups_Ouminus__class_Ouminus(
% 1.63/2.01 tc_Polynomial_Opoly( X ), Y ) ) = c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 1.63/2.01 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.63/2.01 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.63/2.01 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.63/2.01 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.63/2.01 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 1.63/2.01 , Y ) ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.63/2.01 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.63/2.01 ), Z ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.63/2.01 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 1.63/2.01 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.63/2.01 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.63/2.01 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 1.63/2.01 X, Z, Y ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.63/2.01 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 1.63/2.01 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.63/2.01 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 1.63/2.01 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.63/2.01 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 1.63/2.01 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.63/2.01 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 1.63/2.01 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 1.63/2.01 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.63/2.01 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.63/2.01 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 1.63/2.01 X ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 1.63/2.01 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.63/2.01 ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.63/2.01 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 1.63/2.01 X ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 1.63/2.01 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 1.63/2.01 ( X, Z, Y ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 1.63/2.01 ( X, Y, Z ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.63/2.01 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 1.63/2.01 , Y ) ), Y ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.63/2.01 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.63/2.01 ), Z ), Y ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.63/2.01 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.63/2.01 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 1.63/2.01 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.63/2.01 T, Z ), Y ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 1.63/2.01 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.63/2.01 T, Y ), Z ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.63/2.01 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.63/2.01 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 1.63/2.01 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 1.63/2.01 ), Z ) }.
% 1.63/2.01 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.63/2.01 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 1.63/2.01 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.63/2.01 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.63/2.01 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 1.63/2.01 , Y ) ), Y ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.63/2.01 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.01 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.63/2.01 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.63/2.01 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.01 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 1.63/2.01 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 1.63/2.01 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.01 Z, c_Polynomial_Odegree( X, Y ) ), c_Orderings_Oord__class_Oless(
% 1.63/2.01 tc_Nat_Onat, Z, skol16( T, U, Z ) ) }.
% 1.63/2.01 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.01 Z, c_Polynomial_Odegree( X, Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.63/2.01 skol16( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.01 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.63/2.01 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.63/2.01 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/2.01 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.63/2.01 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.63/2.01 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.01 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 1.63/2.01 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 1.63/2.01 }.
% 1.63/2.01 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.63/2.01 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 1.63/2.01 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.63/2.01 tc_Nat_Onat, X, Y ), Y ) }.
% 1.63/2.01 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.63/2.01 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 1.63/2.01 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 1.63/2.01 Y ) ), Y ) }.
% 1.63/2.01 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.63/2.01 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 1.63/2.01 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 1.63/2.01 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 1.63/2.01 , U ), Z ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) }.
% 1.63/2.01 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.63/2.01 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.63/2.01 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 1.63/2.01 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 1.63/2.01 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.63/2.01 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.63/2.01 tc_Nat_Onat, Y, X ), X ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.63/2.01 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.63/2.01 tc_Nat_Onat, Y, X ), X ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.63/2.01 ( tc_Int_Oint, Y, X ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/2.01 { ! c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/2.01 { c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) = X,
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.63/2.01 c_Nat_OSuc( c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.63/2.01 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 1.63/2.01 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.63/2.01 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 1.63/2.01 ( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ), X ) ) }
% 1.63/2.01 .
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.63/2.01 ( tc_Int_Oint, Y ), c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.63/2.01 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Divides_Odiv__class_Omod
% 1.63/2.01 ( tc_Int_Oint, Y, X ) ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.63/2.01 ( tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.63/2.01 ( tc_Int_Oint, Y ), X ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Int_Oint, Y,
% 1.63/2.01 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! c_Divides_Odiv__class_Omod
% 1.63/2.01 ( tc_Int_Oint, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.63/2.01 ( tc_Int_Oint, Y ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), !
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Int_Oint, X, Y ) ) }.
% 1.63/2.01 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol17( X, Y ) ) }.
% 1.63/2.01 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 1.63/2.01 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.01 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 1.63/2.01 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 1.63/2.01 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol18( X, Y ) ) }.
% 1.63/2.01 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 1.63/2.01 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/2.01 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.63/2.01 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.63/2.01 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.63/2.01 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/2.01 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.63/2.01 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.63/2.01 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.63/2.01 ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.63/2.01 ) }.
% 1.63/2.01 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y )
% 1.63/2.01 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.63/2.01 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ) }.
% 1.63/2.01 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X )
% 1.63/2.01 , ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ),
% 1.63/2.01 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.01 tc_Nat_Onat, Z, Y ), X ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.01 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.01 tc_Nat_Onat, Z, X ), Y ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.63/2.01 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.01 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.63/2.01 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.01 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.63/2.01 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.63/2.01 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.63/2.01 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.63/2.01 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.63/2.01 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.63/2.01 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.63/2.01 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.63/2.01 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/2.01 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.63/2.01 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.63/2.01 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.63/2.01 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/2.01 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.63/2.01 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.63/2.01 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 1.63/2.01 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.63/2.01 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.63/2.01 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.63/2.01 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.63/2.01 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.63/2.01 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.63/2.01 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.63/2.01 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.63/2.01 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.63/2.01 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.63/2.01 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.63/2.01 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 1.63/2.01 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 1.63/2.01 hAPP( Z, Y ) ) }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.63/2.01 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.63/2.01 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.01 tc_Nat_Onat, Z, X ), Y ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.63/2.01 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.63/2.01 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.63/2.01 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/2.01 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.01 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.63/2.01 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.63/2.01 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.63/2.01 ) }.
% 1.63/2.01 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.63/2.01 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.63/2.01 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.63/2.01 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.63/2.01 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.01 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.01 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.63/2.01 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.01 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.63/2.01 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.63/2.01 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.63/2.01 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.63/2.01 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.63/2.01 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.63/2.01 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.63/2.01 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.63/2.01 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.01 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.63/2.01 ) }.
% 1.63/2.01 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.63/2.01 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.63/2.01 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.63/2.01 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.63/2.01 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.63/2.01 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.63/2.01 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.63/2.01 X, Y ) ) }.
% 1.63/2.01 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.63/2.01 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.63/2.01 , Y ) ) }.
% 1.63/2.01 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.63/2.01 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.63/2.01 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.63/2.01 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.63/2.01 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.63/2.01 X, Z, Y ) }.
% 1.63/2.01 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.63/2.01 X, Y ) }.
% 1.63/2.01 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.63/2.01 W ) ), U ), Y ) }.
% 1.63/2.01 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.63/2.01 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.63/2.01 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), Z ), U ), Y ) }.
% 1.63/2.01 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.63/2.01 Z ) ), U ), T ) = Y }.
% 1.63/2.01 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.63/2.01 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), Z ), U ), Y ) }.
% 1.63/2.01 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.63/2.01 Z ) ), Y ) ) }.
% 1.63/2.01 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.63/2.01 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.63/2.01 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.63/2.01 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.63/2.01 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.63/2.01 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( X ) ) }.
% 1.63/2.01 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.63/2.01 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.63/2.01 , Z, Y ) }.
% 1.63/2.01 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/2.01 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.63/2.01 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/2.01 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.63/2.01 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.63/2.01 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/2.01 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.63/2.01 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.63/2.01 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.63/2.01 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.63/2.01 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.63/2.01 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.63/2.01 ( X, Z, W ) ), U ), Y ) ) }.
% 1.63/2.01 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.63/2.01 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.63/2.01 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.63/2.01 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.63/2.01 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.63/2.01 X, W, Z ) ), U ), T ), Y ) }.
% 1.63/2.01 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.63/2.01 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.63/2.01 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.63/2.01 ( X ), Z ), U ), Y ) ) }.
% 1.63/2.01 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.63/2.01 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.63/2.01 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.63/2.01 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.63/2.01 .
% 1.63/2.01 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.63/2.01 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.63/2.01 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.63/2.01 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.63/2.01 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.63/2.01 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.63/2.01 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.63/2.01 }.
% 1.63/2.01 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.63/2.01 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.63/2.01 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.63/2.01 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.63/2.01 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.63/2.01 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.63/2.01 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.63/2.01 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.63/2.01 }.
% 1.63/2.01 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.63/2.01 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.63/2.01 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.63/2.01 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 1.63/2.01 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.63/2.01 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc(
% 1.63/2.01 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.63/2.01 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) ), Y ) =
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Int_Oint, Y, X ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.63/2.01 tc_Int_Oint, Y, X ) ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.63/2.01 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.63/2.01 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 1.63/2.01 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.63/2.01 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.63/2.01 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 1.63/2.01 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.63/2.01 ( X ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__add(
% 1.63/2.01 X ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ocomm__monoid__add( X
% 1.63/2.01 ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring( X ) }
% 1.63/2.01 .
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Omonoid__add( X ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0( X ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero( X ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring( X ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ozero( X ) }.
% 1.63/2.01 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.63/2.01 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { class_Enum_Oenum( tc_HOL_Obool ) }.
% 1.63/2.01 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.63/2.01 { ! class_Enum_Oenum( Y ), ! class_Enum_Oenum( X ), class_Enum_Oenum(
% 1.63/2.01 tc_fun( Y, X ) ) }.
% 1.63/2.01 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.63/2.01 ( tc_fun( Y, X ) ) }.
% 1.63/2.01 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.63/2.01 ) ) }.
% 1.63/2.01 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.63/2.01 .
% 1.63/2.01 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.63/2.01 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.63/2.01 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.63/2.01 { ! class_Enum_Oenum( Y ), ! class_HOL_Oequal( X ), class_HOL_Oequal(
% 1.63/2.01 tc_fun( Y, X ) ) }.
% 1.63/2.01 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.63/2.01 tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.63/2.01 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.63/2.01 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.63/2.01 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.63/2.01 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.63/2.01 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.63/2.01 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.63/2.01 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.63/2.01 { class_Power_Opower( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.63/2.01 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.63/2.01 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.63/2.01 { class_HOL_Oequal( tc_Int_Oint ) }.
% 1.63/2.01 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.63/2.01 tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.63/2.01 { class_HOL_Oequal( tc_Nat_Onat ) }.
% 1.63/2.01 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.63/2.01 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.63/2.01 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.63/2.01 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.63/2.01 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.63/2.01 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.63/2.01 { class_HOL_Oequal( tc_HOL_Obool ) }.
% 1.63/2.01 { ! class_Rings_Oidom( X ),
% 1.63/2.01 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.63/2.01 ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.63/2.01 X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.63/2.01 ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.63/2.01 }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.63/2.01 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ),
% 1.63/2.01 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.63/2.01 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.63/2.01 ( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.63/2.01 ( tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.63/2.01 ( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.63/2.01 }.
% 1.63/2.01 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.63/2.01 ) ) }.
% 1.63/2.01 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.63/2.01 .
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! class_Groups_Ozero( X ), ! class_HOL_Oequal( X ), class_HOL_Oequal(
% 1.63/2.01 tc_Polynomial_Opoly( X ) ) }.
% 1.63/2.01 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.63/2.01 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.63/2.01 { ! hBOOL( c_fFalse ) }.
% 1.63/2.01 { hBOOL( c_fTrue ) }.
% 1.63/2.01 { c_Polynomial_Odegree( t_a,
% 1.63/2.01 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a, v_p, v_h )
% 1.63/2.01 ) = c_Polynomial_Odegree( t_a, v_p ) }.
% 1.63/2.01 { ! c_Polynomial_Odegree( t_a,
% 1.63/2.01 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a,
% 1.63/2.01 c_Polynomial_OpCons( t_a, v_a, v_p ), v_h ) ) = c_Polynomial_Odegree( t_a
% 1.63/2.01 , c_Polynomial_OpCons( t_a, v_a, v_p ) ) }.
% 1.63/2.01 { class_Rings_Ocomm__semiring__0( t_a ) }.
% 1.63/2.01
% 1.63/2.01 *** allocated 15000 integers for clauses
% 1.63/2.01 *** allocated 22500 integers for clauses
% 1.63/2.01 *** allocated 33750 integers for clauses
% 1.63/2.01 *** allocated 50625 integers for clauses
% 1.63/2.01 *** allocated 75937 integers for clauses
% 1.63/2.01 percentage equality = 0.269403, percentage horn = 0.906140
% 1.63/2.01 This is a problem with some equality
% 1.63/2.01
% 1.63/2.01
% 1.63/2.01
% 1.63/2.01 Options Used:
% 1.63/2.01
% 1.63/2.01 useres = 1
% 1.63/2.01 useparamod = 1
% 1.63/2.01 useeqrefl = 1
% 1.63/2.01 useeqfact = 1
% 1.63/2.01 usefactor = 1
% 1.63/2.01 usesimpsplitting = 0
% 1.63/2.01 usesimpdemod = 5
% 1.63/2.01 usesimpres = 3
% 1.63/2.01
% 1.63/2.01 resimpinuse = 1000
% 1.63/2.01 resimpclauses = 20000
% 1.63/2.01 substype = eqrewr
% 1.63/2.01 backwardsubs = 1
% 1.63/2.01 selectoldest = 5
% 1.63/2.01
% 1.63/2.01 litorderings [0] = split
% 1.63/2.01 litorderings [1] = extend the termordering, first sorting on arguments
% 1.63/2.01
% 1.63/2.01 termordering = kbo
% 1.63/2.01
% 1.63/2.01 litapriori = 0
% 1.63/2.01 termapriori = 1
% 1.63/2.01 litaposteriori = 0
% 1.63/2.01 termaposteriori = 0
% 1.63/2.01 demodaposteriori = 0
% 1.63/2.01 ordereqreflfact = 0
% 1.63/2.01
% 1.63/2.01 litselect = negord
% 1.63/2.01
% 1.63/2.01 maxweight = 15
% 1.63/2.01 maxdepth = 30000
% 1.63/2.01 maxlength = 115
% 1.63/2.01 maxnrvars = 195
% 1.63/2.01 excuselevel = 1
% 1.63/2.01 increasemaxweight = 1
% 1.63/2.01
% 1.63/2.01 maxselected = 10000000
% 1.63/2.01 maxnrclauses = 10000000
% 1.63/2.01
% 1.63/2.01 showgenerated = 0
% 1.63/2.01 showkept = 0
% 1.63/2.01 showselected = 0
% 1.63/2.01 showdeleted = 0
% 1.63/2.01 showresimp = 1
% 1.63/2.02 showstatus = 2000
% 1.63/2.02
% 1.63/2.02 prologoutput = 0
% 1.63/2.02 nrgoals = 5000000
% 1.63/2.02 totalproof = 1
% 1.63/2.02
% 1.63/2.02 Symbols occurring in the translation:
% 1.63/2.02
% 1.63/2.02 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.63/2.02 . [1, 2] (w:1, o:192, a:1, s:1, b:0),
% 1.63/2.02 ! [4, 1] (w:0, o:107, a:1, s:1, b:0),
% 1.63/2.02 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.63/2.02 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.63/2.02 hAPP [38, 2] (w:1, o:216, a:1, s:1, b:0),
% 1.63/2.02 class_Groups_Ozero [44, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.63/2.02 c_Polynomial_OpCons [45, 3] (w:1, o:247, a:1, s:1, b:0),
% 1.63/2.02 class_Rings_Ocomm__semiring__0 [49, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.63/2.02 tc_Polynomial_Opoly [50, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.63/2.02 c_Groups_Ozero__class_Ozero [51, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.63/2.02 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [52, 3] (w:1
% 1.63/2.02 , o:248, a:1, s:1, b:0),
% 1.63/2.02 c_Polynomial_Osmult [55, 3] (w:1, o:249, a:1, s:1, b:0),
% 1.63/2.02 c_Groups_Oplus__class_Oplus [56, 3] (w:1, o:250, a:1, s:1, b:0),
% 1.63/2.02 c_Polynomial_Odegree [57, 2] (w:1, o:218, a:1, s:1, b:0),
% 1.63/2.02 tc_Nat_Onat [58, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.63/2.02 c_Nat_OSuc [61, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.63/2.02 c_Orderings_Oord__class_Oless__eq [62, 3] (w:1, o:244, a:1, s:1, b:0)
% 1.63/2.02 ,
% 1.63/2.02 c_Polynomial_Opoly [64, 2] (w:1, o:219, a:1, s:1, b:0),
% 1.63/2.02 class_Groups_Oab__group__add [65, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.63/2.02 c_Groups_Ouminus__class_Ouminus [66, 2] (w:1, o:220, a:1, s:1, b:0),
% 1.63/2.02
% 1.63/2.02 class_HOL_Oequal [67, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.63/2.02 c_HOL_Oequal__class_Oequal [68, 3] (w:1, o:252, a:1, s:1, b:0),
% 1.63/2.02 class_Rings_Oidom [69, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.63/2.02 class_Groups_Ocomm__monoid__add [71, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.63/2.02
% 1.63/2.02 class_Rings_Ocomm__ring [72, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.63/2.02 class_Int_Oring__char__0 [73, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.63/2.02 class_Groups_Ogroup__add [77, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.63/2.02 class_Groups_Oordered__ab__group__add [80, 1] (w:1, o:128, a:1, s:1
% 1.63/2.02 , b:0),
% 1.63/2.02 class_Groups_Olinordered__ab__group__add [81, 1] (w:1, o:129, a:1, s:
% 1.63/2.02 1, b:0),
% 1.63/2.02 class_Groups_Ocancel__semigroup__add [82, 1] (w:1, o:130, a:1, s:1
% 1.63/2.02 , b:0),
% 1.63/2.02 class_Groups_Ocancel__ab__semigroup__add [83, 1] (w:1, o:131, a:1, s:
% 1.63/2.02 1, b:0),
% 1.63/2.02 class_Groups_Oab__semigroup__add [85, 1] (w:1, o:132, a:1, s:1, b:0)
% 1.63/2.02 ,
% 1.63/2.02 class_Groups_Omonoid__add [98, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.63/2.02 class_Groups_Oordered__ab__semigroup__add__imp__le [99, 1] (w:1, o:
% 1.63/2.02 134, a:1, s:1, b:0),
% 1.63/2.02 class_Groups_Oordered__ab__semigroup__add [101, 1] (w:1, o:135, a:1
% 1.63/2.02 , s:1, b:0),
% 1.63/2.02 class_Groups_Oordered__comm__monoid__add [104, 1] (w:1, o:136, a:1
% 1.63/2.02 , s:1, b:0),
% 1.63/2.02 c_Polynomial_Oorder [105, 3] (w:1, o:246, a:1, s:1, b:0),
% 1.63/2.02 class_Orderings_Opreorder [106, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.63/2.02 c_Polynomial_Osynthetic__div [108, 3] (w:1, o:253, a:1, s:1, b:0),
% 1.63/2.02 class_Lattices_Oboolean__algebra [109, 1] (w:1, o:152, a:1, s:1, b:0)
% 1.63/2.02 ,
% 1.63/2.02 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.63/2.02 110, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.63/2.02 class_Rings_Ocomm__semiring__1 [111, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.63/2.02
% 1.63/2.02 class_Orderings_Oord [114, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.63/2.02 tc_fun [115, 2] (w:1, o:232, a:1, s:1, b:0),
% 1.63/2.02 class_Orderings_Olinorder [116, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.63/2.02 class_Orderings_Oorder [117, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.63/2.02 class_Groups_Ouminus [119, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.63/2.02 c_Polynomial_Opoly__rec [123, 5] (w:1, o:289, a:1, s:1, b:0),
% 1.63/2.02 c_Nat_Onat_Onat__size [125, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.63/2.02 c_fequal [126, 2] (w:1, o:233, a:1, s:1, b:0),
% 1.63/2.02 c_If [127, 4] (w:1, o:278, a:1, s:1, b:0),
% 1.63/2.02 c_Groups_Otimes__class_Otimes [128, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.63/2.02 class_Lattices_Oab__semigroup__idem__mult [129, 1] (w:1, o:151, a:1
% 1.63/2.02 , s:1, b:0),
% 1.63/2.02 class_Groups_Oab__semigroup__mult [134, 1] (w:1, o:138, a:1, s:1, b:0
% 1.63/2.02 ),
% 1.63/2.02 class_Rings_Olinordered__ring__strict [137, 1] (w:1, o:154, a:1, s:1
% 1.63/2.02 , b:0),
% 2.06/2.42 class_Rings_Olinordered__ring [138, 1] (w:1, o:155, a:1, s:1, b:0),
% 2.06/2.42 c_Polynomial_Opcompose [139, 3] (w:1, o:254, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Oordered__cancel__semiring [140, 1] (w:1, o:165, a:1, s:1
% 2.06/2.42 , b:0),
% 2.06/2.42 class_Rings_Oordered__ring [141, 1] (w:1, o:166, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Oordered__semiring [142, 1] (w:1, o:167, a:1, s:1, b:0),
% 2.06/2.42
% 2.06/2.42 class_Rings_Oordered__comm__semiring [143, 1] (w:1, o:168, a:1, s:1
% 2.06/2.42 , b:0),
% 2.06/2.42 class_Rings_Ono__zero__divisors [144, 1] (w:1, o:164, a:1, s:1, b:0)
% 2.06/2.42 ,
% 2.06/2.42 class_Rings_Oring__no__zero__divisors [145, 1] (w:1, o:169, a:1, s:1
% 2.06/2.42 , b:0),
% 2.06/2.42 class_Rings_Omult__zero [146, 1] (w:1, o:163, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Osemiring [148, 1] (w:1, o:173, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Ocomm__semiring [149, 1] (w:1, o:174, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Oring [150, 1] (w:1, o:170, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Ocomm__ring__1 [151, 1] (w:1, o:119, a:1, s:1, b:0),
% 2.06/2.42 c_Groups_Oone__class_Oone [152, 1] (w:1, o:185, a:1, s:1, b:0),
% 2.06/2.42 c_Nat_Osize__class_Osize [153, 2] (w:1, o:234, a:1, s:1, b:0),
% 2.06/2.42 class_RealVector_Oreal__normed__algebra [154, 1] (w:1, o:175, a:1, s:
% 2.06/2.42 1, b:0),
% 2.06/2.42 class_Groups_Oone [157, 1] (w:1, o:139, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Ozero__neq__one [158, 1] (w:1, o:176, a:1, s:1, b:0),
% 2.06/2.42 class_Groups_Omonoid__mult [159, 1] (w:1, o:140, a:1, s:1, b:0),
% 2.06/2.42 class_Groups_Ocomm__monoid__mult [160, 1] (w:1, o:141, a:1, s:1, b:0)
% 2.06/2.42 ,
% 2.06/2.42 class_Rings_Olinordered__semidom [161, 1] (w:1, o:156, a:1, s:1, b:0)
% 2.06/2.42 ,
% 2.06/2.42 class_Rings_Oring__1__no__zero__divisors [162, 1] (w:1, o:171, a:1
% 2.06/2.42 , s:1, b:0),
% 2.06/2.42 class_Rings_Olinordered__idom [163, 1] (w:1, o:157, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Olinordered__semiring__1 [166, 1] (w:1, o:158, a:1, s:1
% 2.06/2.42 , b:0),
% 2.06/2.42 c_Rings_Odvd__class_Odvd [169, 3] (w:1, o:255, a:1, s:1, b:0),
% 2.06/2.42 c_fFalse [170, 0] (w:1, o:82, a:1, s:1, b:0),
% 2.06/2.42 c_HOL_Obool_Obool__size [171, 1] (w:1, o:186, a:1, s:1, b:0),
% 2.06/2.42 c_fTrue [172, 0] (w:1, o:83, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Odvd [173, 1] (w:1, o:177, a:1, s:1, b:0),
% 2.06/2.42 class_Fields_Ofield [174, 1] (w:1, o:113, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Osemiring__0 [176, 1] (w:1, o:178, a:1, s:1, b:0),
% 2.06/2.42 hBOOL [177, 1] (w:1, o:187, a:1, s:1, b:0),
% 2.06/2.42 c_Power_Opower__class_Opower [178, 1] (w:1, o:188, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Olinordered__semiring__1__strict [179, 1] (w:1, o:159, a:
% 2.06/2.42 1, s:1, b:0),
% 2.06/2.42 c_Orderings_Oord__class_Oless [180, 3] (w:1, o:245, a:1, s:1, b:0),
% 2.06/2.42 c_Polynomial_Ocoeff [181, 2] (w:1, o:217, a:1, s:1, b:0),
% 2.06/2.42 class_Groups_Oordered__cancel__ab__semigroup__add [182, 1] (w:1, o:
% 2.06/2.42 142, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Olinordered__comm__semiring__strict [183, 1] (w:1, o:160
% 2.06/2.42 , a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Olinordered__semiring__strict [184, 1] (w:1, o:161, a:1
% 2.06/2.42 , s:1, b:0),
% 2.06/2.42 class_Rings_Olinordered__semiring [187, 1] (w:1, o:162, a:1, s:1, b:0
% 2.06/2.42 ),
% 2.06/2.42 tc_Int_Oint [191, 0] (w:1, o:92, a:1, s:1, b:0),
% 2.06/2.42 class_Power_Opower [192, 1] (w:1, o:189, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Oring__1 [193, 1] (w:1, o:172, a:1, s:1, b:0),
% 2.06/2.42 c_Power_Opower_Opower [194, 3] (w:1, o:256, a:1, s:1, b:0),
% 2.06/2.42 c_Polynomial_Opdivmod__rel [203, 5] (w:1, o:290, a:1, s:1, b:0),
% 2.06/2.42 c_Polynomial_Opos__poly [204, 2] (w:1, o:235, a:1, s:1, b:0),
% 2.06/2.42 c_Polynomial_Opoly__gcd [214, 3] (w:1, o:257, a:1, s:1, b:0),
% 2.06/2.42 c_Rings_Oinverse__class_Oinverse [215, 2] (w:1, o:236, a:1, s:1, b:0)
% 2.06/2.42 ,
% 2.06/2.42 class_Rings_Odivision__ring [216, 1] (w:1, o:179, a:1, s:1, b:0),
% 2.06/2.42 class_Rings_Odivision__ring__inverse__zero [217, 1] (w:1, o:180, a:1
% 2.06/2.42 , s:1, b:0),
% 2.06/2.42 class_Fields_Olinordered__field [218, 1] (w:1, o:114, a:1, s:1, b:0)
% 2.06/2.42 ,
% 2.06/2.42 class_Fields_Olinordered__field__inverse__zero [219, 1] (w:1, o:115
% 2.06/2.42 , a:1, s:1, b:0),
% 2.06/2.42 class_Fields_Ofield__inverse__zero [220, 1] (w:1, o:116, a:1, s:1, b:
% 2.06/2.42 0),
% 2.06/2.42 c_Divides_Odiv__class_Omod [221, 3] (w:1, o:258, a:1, s:1, b:0),
% 2.06/2.42 class_Divides_Osemiring__div [223, 1] (w:1, o:191, a:1, s:1, b:0),
% 9.74/10.12 class_Divides_Oring__div [224, 1] (w:1, o:190, a:1, s:1, b:0),
% 9.74/10.12 c_Groups_Ominus__class_Ominus [225, 3] (w:1, o:251, a:1, s:1, b:0),
% 9.74/10.12 class_Groups_Ominus [230, 1] (w:1, o:143, a:1, s:1, b:0),
% 9.74/10.12 class_Groups_Ocancel__comm__monoid__add [235, 1] (w:1, o:144, a:1, s:
% 9.74/10.12 1, b:0),
% 9.74/10.12 tc_HOL_Obool [236, 0] (w:1, o:91, a:1, s:1, b:0),
% 9.74/10.12 class_Enum_Oenum [237, 1] (w:1, o:112, a:1, s:1, b:0),
% 9.74/10.12 t_a [239, 0] (w:1, o:103, a:1, s:1, b:0),
% 9.74/10.12 v_p [240, 0] (w:1, o:104, a:1, s:1, b:0),
% 9.74/10.12 v_h [241, 0] (w:1, o:105, a:1, s:1, b:0),
% 9.74/10.12 v_a [242, 0] (w:1, o:106, a:1, s:1, b:0),
% 9.74/10.12 alpha1 [243, 2] (w:1, o:237, a:1, s:1, b:1),
% 9.74/10.12 alpha2 [244, 2] (w:1, o:241, a:1, s:1, b:1),
% 9.74/10.12 alpha3 [245, 3] (w:1, o:264, a:1, s:1, b:1),
% 9.74/10.12 alpha4 [246, 3] (w:1, o:265, a:1, s:1, b:1),
% 9.74/10.12 alpha5 [247, 3] (w:1, o:266, a:1, s:1, b:1),
% 9.74/10.12 alpha6 [248, 4] (w:1, o:279, a:1, s:1, b:1),
% 9.74/10.12 alpha7 [249, 4] (w:1, o:280, a:1, s:1, b:1),
% 9.74/10.12 alpha8 [250, 2] (w:1, o:242, a:1, s:1, b:1),
% 9.74/10.12 alpha9 [251, 2] (w:1, o:243, a:1, s:1, b:1),
% 9.74/10.12 alpha10 [252, 2] (w:1, o:238, a:1, s:1, b:1),
% 9.74/10.12 alpha11 [253, 3] (w:1, o:267, a:1, s:1, b:1),
% 9.74/10.12 alpha12 [254, 3] (w:1, o:268, a:1, s:1, b:1),
% 9.74/10.12 alpha13 [255, 2] (w:1, o:239, a:1, s:1, b:1),
% 9.74/10.12 alpha14 [256, 2] (w:1, o:240, a:1, s:1, b:1),
% 9.74/10.12 alpha15 [257, 3] (w:1, o:269, a:1, s:1, b:1),
% 9.74/10.12 alpha16 [258, 3] (w:1, o:270, a:1, s:1, b:1),
% 9.74/10.12 alpha17 [259, 4] (w:1, o:281, a:1, s:1, b:1),
% 9.74/10.12 alpha18 [260, 4] (w:1, o:282, a:1, s:1, b:1),
% 9.74/10.12 alpha19 [261, 4] (w:1, o:283, a:1, s:1, b:1),
% 9.74/10.12 alpha20 [262, 3] (w:1, o:259, a:1, s:1, b:1),
% 9.74/10.12 alpha21 [263, 4] (w:1, o:284, a:1, s:1, b:1),
% 9.74/10.12 alpha22 [264, 3] (w:1, o:260, a:1, s:1, b:1),
% 9.74/10.12 alpha23 [265, 3] (w:1, o:261, a:1, s:1, b:1),
% 9.74/10.12 alpha24 [266, 3] (w:1, o:262, a:1, s:1, b:1),
% 9.74/10.12 alpha25 [267, 3] (w:1, o:263, a:1, s:1, b:1),
% 9.74/10.12 alpha26 [268, 4] (w:1, o:285, a:1, s:1, b:1),
% 9.74/10.12 alpha27 [269, 4] (w:1, o:286, a:1, s:1, b:1),
% 9.74/10.12 alpha28 [270, 4] (w:1, o:287, a:1, s:1, b:1),
% 9.74/10.12 skol1 [271, 2] (w:1, o:221, a:1, s:1, b:1),
% 9.74/10.12 skol2 [272, 2] (w:1, o:228, a:1, s:1, b:1),
% 9.74/10.12 skol3 [273, 2] (w:1, o:229, a:1, s:1, b:1),
% 9.74/10.12 skol4 [274, 3] (w:1, o:271, a:1, s:1, b:1),
% 9.74/10.12 skol5 [275, 2] (w:1, o:230, a:1, s:1, b:1),
% 9.74/10.12 skol6 [276, 3] (w:1, o:272, a:1, s:1, b:1),
% 9.74/10.12 skol7 [277, 3] (w:1, o:273, a:1, s:1, b:1),
% 9.74/10.12 skol8 [278, 2] (w:1, o:231, a:1, s:1, b:1),
% 9.74/10.12 skol9 [279, 1] (w:1, o:121, a:1, s:1, b:1),
% 9.74/10.12 skol10 [280, 2] (w:1, o:222, a:1, s:1, b:1),
% 9.74/10.12 skol11 [281, 3] (w:1, o:274, a:1, s:1, b:1),
% 9.74/10.12 skol12 [282, 4] (w:1, o:288, a:1, s:1, b:1),
% 9.74/10.12 skol13 [283, 2] (w:1, o:223, a:1, s:1, b:1),
% 9.74/10.12 skol14 [284, 2] (w:1, o:224, a:1, s:1, b:1),
% 9.74/10.12 skol15 [285, 3] (w:1, o:275, a:1, s:1, b:1),
% 9.74/10.12 skol16 [286, 3] (w:1, o:276, a:1, s:1, b:1),
% 9.74/10.12 skol17 [287, 2] (w:1, o:225, a:1, s:1, b:1),
% 9.74/10.12 skol18 [288, 2] (w:1, o:226, a:1, s:1, b:1),
% 9.74/10.12 skol19 [289, 2] (w:1, o:227, a:1, s:1, b:1),
% 9.74/10.12 skol20 [290, 3] (w:1, o:277, a:1, s:1, b:1).
% 9.74/10.12
% 9.74/10.12
% 9.74/10.12 Starting Search:
% 9.74/10.12
% 9.74/10.12 *** allocated 113905 integers for clauses
% 9.74/10.12 *** allocated 170857 integers for clauses
% 9.74/10.12 Resimplifying inuse:
% 9.74/10.12 Done
% 9.74/10.12
% 9.74/10.12
% 9.74/10.12 Intermediate Status:
% 9.74/10.12 Generated: 3408
% 9.74/10.12 Kept: 2001
% 9.74/10.12 Inuse: 49
% 9.74/10.12 Deleted: 0
% 9.74/10.12 Deletedinuse: 0
% 9.74/10.12
% 9.74/10.12 *** allocated 256285 integers for clauses
% 9.74/10.12 Resimplifying inuse:
% 9.74/10.12 Done
% 9.74/10.12
% 9.74/10.12 *** allocated 170857 integers for termspace/termends
% 9.74/10.12 Resimplifying inuse:
% 9.74/10.12 Done
% 9.74/10.12
% 9.74/10.12
% 9.74/10.12 Intermediate Status:
% 9.74/10.12 Generated: 7596
% 9.74/10.12 Kept: 4013
% 9.74/10.12 Inuse: 178
% 9.74/10.12 Deleted: 3
% 9.74/10.12 Deletedinuse: 1
% 9.74/10.12
% 9.74/10.12 *** allocated 384427 integers for clauses
% 9.74/10.12 Resimplifying inuse:
% 9.74/10.12 Done
% 9.74/10.12
% 9.74/10.12 *** allocated 256285 integers for termspace/termends
% 9.74/10.12
% 9.74/10.12 Intermediate Status:
% 9.74/10.12 Generated: 14677
% 9.74/10.12 Kept: 6525
% 9.74/10.12 Inuse: 236
% 9.74/10.12 Deleted: 6
% 9.74/10.12 Deletedinuse: 1
% 9.74/10.12
% 9.74/10.12 Resimplifying inuse:
% 9.74/10.12 Done
% 9.74/10.12
% 9.74/10.12 *** allocated 576640 integers for clauses
% 9.74/10.12 Resimplifying inuse:
% 9.74/10.12 Done
% 9.74/10.12
% 9.74/10.12
% 9.74/10.12 Intermediate Status:
% 9.74/10.12 Generated: 20054
% 9.74/10.12 Kept: 8744
% 9.74/10.12 Inuse: 291
% 9.74/10.12 Deleted: 7
% 9.74/10.12 Deletedinuse: 2
% 9.74/10.12
% 9.74/10.12 Resimplifying inuse:
% 9.74/10.12 Done
% 51.97/52.35
% 51.97/52.35 *** allocated 384427 integers for termspace/termends
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 24280
% 51.97/52.35 Kept: 10775
% 51.97/52.35 Inuse: 330
% 51.97/52.35 Deleted: 8
% 51.97/52.35 Deletedinuse: 2
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 *** allocated 864960 integers for clauses
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 29349
% 51.97/52.35 Kept: 13136
% 51.97/52.35 Inuse: 385
% 51.97/52.35 Deleted: 8
% 51.97/52.35 Deletedinuse: 2
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 *** allocated 576640 integers for termspace/termends
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 37366
% 51.97/52.35 Kept: 15626
% 51.97/52.35 Inuse: 400
% 51.97/52.35 Deleted: 8
% 51.97/52.35 Deletedinuse: 2
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 41877
% 51.97/52.35 Kept: 18089
% 51.97/52.35 Inuse: 425
% 51.97/52.35 Deleted: 8
% 51.97/52.35 Deletedinuse: 2
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 *** allocated 1297440 integers for clauses
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 48480
% 51.97/52.35 Kept: 20729
% 51.97/52.35 Inuse: 450
% 51.97/52.35 Deleted: 8
% 51.97/52.35 Deletedinuse: 2
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying clauses:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 55274
% 51.97/52.35 Kept: 23204
% 51.97/52.35 Inuse: 470
% 51.97/52.35 Deleted: 313
% 51.97/52.35 Deletedinuse: 4
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 62944
% 51.97/52.35 Kept: 25501
% 51.97/52.35 Inuse: 500
% 51.97/52.35 Deleted: 313
% 51.97/52.35 Deletedinuse: 4
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 *** allocated 864960 integers for termspace/termends
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 71278
% 51.97/52.35 Kept: 27531
% 51.97/52.35 Inuse: 546
% 51.97/52.35 Deleted: 313
% 51.97/52.35 Deletedinuse: 4
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 *** allocated 1946160 integers for clauses
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 77900
% 51.97/52.35 Kept: 29638
% 51.97/52.35 Inuse: 575
% 51.97/52.35 Deleted: 313
% 51.97/52.35 Deletedinuse: 4
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 86175
% 51.97/52.35 Kept: 31784
% 51.97/52.35 Inuse: 602
% 51.97/52.35 Deleted: 316
% 51.97/52.35 Deletedinuse: 5
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 90896
% 51.97/52.35 Kept: 33983
% 51.97/52.35 Inuse: 628
% 51.97/52.35 Deleted: 317
% 51.97/52.35 Deletedinuse: 6
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 95319
% 51.97/52.35 Kept: 36002
% 51.97/52.35 Inuse: 653
% 51.97/52.35 Deleted: 317
% 51.97/52.35 Deletedinuse: 6
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 100294
% 51.97/52.35 Kept: 38232
% 51.97/52.35 Inuse: 683
% 51.97/52.35 Deleted: 317
% 51.97/52.35 Deletedinuse: 6
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 104514
% 51.97/52.35 Kept: 41195
% 51.97/52.35 Inuse: 693
% 51.97/52.35 Deleted: 317
% 51.97/52.35 Deletedinuse: 6
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying clauses:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 109111
% 51.97/52.35 Kept: 44180
% 51.97/52.35 Inuse: 703
% 51.97/52.35 Deleted: 1078
% 51.97/52.35 Deletedinuse: 6
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 *** allocated 1297440 integers for termspace/termends
% 51.97/52.35 *** allocated 2919240 integers for clauses
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 114715
% 51.97/52.35 Kept: 46240
% 51.97/52.35 Inuse: 733
% 51.97/52.35 Deleted: 1078
% 51.97/52.35 Deletedinuse: 6
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 125089
% 51.97/52.35 Kept: 48661
% 51.97/52.35 Inuse: 763
% 51.97/52.35 Deleted: 1078
% 51.97/52.35 Deletedinuse: 6
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 132130
% 51.97/52.35 Kept: 50671
% 51.97/52.35 Inuse: 790
% 51.97/52.35 Deleted: 1078
% 51.97/52.35 Deletedinuse: 6
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 138996
% 51.97/52.35 Kept: 52775
% 51.97/52.35 Inuse: 806
% 51.97/52.35 Deleted: 1078
% 51.97/52.35 Deletedinuse: 6
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 144478
% 51.97/52.35 Kept: 54916
% 51.97/52.35 Inuse: 823
% 51.97/52.35 Deleted: 1078
% 51.97/52.35 Deletedinuse: 6
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 147640
% 51.97/52.35 Kept: 56955
% 51.97/52.35 Inuse: 829
% 51.97/52.35 Deleted: 1078
% 51.97/52.35 Deletedinuse: 6
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 157878
% 51.97/52.35 Kept: 59948
% 51.97/52.35 Inuse: 853
% 51.97/52.35 Deleted: 1078
% 51.97/52.35 Deletedinuse: 6
% 51.97/52.35
% 51.97/52.35 Resimplifying inuse:
% 51.97/52.35 Done
% 51.97/52.35
% 51.97/52.35
% 51.97/52.35 Intermediate Status:
% 51.97/52.35 Generated: 165917
% 51.97/52.35 Kept: 62166
% 115.18/115.58 Inuse: 863
% 115.18/115.58 Deleted: 1078
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying clauses:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 *** allocated 1946160 integers for termspace/termends
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 177947
% 115.18/115.58 Kept: 65407
% 115.18/115.58 Inuse: 898
% 115.18/115.58 Deleted: 1195
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 184898
% 115.18/115.58 Kept: 67441
% 115.18/115.58 Inuse: 934
% 115.18/115.58 Deleted: 1195
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 *** allocated 4378860 integers for clauses
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 198459
% 115.18/115.58 Kept: 70944
% 115.18/115.58 Inuse: 968
% 115.18/115.58 Deleted: 1195
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 206726
% 115.18/115.58 Kept: 73601
% 115.18/115.58 Inuse: 1003
% 115.18/115.58 Deleted: 1195
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 212586
% 115.18/115.58 Kept: 75652
% 115.18/115.58 Inuse: 1028
% 115.18/115.58 Deleted: 1195
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 222312
% 115.18/115.58 Kept: 77743
% 115.18/115.58 Inuse: 1063
% 115.18/115.58 Deleted: 1195
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 250360
% 115.18/115.58 Kept: 81017
% 115.18/115.58 Inuse: 1078
% 115.18/115.58 Deleted: 1195
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying clauses:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 259459
% 115.18/115.58 Kept: 83242
% 115.18/115.58 Inuse: 1098
% 115.18/115.58 Deleted: 1559
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 267467
% 115.18/115.58 Kept: 85398
% 115.18/115.58 Inuse: 1128
% 115.18/115.58 Deleted: 1559
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 *** allocated 2919240 integers for termspace/termends
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 293245
% 115.18/115.58 Kept: 87806
% 115.18/115.58 Inuse: 1138
% 115.18/115.58 Deleted: 1559
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 304102
% 115.18/115.58 Kept: 90673
% 115.18/115.58 Inuse: 1148
% 115.18/115.58 Deleted: 1559
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 315639
% 115.18/115.58 Kept: 93563
% 115.18/115.58 Inuse: 1168
% 115.18/115.58 Deleted: 1559
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 322723
% 115.18/115.58 Kept: 95633
% 115.18/115.58 Inuse: 1178
% 115.18/115.58 Deleted: 1559
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 343317
% 115.18/115.58 Kept: 98626
% 115.18/115.58 Inuse: 1188
% 115.18/115.58 Deleted: 1559
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 351098
% 115.18/115.58 Kept: 100663
% 115.18/115.58 Inuse: 1210
% 115.18/115.58 Deleted: 1559
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 *** allocated 6568290 integers for clauses
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 362128
% 115.18/115.58 Kept: 102789
% 115.18/115.58 Inuse: 1228
% 115.18/115.58 Deleted: 1559
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying clauses:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 372918
% 115.18/115.58 Kept: 104844
% 115.18/115.58 Inuse: 1243
% 115.18/115.58 Deleted: 1963
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 396106
% 115.18/115.58 Kept: 108533
% 115.18/115.58 Inuse: 1263
% 115.18/115.58 Deleted: 1963
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 425098
% 115.18/115.58 Kept: 111726
% 115.18/115.58 Inuse: 1278
% 115.18/115.58 Deleted: 1963
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 *** allocated 4378860 integers for termspace/termends
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 453513
% 115.18/115.58 Kept: 114556
% 115.18/115.58 Inuse: 1288
% 115.18/115.58 Deleted: 1963
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 467274
% 115.18/115.58 Kept: 116891
% 115.18/115.58 Inuse: 1298
% 115.18/115.58 Deleted: 1963
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 475744
% 115.18/115.58 Kept: 119054
% 115.18/115.58 Inuse: 1318
% 115.18/115.58 Deleted: 1963
% 115.18/115.58 Deletedinuse: 6
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58 Resimplifying inuse:
% 115.18/115.58 Done
% 115.18/115.58
% 115.18/115.58
% 115.18/115.58 Intermediate Status:
% 115.18/115.58 Generated: 483358
% 235.05/235.47 Kept: 121233
% 235.05/235.47 Inuse: 1338
% 235.05/235.47 Deleted: 1963
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying clauses:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 511633
% 235.05/235.47 Kept: 125598
% 235.05/235.47 Inuse: 1363
% 235.05/235.47 Deleted: 2569
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 533315
% 235.05/235.47 Kept: 128217
% 235.05/235.47 Inuse: 1368
% 235.05/235.47 Deleted: 2569
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 543582
% 235.05/235.47 Kept: 130553
% 235.05/235.47 Inuse: 1393
% 235.05/235.47 Deleted: 2569
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 574213
% 235.05/235.47 Kept: 134780
% 235.05/235.47 Inuse: 1403
% 235.05/235.47 Deleted: 2569
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 584077
% 235.05/235.47 Kept: 136799
% 235.05/235.47 Inuse: 1422
% 235.05/235.47 Deleted: 2569
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 590690
% 235.05/235.47 Kept: 138820
% 235.05/235.47 Inuse: 1442
% 235.05/235.47 Deleted: 2569
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 597845
% 235.05/235.47 Kept: 141026
% 235.05/235.47 Inuse: 1473
% 235.05/235.47 Deleted: 2569
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 603714
% 235.05/235.47 Kept: 143091
% 235.05/235.47 Inuse: 1496
% 235.05/235.47 Deleted: 2571
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying clauses:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 612139
% 235.05/235.47 Kept: 145485
% 235.05/235.47 Inuse: 1526
% 235.05/235.47 Deleted: 2837
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 619436
% 235.05/235.47 Kept: 147488
% 235.05/235.47 Inuse: 1538
% 235.05/235.47 Deleted: 2837
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 634336
% 235.05/235.47 Kept: 151680
% 235.05/235.47 Inuse: 1561
% 235.05/235.47 Deleted: 2837
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 641450
% 235.05/235.47 Kept: 154267
% 235.05/235.47 Inuse: 1566
% 235.05/235.47 Deleted: 2837
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 652211
% 235.05/235.47 Kept: 156430
% 235.05/235.47 Inuse: 1590
% 235.05/235.47 Deleted: 2838
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 *** allocated 9852435 integers for clauses
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 661641
% 235.05/235.47 Kept: 158547
% 235.05/235.47 Inuse: 1615
% 235.05/235.47 Deleted: 2838
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 *** allocated 6568290 integers for termspace/termends
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 691027
% 235.05/235.47 Kept: 162777
% 235.05/235.47 Inuse: 1635
% 235.05/235.47 Deleted: 2838
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying clauses:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 699425
% 235.05/235.47 Kept: 164837
% 235.05/235.47 Inuse: 1655
% 235.05/235.47 Deleted: 2995
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 708836
% 235.05/235.47 Kept: 167230
% 235.05/235.47 Inuse: 1670
% 235.05/235.47 Deleted: 2995
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 727146
% 235.05/235.47 Kept: 170228
% 235.05/235.47 Inuse: 1675
% 235.05/235.47 Deleted: 2995
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 738360
% 235.05/235.47 Kept: 172347
% 235.05/235.47 Inuse: 1700
% 235.05/235.47 Deleted: 2995
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 748086
% 235.05/235.47 Kept: 174368
% 235.05/235.47 Inuse: 1717
% 235.05/235.47 Deleted: 2995
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 762214
% 235.05/235.47 Kept: 176589
% 235.05/235.47 Inuse: 1730
% 235.05/235.47 Deleted: 2995
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 770273
% 235.05/235.47 Kept: 178790
% 235.05/235.47 Inuse: 1745
% 235.05/235.47 Deleted: 2995
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47 Resimplifying inuse:
% 235.05/235.47 Done
% 235.05/235.47
% 235.05/235.47
% 235.05/235.47 Intermediate Status:
% 235.05/235.47 Generated: 777413
% 235.05/235.47 Kept: 180895
% 235.05/235.47 Inuse: 1760
% 235.05/235.47 Deleted: 2995
% 235.05/235.47 Deletedinuse: 6
% 235.05/235.47
% 300.02/300.44 Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------