TSTP Solution File: SWW251+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW251+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.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 23:21:34 EDT 2022
% Result : Timeout 300.08s 300.70s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWW251+1 : TPTP v8.1.0. Released v5.2.0.
% 0.08/0.13 % Command : bliksem %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jun 4 14:38:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.97/1.62 *** allocated 10000 integers for termspace/termends
% 0.97/1.62 *** allocated 10000 integers for clauses
% 0.97/1.62 *** allocated 10000 integers for justifications
% 0.97/1.62 *** allocated 15000 integers for termspace/termends
% 0.97/1.62 *** allocated 22500 integers for termspace/termends
% 0.97/1.62 *** allocated 33750 integers for termspace/termends
% 0.97/1.62 Bliksem 1.12
% 0.97/1.62
% 0.97/1.62
% 0.97/1.62 Automatic Strategy Selection
% 0.97/1.62
% 0.97/1.62 *** allocated 50625 integers for termspace/termends
% 0.97/1.62 *** allocated 75937 integers for termspace/termends
% 0.97/1.62 *** allocated 113905 integers for termspace/termends
% 0.97/1.62
% 0.97/1.62 Clauses:
% 0.97/1.62
% 0.97/1.62 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 0.97/1.62 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 0.97/1.62 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 0.97/1.62 tc_Complex_Ocomplex, v_p ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.97/1.62 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 0.97/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 0.97/1.62 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 0.97/1.62 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.62 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 0.97/1.62 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.62 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 0.97/1.62 X, T ) = hAPP( X, U ) }.
% 0.97/1.62 { ! hAPP( X, skol2( X ) ) = hAPP( X, skol24( X ) ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 0.97/1.62 { ! class_Groups_Oab__group__add( Y ), ! class_Groups_Oab__group__add( X )
% 0.97/1.62 , ! c_RealVector_Oadditive( Y, X, Z ), hAPP( Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Osemiring__1( X ), c_Int_Oiszero( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Osemiring__1( X ), ! c_Int_Oiszero( X, Y ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Osemiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Int_Oiszero( X, Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 0.97/1.62 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), !
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 0.97/1.62 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 0.97/1.62 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), !
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! Z = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 0.97/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 0.97/1.62 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 0.97/1.62 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 0.97/1.62 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol3( X
% 0.97/1.62 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol3( X, Y, Z ) ), Z = Y
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 0.97/1.62 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 0.97/1.62 c_Polynomial_Ocoeff( X, Y ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 0.97/1.62 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 0.97/1.62 c_Polynomial_Omonom( X, Y, Z ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.97/1.62 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 0.97/1.62 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 0.97/1.62 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ) ) = Z }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 0.97/1.62 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.97/1.62 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 0.97/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 0.97/1.62 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 0.97/1.62 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 0.97/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 0.97/1.62 , Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.97/1.62 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 0.97/1.62 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X
% 0.97/1.62 , Z, Y ) ) = c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 0.97/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 0.97/1.62 c_Polynomial_OpCons( X, T,
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 0.97/1.62 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.97/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 0.97/1.62 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 0.97/1.62 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ),
% 0.97/1.62 alpha1( X, Y, T ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ),
% 0.97/1.62 alpha13( X, Y, Z, T ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! alpha1( X, Y, T ), ! alpha13( X, Y, Z, T )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.97/1.62 , c_Polynomial_Osmult( X, T, Z ) ), Y ) ) }.
% 0.97/1.62 { ! alpha13( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.97/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha13( X, Y, Z, T ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.97/1.62 , Z ), Y ) ), alpha13( X, Y, Z, T ) }.
% 0.97/1.62 { ! alpha1( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { Z = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 0.97/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha1( X
% 0.97/1.62 , Y, Z ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 0.97/1.62 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.62 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.62 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.62 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Y, T ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 T, Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 T, Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Y, Z ), T = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Y, Z ) }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 T, Y ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 T, Y ) }.
% 0.97/1.62 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.97/1.62 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.62 c_Polynomial_Odegree( X, Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL
% 0.97/1.62 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Y ),
% 0.97/1.62 Z ) ), Z = Y }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 0.97/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.97/1.62 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 0.97/1.62 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 0.97/1.62 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 0.97/1.62 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.97/1.62 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.62 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.62 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.62 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult
% 0.97/1.62 ( X, T, Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), hBOOL(
% 0.97/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.97/1.62 c_Polynomial_Osmult( X, T, Y ) ) ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 0.97/1.62 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) =
% 0.97/1.62 c_Polynomial_Odegree( X, Z ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.97/1.62 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 0.97/1.62 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oab__group__add( Y ), ! class_Groups_Oab__group__add( X )
% 0.97/1.62 , ! c_RealVector_Oadditive( X, Y, Z ), hAPP( Z,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, U, T ) ) = c_Groups_Oplus__class_Oplus( Y
% 0.97/1.62 , hAPP( Z, U ), hAPP( Z, T ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) = c_Nat_OSuc(
% 0.97/1.62 c_Polynomial_Odegree( X, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.97/1.62 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.97/1.62 c_Polynomial_Osmult( X, Y, Z ) ) ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 0.97/1.62 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.97/1.62 Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.97/1.62 X ) ), T ), c_Polynomial_Osmult( X, Y, Z ) ) ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), T = c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 0.97/1.62 X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ) }.
% 0.97/1.62 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.62 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Osmult( X, Z, Y ) ) ), Z
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 0.97/1.62 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 0.97/1.62 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.62 , Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 0.97/1.62 c_Polynomial_Odegree( X, Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 0.97/1.62 }.
% 0.97/1.62 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), c_Nat_OSuc( X ) ) = hAPP( Y, X )
% 0.97/1.62 }.
% 0.97/1.62 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ) ) = Y }.
% 0.97/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.62 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 0.97/1.62 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, Y, T
% 0.97/1.62 ) ) ) }.
% 0.97/1.62 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), c_Nat_OSuc(
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 0.97/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ) ) = X }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), X ) = X }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 0.97/1.62 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 0.97/1.62 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.97/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.97/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hBOOL(
% 0.97/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Nat_OSuc(
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y ), alpha14( X
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! alpha2( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! alpha14( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.62 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! alpha14( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! alpha14( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha14( X, Y ) }.
% 0.97/1.62 { ! alpha2( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 0.97/1.62 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha3( X, Y ), alpha15
% 0.97/1.62 ( X, Y ) }.
% 0.97/1.62 { ! alpha3( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.62 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! alpha15( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.62 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! alpha15( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! alpha15( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha15( X, Y ) }.
% 0.97/1.62 { ! alpha3( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! alpha3( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha3( X, Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 0.97/1.62 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.62 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 0.97/1.62 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 0.97/1.62 { ! c_Nat_OSuc( X ) = X }.
% 0.97/1.62 { ! X = c_Nat_OSuc( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 0.97/1.62 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X, Z, Y ) =
% 0.97/1.62 c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 0.97/1.62 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 0.97/1.62 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.97/1.62 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.97/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 0.97/1.62 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 0.97/1.62 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.97/1.62 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 0.97/1.62 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.97/1.62 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 0.97/1.62 .
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol4( X, Y ) ) }.
% 0.97/1.62 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.62 , X ) ) }.
% 0.97/1.62 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 0.97/1.62 , Y ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.62 ), Y = X }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , alpha4( X, Y ), Y = X }.
% 0.97/1.62 { ! alpha4( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.62 , X ) ) }.
% 0.97/1.62 { ! alpha4( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! alpha4( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , alpha4( X, Y ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.62 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.62 { ! alpha5( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! alpha5( X, Y ), ! Y = X }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , Y = X, alpha5( X, Y ) }.
% 0.97/1.62 { ! alpha5( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.62 { ! alpha5( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.62 tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , alpha5( X, Y ) }.
% 0.97/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 0.97/1.62 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 0.97/1.62 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 0.97/1.62 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.62 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.62 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.62 , X ) ) }.
% 0.97/1.62 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.62 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.62 ), Y ) ) }.
% 0.97/1.62 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.62 , X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.62 ), X = Y }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.62 ), Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , Y = X }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.62 ), Y = X }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 0.97/1.62 , X ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.62 ), Y ) ) }.
% 0.97/1.62 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.62 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.97/1.62 ), Z ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.97/1.62 ), Z ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.62 ), Y = X }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.62 ), Y = X }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.62 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.62 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.97/1.62 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.97/1.62 ), Z ) ) }.
% 0.97/1.62 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 0.97/1.62 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.97/1.62 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.97/1.62 Z ), Y ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.97/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.97/1.62 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! Y = X }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! Y = X }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! X = Y }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 0.97/1.62 ), Z ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.97/1.62 Z ), Y ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.62 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.97/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 0.97/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 0.97/1.62 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.62 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 0.97/1.62 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 0.97/1.62 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 0.97/1.62 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 0.97/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__comm__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ), alpha6( X, Y, Z ), alpha16( X, Y, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha6( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha16( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ) ) }.
% 0.97/1.62 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( X ), Y ), alpha16( X, Y, Z ) }.
% 0.97/1.62 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.62 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), alpha6( X, Y, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha7( X, Y
% 0.97/1.62 , Z ), alpha17( X, Y, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha17( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), alpha17( X, Y, Z ) }.
% 0.97/1.62 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.62 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y ), alpha7( X, Y, Z ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 0.97/1.62 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.97/1.62 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 0.97/1.62 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.62 ), ! U = T }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 0.97/1.62 ), ! Z = Y }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 0.97/1.62 ) ), Z ) }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.62 ), U = Z, T = Y }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.97/1.62 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 0.97/1.62 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.97/1.62 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.97/1.62 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.97/1.62 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.62 c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 0.97/1.62 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 0.97/1.62 ) ), T ), Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.62 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.62 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.62 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.62 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 0.97/1.62 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 0.97/1.62 ) ) ) }.
% 0.97/1.62 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.97/1.62 ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 0.97/1.62 ), Z ), Y ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.62 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 0.97/1.62 .
% 0.97/1.62 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.62 ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.62 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.62 , c_Nat_OSuc( X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.97/1.62 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 0.97/1.62 }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 0.97/1.62 c_Nat_OSuc( X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 0.97/1.62 ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.97/1.62 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.97/1.62 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 0.97/1.62 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 0.97/1.62 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 0.97/1.62 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 0.97/1.62 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.62 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.62 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.62 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.62 ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.62 .
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 0.97/1.62 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Y, Z ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 Z, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.62 ) ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.62 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.97/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.62 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.62 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 0.97/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.62 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 0.97/1.62 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 0.97/1.62 c_Polynomial_Odegree( X, Z ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.97/1.62 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 0.97/1.62 Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.62 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 0.97/1.62 ), Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.97/1.62 , Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 0.97/1.62 , c_Polynomial_Odegree( X, Y ) ) }.
% 0.97/1.62 { ! class_Groups_Ocomm__monoid__add( X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.97/1.62 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.62 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 0.97/1.62 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.97/1.62 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.62 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.62 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 0.97/1.62 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.62 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 0.97/1.62 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.62 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 0.97/1.62 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 0.97/1.62 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 0.97/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.62 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.97/1.62 hAPP( Z, skol5( U, W, Z ) ) ) }.
% 0.97/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.62 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 0.97/1.62 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ),
% 0.97/1.62 c_Groups_Oplus__class_Oplus( X, skol5( X, Y, Z ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 0.97/1.62 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 0.97/1.62 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.62 , T, c_Groups_Ozero__class_Ozero( X ) ) ) ), ! hBOOL( hAPP( Z, T ) ),
% 0.97/1.62 hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.97/1.62 skol25( X, Y, Z ) ) ) ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol6( X, Y ) ) }.
% 0.97/1.62 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 0.97/1.62 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.62 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.62 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.62 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 0.97/1.62 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 0.97/1.62 , Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 0.97/1.62 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 0.97/1.62 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.97/1.62 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.62 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.62 X ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 0.97/1.62 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.62 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.62 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.62 ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 0.97/1.62 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 0.97/1.62 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), Z ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.62 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.62 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.62 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.62 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.62 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.62 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.62 Y ), X ) ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.62 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.62 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.62 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 0.97/1.62 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 0.97/1.62 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Y = Z }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 0.97/1.62 , ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 0.97/1.62 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 0.97/1.62 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 0.97/1.62 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.62 Y ), ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 Z ), ! Z = Y }.
% 0.97/1.62 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.62 Y ) }.
% 0.97/1.62 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.62 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 0.97/1.63 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, Y, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.63 { alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 0.97/1.63 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.63 { alpha23( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 0.97/1.63 ( X, Y ), Z ) ) }.
% 0.97/1.63 { ! alpha23( X, Y, Z ), alpha25( X, Y, Z ), Z = Y }.
% 0.97/1.63 { ! alpha23( X, Y, Z ), alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! alpha25( X, Y, Z ), alpha23( X, Y, Z ) }.
% 0.97/1.63 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha23( X, Y, Z ) }.
% 0.97/1.63 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 0.97/1.63 }.
% 0.97/1.63 { ! alpha25( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 0.97/1.63 X, Y ), Z ) ), alpha25( X, Y, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.63 ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 0.97/1.63 ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, T, Y ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.63 , Y, Z ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.63 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, Z, Y ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.63 , T, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.63 , Y, T ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.63 , T, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.63 , T ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 0.97/1.63 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, Z, Y ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 0.97/1.63 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, Z, Y ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 0.97/1.63 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 0.97/1.63 .
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 0.97/1.63 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.63 .
% 0.97/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 0.97/1.63 .
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 0.97/1.63 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 0.97/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.63 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 0.97/1.63 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 0.97/1.63 .
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 0.97/1.63 .
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 0.97/1.63 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 0.97/1.63 X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.63 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 0.97/1.63 }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 0.97/1.63 , X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( tc_Nat_Onat, Y, X ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( tc_Nat_Onat, Y, X ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Nat_Onat ), Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 0.97/1.63 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha8( X, Y, Z, T ),
% 0.97/1.63 alpha18( X, Y, Z, T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha18( X, Y, Z, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! alpha18( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.63 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha18( X, Y, Z, T ) }.
% 0.97/1.63 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.63 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.63 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha8( X, Y, Z, T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha9( X, Y, Z, T ),
% 0.97/1.63 alpha19( X, Y, Z, T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha19( X, Y, Z, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.63 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha19( X, Y, Z, T ) }.
% 0.97/1.63 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 0.97/1.63 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 0.97/1.63 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha9( X, Y, Z, T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.63 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 0.97/1.63 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.63 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 0.97/1.63 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 0.97/1.63 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.63 , Y, T ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 0.97/1.63 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 0.97/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 0.97/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.63 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 0.97/1.63 c_Nat_OSuc( X ) ) }.
% 0.97/1.63 { ! alpha10( X, Y ), Y = c_Nat_OSuc( skol7( Z, Y ) ) }.
% 0.97/1.63 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol7( X,
% 0.97/1.63 Y ), X ) }.
% 0.97/1.63 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 0.97/1.63 ), alpha10( X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol8( X ) ) }.
% 0.97/1.63 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 0.97/1.63 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat, Y, X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 0.97/1.63 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 0.97/1.63 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.63 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 0.97/1.63 ), X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol9( X, Y ) ) ) }.
% 0.97/1.63 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 0.97/1.63 .
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 0.97/1.63 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 0.97/1.63 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.97/1.63 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.97/1.63 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.63 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 0.97/1.63 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.63 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.63 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.63 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 0.97/1.63 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.63 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.63 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.63 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.63 hAPP( Y, U ) ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.63 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 0.97/1.63 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.63 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 0.97/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 0.97/1.63 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 0.97/1.63 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.63 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.63 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.63 hAPP( Y, U ) ) }.
% 0.97/1.63 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( X, Z, Y ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( X, Y, Z ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.63 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 0.97/1.63 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.63 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.63 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 0.97/1.63 hAPP( Y, U ) ) }.
% 0.97/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 0.97/1.63 ( Z, skol10( X, Y, Z ) ), hAPP( Y, skol10( X, Y, Z ) ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.63 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 0.97/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 0.97/1.63 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 0.97/1.63 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.97/1.63 , Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 0.97/1.63 ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 0.97/1.63 , Y ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 0.97/1.63 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.63 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 0.97/1.63 }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.63 , alpha21( X, Y, Z, T ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha21( X, Y, Z, T ),
% 0.97/1.63 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 0.97/1.63 { ! alpha21( X, Y, Z, T ), alpha11( X, Z, T ) }.
% 0.97/1.63 { ! alpha21( X, Y, Z, T ), alpha20( X, Y, T ) }.
% 0.97/1.63 { ! alpha11( X, Z, T ), ! alpha20( X, Y, T ), alpha21( X, Y, Z, T ) }.
% 0.97/1.63 { ! alpha20( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), alpha22( X, Y, Z ) }.
% 0.97/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha20( X
% 0.97/1.63 , Y, Z ) }.
% 0.97/1.63 { ! alpha22( X, Y, Z ), alpha20( X, Y, Z ) }.
% 0.97/1.63 { ! alpha22( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha22( X
% 0.97/1.63 , Y, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 0.97/1.63 ), c_Polynomial_Odegree( X, Z ) ), alpha22( X, Y, Z ) }.
% 0.97/1.63 { ! alpha11( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X,
% 0.97/1.63 Y, Z ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X
% 0.97/1.63 , Y, Z ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 0.97/1.63 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.63 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.63 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 0.97/1.63 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 0.97/1.63 }.
% 0.97/1.63 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 0.97/1.63 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 0.97/1.63 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.63 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.63 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.97/1.63 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 0.97/1.63 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.63 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 0.97/1.63 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.63 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.63 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 0.97/1.63 .
% 0.97/1.63 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 0.97/1.63 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 0.97/1.63 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 0.97/1.63 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 0.97/1.63 ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 0.97/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 0.97/1.63 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 0.97/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 0.97/1.63 .
% 0.97/1.63 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 0.97/1.63 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.63 alpha12( X, Y, Z ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.63 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! alpha12( X, Y, Z ),
% 0.97/1.63 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 0.97/1.63 { ! alpha12( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.63 alpha12( X, Y, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.63 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Nat_Onat ), X ), Y ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 0.97/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 0.97/1.63 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.63 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 0.97/1.63 }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 0.97/1.63 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 0.97/1.63 , skol11( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_Polynomial_Odegree( X, Y ), Z ) }.
% 0.97/1.63 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol11( X
% 0.97/1.63 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 0.97/1.63 Y ), Z ) }.
% 0.97/1.63 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 Z, c_Polynomial_Odegree( X, Y ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 tc_Nat_Onat, Z, skol12( T, U, Z ) ) }.
% 0.97/1.63 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 Z, c_Polynomial_Odegree( X, Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 0.97/1.63 skol12( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), U ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 0.97/1.63 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 0.97/1.63 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 0.97/1.63 { c_HOL_Obool_Obool__size( c_fFalse ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 0.97/1.63 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) = Y }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 0.97/1.63 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Rings_Osemiring__1( X ), ! c_Int_Oiszero( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.63 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 0.97/1.63 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Nat_Onat ) ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.63 = Y }.
% 0.97/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.63 = Y }.
% 0.97/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.63 = Y }.
% 0.97/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.63 = Y }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 0.97/1.63 = Y }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.63 = Y }.
% 0.97/1.63 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 0.97/1.63 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 0.97/1.63 , Y ), X ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Nat_Onat ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Nat_Onat ) }.
% 0.97/1.63 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 0.97/1.63 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 0.97/1.63 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 0.97/1.63 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 0.97/1.63 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.63 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 0.97/1.63 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 0.97/1.63 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 0.97/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semiring__1( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.63 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 0.97/1.63 ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 X ), Y ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.97/1.63 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 Y ), X ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 0.97/1.63 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 0.97/1.63 { c_HOL_Obool_Obool__size( c_fTrue ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 0.97/1.63 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons
% 0.97/1.63 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ), hAPP( c_Polynomial_Opoly( X, Z )
% 0.97/1.63 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Z ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Y ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.63 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), T ) ), hBOOL(
% 0.97/1.63 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Y, T ) ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.63 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 0.97/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.97/1.63 , T ), Z ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.63 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 0.97/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.97/1.63 , T ), Y ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.63 ( tc_Polynomial_Opoly( X ) ), T ), Z ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL(
% 0.97/1.63 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.63 = Y }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.63 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Y ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 = Y }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 0.97/1.63 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 0.97/1.63 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 0.97/1.63 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.63 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.63 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.63 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.63 ) ), Y ) }.
% 0.97/1.63 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.63 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.63 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.63 Z, Y ) ) = Y }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.63 Y ) ) = Y }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.97/1.63 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 0.97/1.63 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.63 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.63 ) ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.97/1.63 , Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 0.97/1.63 , Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.63 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.97/1.63 c_Polynomial_Odegree( X, Y ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.97/1.63 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( Y ), ! class_Groups_Oab__group__add( X )
% 0.97/1.63 , ! c_RealVector_Oadditive( X, Y, Z ), hAPP( Z,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, T ) ) =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( Y, hAPP( Z, T ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 0.97/1.63 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.63 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.63 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 0.97/1.63 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 0.97/1.63 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.97/1.63 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.63 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 0.97/1.63 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.63 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.63 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.63 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Y ), Z ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.63 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Z ), Y ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.63 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Y ), Y ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.63 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.63 { ! class_Groups_Oordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.63 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.63 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 , Y ) }.
% 0.97/1.63 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 0.97/1.63 , Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.63 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Z ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.63 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.63 Z ) = Y }.
% 0.97/1.63 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 0.97/1.63 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Y ) }.
% 0.97/1.63 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 X ) }.
% 0.97/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 0.97/1.63 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.63 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 0.97/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 0.97/1.63 ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 0.97/1.63 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 0.97/1.63 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 0.97/1.63 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.63 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 0.97/1.63 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 0.97/1.63 tc_Polynomial_Opoly( X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z,
% 0.97/1.63 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 0.97/1.63 hAPP( c_Polynomial_Opoly( X, Y ), c_Groups_Ouminus__class_Ouminus( X, Z )
% 0.97/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 0.97/1.63 ) ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.63 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha26( X, Y, Z, T ), ! Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 0.97/1.63 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.63 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha26( X, Y, Z, T ), ! hAPP(
% 0.97/1.63 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 0.97/1.63 .
% 0.97/1.63 { ! alpha26( X, Y, Z, T ), alpha27( X, Y, Z, T ), alpha24( X, Y, T ) }.
% 0.97/1.63 { ! alpha26( X, Y, Z, T ), alpha27( X, Y, Z, T ), ! hAPP(
% 0.97/1.63 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! alpha27( X, Y, Z, T ), alpha26( X, Y, Z, T ) }.
% 0.97/1.63 { ! alpha24( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 0.97/1.63 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.63 alpha26( X, Y, Z, T ) }.
% 0.97/1.63 { ! alpha27( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), Z ), T ) ), alpha28( X, Y, Z, T ) }.
% 0.97/1.63 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 0.97/1.63 Z ), T ) ), alpha27( X, Y, Z, T ) }.
% 0.97/1.63 { ! alpha28( X, Y, Z, T ), alpha27( X, Y, Z, T ) }.
% 0.97/1.63 { ! alpha28( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), skol13( X, Y, U, W ) ), Y ) ) }.
% 0.97/1.63 { ! alpha28( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), skol13( X, Y, U, T ) ), T ) ) }.
% 0.97/1.63 { ! alpha28( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), skol13( X, Y, Z, T ) ), Z ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 0.97/1.63 , U ), Y ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), U ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), U ), Z ) ), alpha28
% 0.97/1.63 ( X, Y, Z, T ) }.
% 0.97/1.63 { ! alpha24( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! alpha24( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.63 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha24( X, Y, Z
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.63 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.97/1.63 Y ) ) ) ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 0.97/1.63 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 0.97/1.63 Y ) ) ) ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Nat_Onat ) ) = Y }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 0.97/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 0.97/1.63 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 0.97/1.63 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat, Z, Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.63 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.63 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 0.97/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 0.97/1.63 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 0.97/1.63 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 0.97/1.63 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 0.97/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 0.97/1.63 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.97/1.63 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 0.97/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 0.97/1.63 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 0.97/1.63 ( X ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 0.97/1.63 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 0.97/1.63 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 0.97/1.63 X, Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.63 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), hBOOL( hAPP
% 0.97/1.63 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 0.97/1.63 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 0.97/1.63 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.63 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.63 ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 0.97/1.63 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 0.97/1.63 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 0.97/1.63 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 0.97/1.63 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 0.97/1.63 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 0.97/1.63 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.97/1.63 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 0.97/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 0.97/1.63 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 0.97/1.63 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), Y ) }.
% 0.97/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 0.97/1.63 ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.63 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 0.97/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 0.97/1.63 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 0.97/1.63 ) }.
% 0.97/1.63 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( X ) }.
% 0.97/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 0.97/1.63 = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.63 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 0.97/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Nat_Onat ) ) = Y }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.63 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.97/1.63 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 0.97/1.63 .
% 0.97/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.63 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ) }.
% 0.97/1.63 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 0.97/1.63 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 0.97/1.63 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 0.97/1.63 = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 0.97/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.63 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 0.97/1.63 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.63 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 0.97/1.63 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 0.97/1.63 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.63 X ), T ), Z ) ), Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 0.97/1.63 , U, Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), U ) ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ), hBOOL( hAPP( hAPP
% 0.97/1.63 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.63 ( X ), Z ), U ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T
% 0.97/1.63 ) ) ) }.
% 0.97/1.63 { ! class_Rings_Ocomm__semiring__1( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP
% 0.97/1.63 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.63 ( X ), T ), Z ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y
% 0.97/1.63 ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 X ), Y ), Z = Y }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.63 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 0.97/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.63 ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.63 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 0.97/1.63 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 0.97/1.63 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 0.97/1.63 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 0.97/1.63 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 0.97/1.63 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 0.97/1.63 c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 0.97/1.63 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 0.97/1.63 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 0.97/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 0.97/1.63 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 0.97/1.63 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 0.97/1.63 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 0.97/1.63 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ) ) }.
% 0.97/1.63 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 0.97/1.63 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.63 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.63 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 0.97/1.63 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 0.97/1.63 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 0.97/1.63 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 0.97/1.63 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 0.97/1.63 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 0.97/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.63 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 0.97/1.63 , Z ), X ) ), T ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 0.97/1.63 tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) )
% 0.97/1.63 }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 0.97/1.63 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 0.97/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( hAPP(
% 0.97/1.63 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 0.97/1.63 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.63 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ), hBOOL( hAPP( hAPP
% 0.97/1.63 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 0.97/1.63 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ) }.
% 0.97/1.63 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ), hBOOL( hAPP(
% 0.97/1.63 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 0.97/1.63 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 0.97/1.63 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.63 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 0.97/1.63 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 0.97/1.63 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 0.97/1.63 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 0.97/1.63 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! class_Lattices_Oboolean__algebra( X ), !
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Y ), Z = Y }.
% 0.97/1.63 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( X, Y ) }.
% 0.97/1.63 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.63 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol14( Z, Y
% 0.97/1.63 ), Y ) }.
% 0.97/1.63 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.63 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 0.97/1.63 skol14( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 0.97/1.63 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 0.97/1.63 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 0.97/1.63 , skol14( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 0.97/1.63 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 0.97/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 0.97/1.63 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 0.97/1.63 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 0.97/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 0.97/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 0.97/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ) ) = X }.
% 0.97/1.63 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), X ) = X }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 0.97/1.63 .
% 0.97/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 0.97/1.63 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 0.97/1.63 ( tc_Int_Oint ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 0.97/1.63 }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Int_Oint ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 0.97/1.63 = X }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Int_Oint ) ) ) }.
% 0.97/1.63 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Int_Oint ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 0.97/1.63 }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Int_Oint ) ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Int_Oint ) ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.63 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 0.97/1.63 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 0.97/1.63 ( tc_Int_Oint ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 0.97/1.63 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 0.97/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.63 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.63 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 0.97/1.63 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.63 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 0.97/1.63 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 0.97/1.63 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 0.97/1.63 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 0.97/1.63 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Int_Oint ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Int_Oint ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint, X, Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol15( Z, Y ) ) ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 0.97/1.63 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 0.97/1.63 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Int_Oint, skol15( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 0.97/1.63 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 0.97/1.63 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 0.97/1.63 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 0.97/1.63 ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.97/1.63 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.63 Y ), c_RComplete_Onatceiling( X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 0.97/1.63 ) }.
% 0.97/1.63 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 0.97/1.63 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.63 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.63 }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 0.97/1.63 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.63 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 0.97/1.63 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.63 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_Nat_Onat ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 0.97/1.63 }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.63 , c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 0.97/1.63 ), c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 0.97/1.63 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.63 , c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 0.97/1.63 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 0.97/1.63 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 0.97/1.63 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.97/1.63 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 0.97/1.63 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 0.97/1.63 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.63 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 0.97/1.63 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_RealDef_Oreal ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 0.97/1.63 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 0.97/1.63 c_RComplete_Onatfloor( X ) = Y }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.63 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 0.97/1.63 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 0.97/1.63 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 0.97/1.63 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.63 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 0.97/1.63 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 0.97/1.63 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.63 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 0.97/1.63 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 0.97/1.63 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 0.97/1.63 ( tc_Nat_Onat, X ) ) }.
% 0.97/1.63 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.97/1.63 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 0.97/1.63 Y = X }.
% 0.97/1.63 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 0.97/1.63 , X ) }.
% 0.97/1.63 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 0.97/1.63 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 0.97/1.63 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, c_Nat_OSuc( X ) ) ) }.
% 0.97/1.63 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 0.97/1.63 tc_Nat_Onat ) ) ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.63 { c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 0.97/1.63 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_RComplete_Onatceiling( Y ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 0.97/1.63 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 0.97/1.63 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.63 tc_Nat_Onat, Y, X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.63 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_RealDef_Oreal ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 0.97/1.63 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 0.97/1.63 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 0.97/1.63 , X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 0.97/1.63 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 0.97/1.63 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 0.97/1.63 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 0.97/1.63 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 0.97/1.63 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 0.97/1.63 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 0.97/1.63 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 0.97/1.63 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 0.97/1.63 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, skol16( X ) ), X ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, c_Nat_OSuc( skol16( X ) ) ) ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.63 tc_Nat_Onat, skol17( X, Y ), skol26( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 hAPP( Y, skol26( X, Y ) ), hAPP( Y, skol17( X, Y ) ) ), c_SEQ_Odecseq( X
% 0.97/1.63 , Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol18( Z, T ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol18( X, Y ) ), X ) =
% 0.97/1.63 Y }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 0.97/1.63 skol18( X, Y ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.63 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol19( Z, T ) ) }.
% 0.97/1.63 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 0.97/1.63 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol19( X, Y ) ), X ) =
% 0.97/1.63 Y }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 0.97/1.63 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.63 tc_Nat_Onat, skol20( X, Y ), skol27( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 0.97/1.63 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.63 hAPP( Y, skol20( X, Y ) ), hAPP( Y, skol27( X, Y ) ) ), c_SEQ_Oincseq( X
% 0.97/1.63 , Y ) }.
% 0.97/1.63 { c_Complex_Ocis( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 0.97/1.63 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, c_Nat_OSuc( Y ) ) ), X
% 0.97/1.63 ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.63 c_Complex_Ocis( X ) ), c_Complex_Ocis( hAPP( hAPP(
% 0.97/1.63 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.63 tc_Nat_Onat, Y ) ), X ) ) ) }.
% 0.97/1.63 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 0.97/1.63 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 0.97/1.63 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.97/1.63 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.97/1.63 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.63 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.63 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.97/1.64 ) ), Z ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 0.97/1.64 ) ), Y ) }.
% 0.97/1.64 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), X ) =
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.97/1.64 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 0.97/1.64 , Y ) ) = Y }.
% 0.97/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.97/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 0.97/1.64 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, c_Complex_Oii ) =
% 0.97/1.64 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, c_Complex_Oii ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.64 { c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 0.97/1.64 X, Y ) ) = Y }.
% 0.97/1.64 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.97/1.64 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 0.97/1.64 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 0.97/1.64 = Y }.
% 0.97/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 0.97/1.64 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.64 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.97/1.64 { c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, c_Complex_Ocis( X
% 0.97/1.64 ) ) = c_Complex_Ocis( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal
% 0.97/1.64 , X ) ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 0.97/1.64 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.97/1.64 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 0.97/1.64 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 0.97/1.64 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 0.97/1.64 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 0.97/1.64 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 0.97/1.64 c_Complex_Ocis( Y ) ), c_Complex_Ocis( X ) ) = c_Complex_Ocis(
% 0.97/1.64 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 0.97/1.64 { c_Complex_Ocis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 0.97/1.64 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { c_Complex_Ocis( X ) = c_Complex_Orcis( c_Groups_Oone__class_Oone(
% 0.97/1.64 tc_RealDef_Oreal ), X ) }.
% 0.97/1.64 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 0.97/1.64 c_Complex_Ocis( Y ) ), X ) = c_Complex_Ocis( hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.64 tc_Nat_Onat, X ) ), Y ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.64 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.97/1.64 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 0.97/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 0.97/1.64 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.97/1.64 ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Fields_Ofield__inverse__zero( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 0.97/1.64 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.97/1.64 { ! class_Fields_Ofield__inverse__zero( X ), !
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 0.97/1.64 , Y = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.64 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 0.97/1.64 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 0.97/1.64 = c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.97/1.64 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 0.97/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 0.97/1.64 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 0.97/1.64 ( X ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.97/1.64 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 0.97/1.64 , Y ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.97/1.64 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 0.97/1.64 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 0.97/1.64 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.97/1.64 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.97/1.64 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.97/1.64 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.97/1.64 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 0.97/1.64 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.97/1.64 , Y ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 ), c_Orderings_Oord__class_Oless__eq( X,
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 0.97/1.64 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 0.97/1.64 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 0.97/1.64 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 0.97/1.64 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 0.97/1.64 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.64 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.64 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 0.97/1.64 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 0.97/1.64 }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 0.97/1.64 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 0.97/1.64 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 0.97/1.64 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 0.97/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) ) }.
% 0.97/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), T ), hAPP(
% 0.97/1.64 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ), Z ) ) }.
% 0.97/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.64 tc_Nat_Onat, skol21( X, Y ) ) ), X ), Y ) }.
% 0.97/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 0.97/1.64 tc_Nat_Onat, c_Nat_OSuc( skol21( X, Y ) ) ) ), X ) ) }.
% 0.97/1.64 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 0.97/1.64 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, c_RealDef_Oreal(
% 0.97/1.64 tc_Nat_Onat, c_Nat_OSuc( skol22( X ) ) ) ), X ) }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.97/1.64 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 0.97/1.64 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Y, Z ) =
% 0.97/1.64 c_Polynomial_Opoly__gcd( X, Z, c_Divides_Odiv__class_Omod(
% 0.97/1.64 tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.64 skol23( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 0.97/1.64 c_Orderings_Oord__class_Oless( X, skol23( X, T, U ),
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 0.97/1.64 , Y ) }.
% 0.97/1.64 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), skol23( X, Y, Z ) ), Z ), Y ),
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ), c_Divides_Odiv__class_Omod(
% 0.97/1.64 tc_Polynomial_Opoly( X ), Z, Y ) = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 0.97/1.64 c_Polynomial_Odegree( X, c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.97/1.64 ( X ), Z, Y ) ), c_Polynomial_Odegree( X, Y ) ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.97/1.64 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.97/1.64 , Y, Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.64 Z ) = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 0.97/1.64 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 0.97/1.64 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 0.97/1.64 = c_Divides_Odiv__class_Omod( X, Y, Z ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Groups_Ouminus__class_Ouminus( X, T ), Z ) = c_Divides_Odiv__class_Omod
% 0.97/1.64 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 0.97/1.64 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.64 ( X, c_Groups_Ouminus__class_Ouminus( X, c_Divides_Odiv__class_Omod( X, Z
% 0.97/1.64 , Y ) ), Y ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.64 ( X, Z, Y ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.97/1.64 ( X, Y, Z ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.64 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 0.97/1.64 , Y ) ), Y ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.64 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.97/1.64 ), Z ), Y ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 0.97/1.64 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 0.97/1.64 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.97/1.64 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.64 T, Z ), Y ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 0.97/1.64 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 0.97/1.64 T, Y ), Z ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.97/1.64 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.97/1.64 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.97/1.64 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 0.97/1.64 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 0.97/1.64 ), Z ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 0.97/1.64 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 0.97/1.64 }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 0.97/1.64 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 0.97/1.64 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 0.97/1.64 X, Z, Y ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.97/1.64 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.64 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.97/1.64 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.64 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 0.97/1.64 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.64 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 0.97/1.64 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 0.97/1.64 , Y ) ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.97/1.64 ), Z ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 0.97/1.64 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 0.97/1.64 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 0.97/1.64 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 0.97/1.64 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 0.97/1.64 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 0.97/1.64 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 0.97/1.64 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y )
% 0.97/1.64 ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Y ) ),
% 0.97/1.64 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), T ), Z ) ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, Y, T )
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), c_Divides_Odiv__class_Omod( X
% 0.97/1.64 , c_Divides_Odiv__class_Omod( X, T, Y ), Z ) = c_Divides_Odiv__class_Omod
% 0.97/1.64 ( X, T, Z ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.97/1.64 ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 0.97/1.64 { ! class_Divides_Osemiring__div( X ), ! hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 0.97/1.64 c_Rings_Odvd__class_Odvd( X ), Z ), c_Divides_Odiv__class_Omod( X, T, Y )
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 0.97/1.64 , c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T, Z ) = Y }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.97/1.64 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 0.97/1.64 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 0.97/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 0.97/1.64 c_Polynomial_Opoly__gcd( X, Y, c_Divides_Odiv__class_Omod(
% 0.97/1.64 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat
% 0.97/1.64 , c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) ),
% 0.97/1.64 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), Z, Y ) = Z }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 0.97/1.64 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 0.97/1.64 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 0.97/1.64 tc_Polynomial_Opoly( X ), T, Z ) }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 0.97/1.64 tc_Polynomial_Opoly( X ), c_Groups_Ouminus__class_Ouminus(
% 0.97/1.64 tc_Polynomial_Opoly( X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 0.97/1.64 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly
% 0.97/1.64 ( X ), Z, Y ) ) }.
% 0.97/1.64 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.64 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.64 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 0.97/1.64 ( tc_fun( Y, X ) ) }.
% 0.97/1.64 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 0.97/1.64 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 0.97/1.64 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.64 tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 0.97/1.64 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 0.97/1.64 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 0.97/1.64 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 0.97/1.64 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 0.97/1.64 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 0.97/1.64 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 0.97/1.64 { class_Orderings_Oord( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 0.97/1.64 { class_Power_Opower( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Ozero( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Oring( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Oidom( tc_Int_Oint ) }.
% 0.97/1.64 { class_Groups_Oone( tc_Int_Oint ) }.
% 0.97/1.64 { class_Rings_Odvd( tc_Int_Oint ) }.
% 0.97/1.64 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.64 tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Power_Opower( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Groups_Oone( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 0.97/1.64 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 0.97/1.64 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 0.97/1.64 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 0.97/1.64 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 0.97/1.64 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 0.97/1.64 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.64 tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 0.97/1.64 .
% 0.97/1.64 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ouminus( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 0.97/1.64 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.64 tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ouminus( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ),
% 0.97/1.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 0.97/1.64 X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 0.97/1.64 ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 0.97/1.64 }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.64 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ),
% 0.97/1.64 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 0.97/1.64 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 0.97/1.64 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 0.97/1.64 ( tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Osemiring__1(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 0.97/1.64 ( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 0.97/1.64 }.
% 0.97/1.64 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 0.97/1.64 ) ) }.
% 0.97/1.64 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 0.97/1.64 .
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 0.97/1.64 tc_Polynomial_Opoly( X ) ) }.
% 0.97/1.64 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 0.97/1.64 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 0.97/1.64 { ! hBOOL( c_fFalse ) }.
% 0.97/1.64 { hBOOL( c_fTrue ) }.
% 0.97/1.64 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_p ), X ) =
% 0.97/1.64 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 0.97/1.64
% 0.97/1.64 *** allocated 15000 integers for clauses
% 0.97/1.64 *** allocated 22500 integers for clauses
% 0.97/1.64 *** allocated 33750 integers for clauses
% 0.97/1.64 *** allocated 50625 integers for clauses
% 0.97/1.64 *** allocated 75937 integers for clauses
% 0.97/1.64 percentage equality = 0.267150, percentage horn = 0.909514
% 0.97/1.64 This is a problem with some equality
% 0.97/1.64
% 0.97/1.64
% 0.97/1.64
% 0.97/1.64 Options Used:
% 0.97/1.64
% 0.97/1.64 useres = 1
% 0.97/1.64 useparamod = 1
% 0.97/1.64 useeqrefl = 1
% 0.97/1.64 useeqfact = 1
% 0.97/1.64 usefactor = 1
% 0.97/1.64 usesimpsplitting = 0
% 0.97/1.64 usesimpdemod = 5
% 0.97/1.64 usesimpres = 3
% 0.97/1.64
% 0.97/1.64 resimpinuse = 1000
% 0.97/1.64 resimpclauses = 20000
% 0.97/1.64 substype = eqrewr
% 0.97/1.64 backwardsubs = 1
% 0.97/1.64 selectoldest = 5
% 0.97/1.64
% 0.97/1.64 litorderings [0] = split
% 0.97/1.64 litorderings [1] = extend the termordering, first sorting on arguments
% 0.97/1.64
% 0.97/1.64 termordering = kbo
% 0.97/1.64
% 0.97/1.64 litapriori = 0
% 0.97/1.64 termapriori = 1
% 0.97/1.64 litaposteriori = 0
% 0.97/1.64 termaposteriori = 0
% 0.97/1.64 demodaposteriori = 0
% 0.97/1.64 ordereqreflfact = 0
% 0.97/1.64
% 0.97/1.64 litselect = negord
% 0.97/1.64
% 0.97/1.64 maxweight = 15
% 0.97/1.64 maxdepth = 30000
% 0.97/1.64 maxlength = 115
% 0.97/1.64 maxnrvars = 195
% 0.97/1.64 excuselevel = 1
% 0.97/1.64 increasemaxweight = 1
% 0.97/1.64
% 0.97/1.64 maxselected = 10000000
% 0.97/1.64 maxnrclauses = 10000000
% 0.97/1.64
% 0.97/1.64 showgenerated = 0
% 0.97/1.64 showkept = 0
% 0.97/1.64 showselected = 0
% 0.97/1.64 showdeleted = 0
% 0.97/1.64 showresimp = 1
% 0.97/1.64 showstatus = 2000
% 0.97/1.64
% 0.97/1.64 prologoutput = 0
% 0.97/1.64 nrgoals = 5000000
% 0.97/1.64 totalproof = 1
% 0.97/1.64
% 0.97/1.64 Symbols occurring in the translation:
% 0.97/1.64
% 0.97/1.64 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.97/1.64 . [1, 2] (w:1, o:195, a:1, s:1, b:0),
% 0.97/1.64 ! [4, 1] (w:0, o:103, a:1, s:1, b:0),
% 0.97/1.64 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.64 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.97/1.64 hAPP [38, 2] (w:1, o:219, a:1, s:1, b:0),
% 0.97/1.64 tc_Complex_Ocomplex [39, 0] (w:1, o:12, a:1, s:1, b:0),
% 0.97/1.64 v_p [40, 0] (w:1, o:13, a:1, s:1, b:0),
% 0.97/1.64 c_Polynomial_Opoly [41, 2] (w:1, o:220, a:1, s:1, b:0),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [42, 3] (w:1, o:
% 0.97/1.64 257, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Ocomm__semiring__0 [45, 1] (w:1, o:110, a:1, s:1, b:0),
% 0.97/1.64 tc_Polynomial_Opoly [46, 1] (w:1, o:116, a:1, s:1, b:0),
% 0.97/1.64 c_Groups_Ozero__class_Ozero [47, 1] (w:1, o:117, a:1, s:1, b:0),
% 0.97/1.64 class_Int_Oring__char__0 [50, 1] (w:1, o:118, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Oidom [51, 1] (w:1, o:119, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Ozero [53, 1] (w:1, o:124, a:1, s:1, b:0),
% 0.97/1.64 c_Polynomial_Oorder [55, 3] (w:1, o:260, a:1, s:1, b:0),
% 0.97/1.64 tc_Nat_Onat [56, 0] (w:1, o:26, a:1, s:1, b:0),
% 0.97/1.64 c_Polynomial_Opcompose [59, 3] (w:1, o:261, a:1, s:1, b:0),
% 0.97/1.64 c_Complex_Oii [60, 0] (w:1, o:28, a:1, s:1, b:0),
% 0.97/1.64 c_Polynomial_Opoly__rec [63, 5] (w:1, o:304, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Oab__group__add [65, 1] (w:1, o:125, a:1, s:1, b:0),
% 0.97/1.64 c_RealVector_Oadditive [66, 3] (w:1, o:262, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Osemiring__1 [67, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.97/1.64 c_Int_Oiszero [68, 2] (w:1, o:221, a:1, s:1, b:0),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [69, 2] (w:1, o:222
% 0.97/1.64 , a:1, s:1, b:0),
% 0.97/1.64 c_Polynomial_OpCons [70, 3] (w:1, o:263, a:1, s:1, b:0),
% 0.97/1.64 c_Polynomial_Omonom [72, 3] (w:1, o:264, a:1, s:1, b:0),
% 0.97/1.64 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [75, 3] (w:1
% 0.97/1.64 , o:265, a:1, s:1, b:0),
% 0.97/1.64 c_fequal [77, 2] (w:1, o:223, a:1, s:1, b:0),
% 0.97/1.64 c_If [78, 4] (w:1, o:292, a:1, s:1, b:0),
% 0.97/1.64 c_Polynomial_Osynthetic__div [80, 3] (w:1, o:266, a:1, s:1, b:0),
% 0.97/1.64 tc_RealDef_Oreal [82, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.97/1.64 c_Complex_Orcis [83, 2] (w:1, o:224, a:1, s:1, b:0),
% 0.97/1.64 c_Polynomial_Osmult [84, 3] (w:1, o:267, a:1, s:1, b:0),
% 0.97/1.64 c_Polynomial_Ocoeff [85, 2] (w:1, o:225, a:1, s:1, b:0),
% 0.97/1.64 c_Groups_Oplus__class_Oplus [90, 3] (w:1, o:268, a:1, s:1, b:0),
% 0.97/1.64 c_Nat_Onat_Onat__case [92, 3] (w:1, o:269, a:1, s:1, b:0),
% 0.97/1.64 c_Nat_OSuc [93, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.97/1.64 c_Polynomial_Odegree [95, 2] (w:1, o:226, a:1, s:1, b:0),
% 0.97/1.64 class_Fields_Ofield [96, 1] (w:1, o:120, a:1, s:1, b:0),
% 0.97/1.64 c_Rings_Odvd__class_Odvd [97, 1] (w:1, o:133, a:1, s:1, b:0),
% 0.97/1.64 hBOOL [98, 1] (w:1, o:134, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Ocancel__semigroup__add [100, 1] (w:1, o:135, a:1, s:1
% 0.97/1.64 , b:0),
% 0.97/1.64 class_Groups_Ocancel__ab__semigroup__add [101, 1] (w:1, o:136, a:1
% 0.97/1.64 , s:1, b:0),
% 0.97/1.64 class_Groups_Oab__semigroup__add [102, 1] (w:1, o:137, a:1, s:1, b:0)
% 0.97/1.64 ,
% 0.97/1.64 class_Groups_Ocomm__monoid__add [103, 1] (w:1, o:138, a:1, s:1, b:0)
% 0.97/1.64 ,
% 0.97/1.64 class_Groups_Olinordered__ab__group__add [104, 1] (w:1, o:139, a:1
% 0.97/1.64 , s:1, b:0),
% 0.97/1.64 class_Groups_Omonoid__add [105, 1] (w:1, o:140, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Ocomm__semiring__1 [106, 1] (w:1, o:141, a:1, s:1, b:0),
% 0.97/1.64
% 0.97/1.64 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 0.97/1.64 116, 1] (w:1, o:164, a:1, s:1, b:0),
% 0.97/1.64 c_Polynomial_OAbs__poly [117, 2] (w:1, o:227, a:1, s:1, b:0),
% 0.97/1.64 c_Groups_Otimes__class_Otimes [118, 1] (w:1, o:165, a:1, s:1, b:0),
% 0.97/1.64 c_Orderings_Oord__class_Oless__eq [119, 3] (w:1, o:258, a:1, s:1, b:0
% 0.97/1.64 ),
% 0.97/1.64 class_Rings_Oordered__cancel__semiring [126, 1] (w:1, o:151, a:1, s:1
% 0.97/1.64 , b:0),
% 0.97/1.64 class_Rings_Oordered__ring [127, 1] (w:1, o:152, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Oordered__semiring [129, 1] (w:1, o:153, a:1, s:1, b:0),
% 0.97/1.64
% 0.97/1.64 class_Rings_Oordered__comm__semiring [130, 1] (w:1, o:154, a:1, s:1
% 0.97/1.64 , b:0),
% 0.97/1.64 class_Rings_Olinordered__ring__strict [131, 1] (w:1, o:155, a:1, s:1
% 0.97/1.64 , b:0),
% 0.97/1.64 class_Rings_Olinordered__ring [132, 1] (w:1, o:156, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Oab__semigroup__mult [137, 1] (w:1, o:166, a:1, s:1, b:0
% 0.97/1.64 ),
% 0.97/1.64 class_RealVector_Oreal__normed__algebra [140, 1] (w:1, o:157, a:1, s:
% 0.97/1.64 1, b:0),
% 0.97/1.64 class_Rings_Ono__zero__divisors [141, 1] (w:1, o:150, a:1, s:1, b:0)
% 0.97/1.64 ,
% 0.97/1.64 class_Rings_Oring__no__zero__divisors [142, 1] (w:1, o:126, a:1, s:1
% 0.97/1.64 , b:0),
% 0.97/1.64 class_Rings_Omult__zero [143, 1] (w:1, o:149, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Ocomm__semiring [148, 1] (w:1, o:158, a:1, s:1, b:0),
% 0.97/1.64 class_Rings_Osemiring [150, 1] (w:1, o:159, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Oordered__ab__semigroup__add__imp__le [151, 1] (w:1, o:
% 0.97/1.64 167, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Oordered__ab__semigroup__add [152, 1] (w:1, o:168, a:1
% 0.97/1.64 , s:1, b:0),
% 0.97/1.64 class_Rings_Odvd [153, 1] (w:1, o:160, a:1, s:1, b:0),
% 0.97/1.64 class_Groups_Oordered__comm__monoid__add [154, 1] (w:1, o:169, a:1
% 0.97/1.64 , s:1, b:0),
% 0.97/1.64 class_Rings_Osemiring__0 [157, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.97/1.64 class_Orderings_Opreorder [158, 1] (w:1, o:172, a:1, s:1, b:0),
% 0.97/1.64 c_Orderings_Oord__class_Oless [159, 3] (w:1, o:259, a:1, s:1, b:0),
% 0.97/1.64 class_Orderings_Oorder [160, 1] (w:1, o:170, a:1, s:1, b:0),
% 0.97/1.64 c_Orderings_Oorder_Omono [161, 4] (w:1, o:293, a:1, s:1, b:0),
% 0.97/1.64 c_Nat_Onat_Onat__size [163, 1] (w:1, o:173, a:1, s:1, b:0),
% 0.97/1.64 class_Orderings_Olinorder [164, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.72/2.08 class_Orderings_Oord [165, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.72/2.08 class_Rings_Olinordered__idom [166, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.72/2.08 class_Groups_Oordered__cancel__ab__semigroup__add [171, 1] (w:1, o:
% 1.72/2.08 175, a:1, s:1, b:0),
% 1.72/2.08 class_Rings_Olinordered__semiring__strict [172, 1] (w:1, o:143, a:1
% 1.72/2.08 , s:1, b:0),
% 1.72/2.08 class_Rings_Olinordered__comm__semiring__strict [173, 1] (w:1, o:144
% 1.72/2.08 , a:1, s:1, b:0),
% 1.72/2.08 class_Rings_Olinordered__semidom [174, 1] (w:1, o:145, a:1, s:1, b:0)
% 1.72/2.08 ,
% 1.72/2.08 class_Rings_Olinordered__semiring [177, 1] (w:1, o:146, a:1, s:1, b:0
% 1.72/2.08 ),
% 1.72/2.08 tc_fun [178, 2] (w:1, o:242, a:1, s:1, b:0),
% 1.72/2.08 c_Nat_Osize__class_Osize [179, 2] (w:1, o:243, a:1, s:1, b:0),
% 1.72/2.08 c_Polynomial_Opdivmod__rel [181, 5] (w:1, o:305, a:1, s:1, b:0),
% 1.72/2.08 c_Polynomial_Opos__poly [182, 2] (w:1, o:244, a:1, s:1, b:0),
% 1.72/2.08 class_Rings_Olinordered__semiring__1__strict [194, 1] (w:1, o:147, a:
% 1.72/2.08 1, s:1, b:0),
% 1.72/2.08 c_Groups_Oone__class_Oone [195, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.72/2.08 c_fFalse [196, 0] (w:1, o:91, a:1, s:1, b:0),
% 1.72/2.08 c_HOL_Obool_Obool__size [197, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.72/2.08 class_Groups_Oone [198, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.72/2.08 class_Groups_Omonoid__mult [199, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.72/2.08 class_Groups_Ocomm__monoid__mult [200, 1] (w:1, o:180, a:1, s:1, b:0)
% 1.72/2.08 ,
% 1.72/2.08 class_Rings_Ozero__neq__one [201, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.72/2.08 class_Rings_Olinordered__semiring__1 [202, 1] (w:1, o:148, a:1, s:1
% 1.72/2.08 , b:0),
% 1.72/2.08 c_fTrue [203, 0] (w:1, o:92, a:1, s:1, b:0),
% 1.72/2.08 class_Rings_Ocomm__ring__1 [204, 1] (w:1, o:108, a:1, s:1, b:0),
% 1.72/2.08 c_Groups_Ouminus__class_Ouminus [205, 2] (w:1, o:245, a:1, s:1, b:0)
% 1.72/2.08 ,
% 1.72/2.08 c_Polynomial_Opoly__gcd [206, 3] (w:1, o:270, a:1, s:1, b:0),
% 1.72/2.08 class_Groups_Oordered__ab__group__add [207, 1] (w:1, o:181, a:1, s:1
% 1.72/2.08 , b:0),
% 1.72/2.08 class_Groups_Ogroup__add [208, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.72/2.08 class_Rings_Oring [209, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.72/2.08 class_Rings_Ocomm__ring [210, 1] (w:1, o:109, a:1, s:1, b:0),
% 1.72/2.08 class_Rings_Oring__1__no__zero__divisors [211, 1] (w:1, o:128, a:1
% 1.72/2.08 , s:1, b:0),
% 1.72/2.08 c_Power_Opower__class_Opower [212, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.72/2.08 tc_Int_Oint [213, 0] (w:1, o:94, a:1, s:1, b:0),
% 1.72/2.08 class_Power_Opower [214, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.72/2.08 class_Rings_Oring__1 [215, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.72/2.08 c_Power_Opower_Opower [217, 3] (w:1, o:271, a:1, s:1, b:0),
% 1.72/2.08 class_Lattices_Oboolean__algebra [218, 1] (w:1, o:186, a:1, s:1, b:0)
% 1.72/2.08 ,
% 1.72/2.08 class_Lattices_Oab__semigroup__idem__mult [222, 1] (w:1, o:185, a:1
% 1.72/2.08 , s:1, b:0),
% 1.72/2.08 class_Groups_Ouminus [224, 1] (w:1, o:187, a:1, s:1, b:0),
% 1.72/2.08 c_Complex_Oexpi [225, 1] (w:1, o:188, a:1, s:1, b:0),
% 1.72/2.08 c_RComplete_Onatceiling [228, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.72/2.08 c_RComplete_Onatfloor [229, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.72/2.08 c_RealDef_Oreal [230, 2] (w:1, o:246, a:1, s:1, b:0),
% 1.72/2.08 c_SEQ_Odecseq [232, 2] (w:1, o:248, a:1, s:1, b:0),
% 1.72/2.08 c_SEQ_Oincseq [234, 2] (w:1, o:249, a:1, s:1, b:0),
% 1.72/2.08 c_Complex_Ocis [235, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.72/2.08 c_Rings_Oinverse__class_Oinverse [236, 2] (w:1, o:247, a:1, s:1, b:0)
% 1.72/2.08 ,
% 1.72/2.08 class_Rings_Odivision__ring [237, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.72/2.08 class_Rings_Odivision__ring__inverse__zero [238, 1] (w:1, o:163, a:1
% 1.72/2.08 , s:1, b:0),
% 1.72/2.08 class_Fields_Olinordered__field [239, 1] (w:1, o:121, a:1, s:1, b:0)
% 1.72/2.08 ,
% 1.72/2.08 class_Fields_Olinordered__field__inverse__zero [240, 1] (w:1, o:122
% 1.72/2.08 , a:1, s:1, b:0),
% 1.72/2.08 class_Fields_Ofield__inverse__zero [241, 1] (w:1, o:123, a:1, s:1, b:
% 1.72/2.08 0),
% 1.72/2.08 c_Divides_Odiv__class_Omod [243, 3] (w:1, o:272, a:1, s:1, b:0),
% 1.72/2.08 class_Divides_Osemiring__div [245, 1] (w:1, o:193, a:1, s:1, b:0),
% 1.72/2.08 class_Divides_Oring__div [246, 1] (w:1, o:192, a:1, s:1, b:0),
% 1.72/2.08 class_Groups_Ocancel__comm__monoid__add [248, 1] (w:1, o:194, a:1, s:
% 1.72/2.08 1, b:0),
% 1.72/2.08 tc_HOL_Obool [250, 0] (w:1, o:93, a:1, s:1, b:0),
% 1.72/2.08 alpha1 [251, 3] (w:1, o:273, a:1, s:1, b:1),
% 1.72/2.08 alpha2 [252, 2] (w:1, o:253, a:1, s:1, b:1),
% 13.53/13.98 alpha3 [253, 2] (w:1, o:254, a:1, s:1, b:1),
% 13.53/13.98 alpha4 [254, 2] (w:1, o:255, a:1, s:1, b:1),
% 13.53/13.98 alpha5 [255, 2] (w:1, o:256, a:1, s:1, b:1),
% 13.53/13.98 alpha6 [256, 3] (w:1, o:274, a:1, s:1, b:1),
% 13.53/13.98 alpha7 [257, 3] (w:1, o:275, a:1, s:1, b:1),
% 13.53/13.98 alpha8 [258, 4] (w:1, o:294, a:1, s:1, b:1),
% 13.53/13.98 alpha9 [259, 4] (w:1, o:295, a:1, s:1, b:1),
% 13.53/13.98 alpha10 [260, 2] (w:1, o:250, a:1, s:1, b:1),
% 13.53/13.98 alpha11 [261, 3] (w:1, o:276, a:1, s:1, b:1),
% 13.53/13.98 alpha12 [262, 3] (w:1, o:277, a:1, s:1, b:1),
% 13.53/13.98 alpha13 [263, 4] (w:1, o:296, a:1, s:1, b:1),
% 13.53/13.98 alpha14 [264, 2] (w:1, o:251, a:1, s:1, b:1),
% 13.53/13.98 alpha15 [265, 2] (w:1, o:252, a:1, s:1, b:1),
% 13.53/13.98 alpha16 [266, 3] (w:1, o:278, a:1, s:1, b:1),
% 13.53/13.98 alpha17 [267, 3] (w:1, o:279, a:1, s:1, b:1),
% 13.53/13.98 alpha18 [268, 4] (w:1, o:297, a:1, s:1, b:1),
% 13.53/13.98 alpha19 [269, 4] (w:1, o:298, a:1, s:1, b:1),
% 13.53/13.98 alpha20 [270, 3] (w:1, o:280, a:1, s:1, b:1),
% 13.53/13.98 alpha21 [271, 4] (w:1, o:299, a:1, s:1, b:1),
% 13.53/13.98 alpha22 [272, 3] (w:1, o:281, a:1, s:1, b:1),
% 13.53/13.98 alpha23 [273, 3] (w:1, o:282, a:1, s:1, b:1),
% 13.53/13.98 alpha24 [274, 3] (w:1, o:283, a:1, s:1, b:1),
% 13.53/13.98 alpha25 [275, 3] (w:1, o:284, a:1, s:1, b:1),
% 13.53/13.98 alpha26 [276, 4] (w:1, o:300, a:1, s:1, b:1),
% 13.53/13.98 alpha27 [277, 4] (w:1, o:301, a:1, s:1, b:1),
% 13.53/13.98 alpha28 [278, 4] (w:1, o:302, a:1, s:1, b:1),
% 13.53/13.98 skol1 [279, 2] (w:1, o:228, a:1, s:1, b:1),
% 13.53/13.98 skol2 [280, 1] (w:1, o:112, a:1, s:1, b:1),
% 13.53/13.98 skol3 [281, 3] (w:1, o:287, a:1, s:1, b:1),
% 13.53/13.98 skol4 [282, 2] (w:1, o:229, a:1, s:1, b:1),
% 13.53/13.98 skol5 [283, 3] (w:1, o:288, a:1, s:1, b:1),
% 13.53/13.98 skol6 [284, 2] (w:1, o:230, a:1, s:1, b:1),
% 13.53/13.98 skol7 [285, 2] (w:1, o:231, a:1, s:1, b:1),
% 13.53/13.98 skol8 [286, 1] (w:1, o:113, a:1, s:1, b:1),
% 13.53/13.98 skol9 [287, 2] (w:1, o:232, a:1, s:1, b:1),
% 13.53/13.98 skol10 [288, 3] (w:1, o:289, a:1, s:1, b:1),
% 13.53/13.98 skol11 [289, 3] (w:1, o:290, a:1, s:1, b:1),
% 13.53/13.98 skol12 [290, 3] (w:1, o:291, a:1, s:1, b:1),
% 13.53/13.98 skol13 [291, 4] (w:1, o:303, a:1, s:1, b:1),
% 13.53/13.98 skol14 [292, 2] (w:1, o:233, a:1, s:1, b:1),
% 13.53/13.98 skol15 [293, 2] (w:1, o:234, a:1, s:1, b:1),
% 13.53/13.98 skol16 [294, 1] (w:1, o:111, a:1, s:1, b:1),
% 13.53/13.98 skol17 [295, 2] (w:1, o:235, a:1, s:1, b:1),
% 13.53/13.98 skol18 [296, 2] (w:1, o:236, a:1, s:1, b:1),
% 13.53/13.98 skol19 [297, 2] (w:1, o:237, a:1, s:1, b:1),
% 13.53/13.98 skol20 [298, 2] (w:1, o:238, a:1, s:1, b:1),
% 13.53/13.98 skol21 [299, 2] (w:1, o:239, a:1, s:1, b:1),
% 13.53/13.98 skol22 [300, 1] (w:1, o:114, a:1, s:1, b:1),
% 13.53/13.98 skol23 [301, 3] (w:1, o:285, a:1, s:1, b:1),
% 13.53/13.98 skol24 [302, 1] (w:1, o:115, a:1, s:1, b:1),
% 13.53/13.98 skol25 [303, 3] (w:1, o:286, a:1, s:1, b:1),
% 13.53/13.98 skol26 [304, 2] (w:1, o:240, a:1, s:1, b:1),
% 13.53/13.98 skol27 [305, 2] (w:1, o:241, a:1, s:1, b:1).
% 13.53/13.98
% 13.53/13.98
% 13.53/13.98 Starting Search:
% 13.53/13.98
% 13.53/13.98 *** allocated 113905 integers for clauses
% 13.53/13.98 *** allocated 170857 integers for clauses
% 13.53/13.98 Resimplifying inuse:
% 13.53/13.98 Done
% 13.53/13.98
% 13.53/13.98
% 13.53/13.98 Intermediate Status:
% 13.53/13.98 Generated: 3121
% 13.53/13.98 Kept: 2009
% 13.53/13.98 Inuse: 36
% 13.53/13.98 Deleted: 0
% 13.53/13.98 Deletedinuse: 0
% 13.53/13.98
% 13.53/13.98 *** allocated 256285 integers for clauses
% 13.53/13.98 Resimplifying inuse:
% 13.53/13.98 Done
% 13.53/13.98
% 13.53/13.98 *** allocated 170857 integers for termspace/termends
% 13.53/13.98 Resimplifying inuse:
% 13.53/13.98 Done
% 13.53/13.98
% 13.53/13.98
% 13.53/13.98 Intermediate Status:
% 13.53/13.98 Generated: 6712
% 13.53/13.98 Kept: 4013
% 13.53/13.98 Inuse: 160
% 13.53/13.98 Deleted: 0
% 13.53/13.98 Deletedinuse: 0
% 13.53/13.98
% 13.53/13.98 *** allocated 384427 integers for clauses
% 13.53/13.98 Resimplifying inuse:
% 13.53/13.98 Done
% 13.53/13.98
% 13.53/13.98 *** allocated 256285 integers for termspace/termends
% 13.53/13.98 Resimplifying inuse:
% 13.53/13.98 Done
% 13.53/13.98
% 13.53/13.98
% 13.53/13.98 Intermediate Status:
% 13.53/13.98 Generated: 12926
% 13.53/13.98 Kept: 6021
% 13.53/13.98 Inuse: 200
% 13.53/13.98 Deleted: 1
% 13.53/13.98 Deletedinuse: 1
% 13.53/13.98
% 13.53/13.98 *** allocated 576640 integers for clauses
% 13.53/13.98 Resimplifying inuse:
% 13.53/13.98 Done
% 13.53/13.98
% 13.53/13.98
% 13.53/13.98 Intermediate Status:
% 13.53/13.98 Generated: 18865
% 13.53/13.98 Kept: 8058
% 13.53/13.98 Inuse: 236
% 13.53/13.98 Deleted: 1
% 13.53/13.98 Deletedinuse: 1
% 13.53/13.98
% 13.53/13.98 *** allocated 384427 integers for termspace/termends
% 13.53/13.98 Resimplifying inuse:
% 13.53/13.98 Done
% 13.53/13.98
% 13.53/13.98
% 13.53/13.98 Intermediate Status:
% 13.53/13.98 Generated: 23160
% 13.53/13.98 Kept: 10073
% 13.53/13.98 Inuse: 271
% 13.53/13.98 Deleted: 1
% 13.53/13.98 Deletedinuse: 1
% 13.53/13.98
% 13.53/13.98 Resimplifying inuse:
% 13.53/13.98 Done
% 13.53/13.98
% 13.53/13.98 *** allocated 864960 integers for clauses
% 13.53/13.98 Resimplifying inuse:
% 13.53/13.98 Done
% 13.53/13.98
% 13.53/13.98
% 13.53/13.98 Intermediate Status:
% 13.53/13.98 Generated: 28443
% 13.53/13.98 Kept: 12481
% 13.53/13.98 Inuse: 296
% 43.80/44.37 Deleted: 1
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 *** allocated 576640 integers for termspace/termends
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 33252
% 43.80/44.37 Kept: 14523
% 43.80/44.37 Inuse: 336
% 43.80/44.37 Deleted: 1
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 *** allocated 1297440 integers for clauses
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 38053
% 43.80/44.37 Kept: 17035
% 43.80/44.37 Inuse: 361
% 43.80/44.37 Deleted: 1
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 42175
% 43.80/44.37 Kept: 19050
% 43.80/44.37 Inuse: 386
% 43.80/44.37 Deleted: 2
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying clauses:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 50020
% 43.80/44.37 Kept: 21505
% 43.80/44.37 Inuse: 400
% 43.80/44.37 Deleted: 146
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 *** allocated 864960 integers for termspace/termends
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 57428
% 43.80/44.37 Kept: 23507
% 43.80/44.37 Inuse: 429
% 43.80/44.37 Deleted: 146
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 61599
% 43.80/44.37 Kept: 25509
% 43.80/44.37 Inuse: 450
% 43.80/44.37 Deleted: 146
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 *** allocated 1946160 integers for clauses
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 66793
% 43.80/44.37 Kept: 27523
% 43.80/44.37 Inuse: 485
% 43.80/44.37 Deleted: 146
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 72870
% 43.80/44.37 Kept: 29531
% 43.80/44.37 Inuse: 516
% 43.80/44.37 Deleted: 146
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 78810
% 43.80/44.37 Kept: 31880
% 43.80/44.37 Inuse: 530
% 43.80/44.37 Deleted: 146
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 *** allocated 1297440 integers for termspace/termends
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 84670
% 43.80/44.37 Kept: 34146
% 43.80/44.37 Inuse: 540
% 43.80/44.37 Deleted: 146
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 89634
% 43.80/44.37 Kept: 36171
% 43.80/44.37 Inuse: 555
% 43.80/44.37 Deleted: 146
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 95177
% 43.80/44.37 Kept: 38185
% 43.80/44.37 Inuse: 575
% 43.80/44.37 Deleted: 146
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 99221
% 43.80/44.37 Kept: 40203
% 43.80/44.37 Inuse: 587
% 43.80/44.37 Deleted: 146
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 *** allocated 2919240 integers for clauses
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying clauses:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 103919
% 43.80/44.37 Kept: 43108
% 43.80/44.37 Inuse: 595
% 43.80/44.37 Deleted: 177
% 43.80/44.37 Deletedinuse: 1
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 110258
% 43.80/44.37 Kept: 45963
% 43.80/44.37 Inuse: 620
% 43.80/44.37 Deleted: 178
% 43.80/44.37 Deletedinuse: 2
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 114661
% 43.80/44.37 Kept: 48966
% 43.80/44.37 Inuse: 630
% 43.80/44.37 Deleted: 178
% 43.80/44.37 Deletedinuse: 2
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 118199
% 43.80/44.37 Kept: 50980
% 43.80/44.37 Inuse: 640
% 43.80/44.37 Deleted: 178
% 43.80/44.37 Deletedinuse: 2
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 124254
% 43.80/44.37 Kept: 53046
% 43.80/44.37 Inuse: 651
% 43.80/44.37 Deleted: 178
% 43.80/44.37 Deletedinuse: 2
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 128114
% 43.80/44.37 Kept: 55234
% 43.80/44.37 Inuse: 660
% 43.80/44.37 Deleted: 178
% 43.80/44.37 Deletedinuse: 2
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 *** allocated 1946160 integers for termspace/termends
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 132320
% 43.80/44.37 Kept: 57652
% 43.80/44.37 Inuse: 675
% 43.80/44.37 Deleted: 178
% 43.80/44.37 Deletedinuse: 2
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 136908
% 43.80/44.37 Kept: 59677
% 43.80/44.37 Inuse: 694
% 43.80/44.37 Deleted: 178
% 43.80/44.37 Deletedinuse: 2
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying clauses:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 43.80/44.37 Generated: 144494
% 43.80/44.37 Kept: 62847
% 43.80/44.37 Inuse: 705
% 43.80/44.37 Deleted: 315
% 43.80/44.37 Deletedinuse: 2
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37 Resimplifying inuse:
% 43.80/44.37 Done
% 43.80/44.37
% 43.80/44.37
% 43.80/44.37 Intermediate Status:
% 112.88/113.53 Generated: 148874
% 112.88/113.53 Kept: 64884
% 112.88/113.53 Inuse: 729
% 112.88/113.53 Deleted: 315
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 *** allocated 4378860 integers for clauses
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 158437
% 112.88/113.53 Kept: 67557
% 112.88/113.53 Inuse: 750
% 112.88/113.53 Deleted: 315
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 163424
% 112.88/113.53 Kept: 70778
% 112.88/113.53 Inuse: 755
% 112.88/113.53 Deleted: 315
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 167956
% 112.88/113.53 Kept: 72886
% 112.88/113.53 Inuse: 775
% 112.88/113.53 Deleted: 315
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 172669
% 112.88/113.53 Kept: 74963
% 112.88/113.53 Inuse: 797
% 112.88/113.53 Deleted: 315
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 177727
% 112.88/113.53 Kept: 78274
% 112.88/113.53 Inuse: 800
% 112.88/113.53 Deleted: 315
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 187312
% 112.88/113.53 Kept: 81545
% 112.88/113.53 Inuse: 815
% 112.88/113.53 Deleted: 315
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying clauses:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 196672
% 112.88/113.53 Kept: 84147
% 112.88/113.53 Inuse: 825
% 112.88/113.53 Deleted: 342
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 *** allocated 2919240 integers for termspace/termends
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 204411
% 112.88/113.53 Kept: 86171
% 112.88/113.53 Inuse: 847
% 112.88/113.53 Deleted: 342
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 212161
% 112.88/113.53 Kept: 88337
% 112.88/113.53 Inuse: 865
% 112.88/113.53 Deleted: 342
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 220047
% 112.88/113.53 Kept: 90392
% 112.88/113.53 Inuse: 885
% 112.88/113.53 Deleted: 342
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 228038
% 112.88/113.53 Kept: 92668
% 112.88/113.53 Inuse: 890
% 112.88/113.53 Deleted: 342
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 235889
% 112.88/113.53 Kept: 94718
% 112.88/113.53 Inuse: 913
% 112.88/113.53 Deleted: 342
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 246689
% 112.88/113.53 Kept: 97066
% 112.88/113.53 Inuse: 930
% 112.88/113.53 Deleted: 342
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 256787
% 112.88/113.53 Kept: 99308
% 112.88/113.53 Inuse: 945
% 112.88/113.53 Deleted: 342
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 *** allocated 6568290 integers for clauses
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 264296
% 112.88/113.53 Kept: 101415
% 112.88/113.53 Inuse: 960
% 112.88/113.53 Deleted: 342
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying clauses:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 271314
% 112.88/113.53 Kept: 103445
% 112.88/113.53 Inuse: 978
% 112.88/113.53 Deleted: 613
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 277852
% 112.88/113.53 Kept: 105458
% 112.88/113.53 Inuse: 1001
% 112.88/113.53 Deleted: 613
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 284497
% 112.88/113.53 Kept: 107525
% 112.88/113.53 Inuse: 1023
% 112.88/113.53 Deleted: 613
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 295686
% 112.88/113.53 Kept: 110834
% 112.88/113.53 Inuse: 1046
% 112.88/113.53 Deleted: 613
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 302442
% 112.88/113.53 Kept: 112852
% 112.88/113.53 Inuse: 1076
% 112.88/113.53 Deleted: 613
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 312815
% 112.88/113.53 Kept: 115141
% 112.88/113.53 Inuse: 1110
% 112.88/113.53 Deleted: 613
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 345454
% 112.88/113.53 Kept: 118613
% 112.88/113.53 Inuse: 1115
% 112.88/113.53 Deleted: 613
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53
% 112.88/113.53 Intermediate Status:
% 112.88/113.53 Generated: 354502
% 112.88/113.53 Kept: 120953
% 112.88/113.53 Inuse: 1135
% 112.88/113.53 Deleted: 613
% 112.88/113.53 Deletedinuse: 2
% 112.88/113.53
% 112.88/113.53 Resimplifying inuse:
% 112.88/113.53 Done
% 112.88/113.53
% 112.88/113.53 *** allocated 4378860 integers for termspace/termends
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying clauses:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 365973
% 282.10/282.73 Kept: 124468
% 282.10/282.73 Inuse: 1145
% 282.10/282.73 Deleted: 985
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 386737
% 282.10/282.73 Kept: 127915
% 282.10/282.73 Inuse: 1160
% 282.10/282.73 Deleted: 985
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 405120
% 282.10/282.73 Kept: 130605
% 282.10/282.73 Inuse: 1165
% 282.10/282.73 Deleted: 985
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 412959
% 282.10/282.73 Kept: 132693
% 282.10/282.73 Inuse: 1190
% 282.10/282.73 Deleted: 985
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 420095
% 282.10/282.73 Kept: 134834
% 282.10/282.73 Inuse: 1215
% 282.10/282.73 Deleted: 985
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 427075
% 282.10/282.73 Kept: 137088
% 282.10/282.73 Inuse: 1245
% 282.10/282.73 Deleted: 985
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 435139
% 282.10/282.73 Kept: 139931
% 282.10/282.73 Inuse: 1265
% 282.10/282.73 Deleted: 985
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 440640
% 282.10/282.73 Kept: 141954
% 282.10/282.73 Inuse: 1281
% 282.10/282.73 Deleted: 985
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 445971
% 282.10/282.73 Kept: 145043
% 282.10/282.73 Inuse: 1285
% 282.10/282.73 Deleted: 985
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying clauses:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 453444
% 282.10/282.73 Kept: 148051
% 282.10/282.73 Inuse: 1300
% 282.10/282.73 Deleted: 1054
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 460075
% 282.10/282.73 Kept: 150124
% 282.10/282.73 Inuse: 1330
% 282.10/282.73 Deleted: 1054
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 *** allocated 9852435 integers for clauses
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 495704
% 282.10/282.73 Kept: 153638
% 282.10/282.73 Inuse: 1340
% 282.10/282.73 Deleted: 1054
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 509777
% 282.10/282.73 Kept: 157536
% 282.10/282.73 Inuse: 1365
% 282.10/282.73 Deleted: 1054
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 516911
% 282.10/282.73 Kept: 159784
% 282.10/282.73 Inuse: 1370
% 282.10/282.73 Deleted: 1054
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 524569
% 282.10/282.73 Kept: 161795
% 282.10/282.73 Inuse: 1385
% 282.10/282.73 Deleted: 1054
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 536118
% 282.10/282.73 Kept: 164546
% 282.10/282.73 Inuse: 1400
% 282.10/282.73 Deleted: 1054
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 *** allocated 6568290 integers for termspace/termends
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying clauses:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 545054
% 282.10/282.73 Kept: 166550
% 282.10/282.73 Inuse: 1407
% 282.10/282.73 Deleted: 1145
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 554874
% 282.10/282.73 Kept: 168556
% 282.10/282.73 Inuse: 1426
% 282.10/282.73 Deleted: 1145
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 563566
% 282.10/282.73 Kept: 171031
% 282.10/282.73 Inuse: 1430
% 282.10/282.73 Deleted: 1145
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 570340
% 282.10/282.73 Kept: 173055
% 282.10/282.73 Inuse: 1442
% 282.10/282.73 Deleted: 1145
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 578754
% 282.10/282.73 Kept: 175449
% 282.10/282.73 Inuse: 1445
% 282.10/282.73 Deleted: 1145
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 612262
% 282.10/282.73 Kept: 180736
% 282.10/282.73 Inuse: 1460
% 282.10/282.73 Deleted: 1145
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 620436
% 282.10/282.73 Kept: 182814
% 282.10/282.73 Inuse: 1480
% 282.10/282.73 Deleted: 1145
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73
% 282.10/282.73 Intermediate Status:
% 282.10/282.73 Generated: 629625
% 282.10/282.73 Kept: 184820
% 282.10/282.73 Inuse: 1504
% 282.10/282.73 Deleted: 1145
% 282.10/282.73 Deletedinuse: 2
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 Resimplifying inuse:
% 282.10/282.73 Done
% 282.10/282.73
% 282.10/282.73 ResimplifCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------