TSTP Solution File: SWW184+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW184+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 23:21:06 EDT 2022
% Result : Timeout 300.04s 300.45s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW184+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.14 % Command : bliksem %s
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Sun Jun 5 05:43:52 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.02/1.66 *** allocated 10000 integers for termspace/termends
% 1.02/1.66 *** allocated 10000 integers for clauses
% 1.02/1.66 *** allocated 10000 integers for justifications
% 1.02/1.66 *** allocated 15000 integers for termspace/termends
% 1.02/1.66 *** allocated 22500 integers for termspace/termends
% 1.02/1.66 *** allocated 33750 integers for termspace/termends
% 1.02/1.66 Bliksem 1.12
% 1.02/1.66
% 1.02/1.66
% 1.02/1.66 Automatic Strategy Selection
% 1.02/1.66
% 1.02/1.66 *** allocated 50625 integers for termspace/termends
% 1.02/1.66 *** allocated 75937 integers for termspace/termends
% 1.02/1.66 *** allocated 113905 integers for termspace/termends
% 1.02/1.66
% 1.02/1.66 Clauses:
% 1.02/1.66
% 1.02/1.66 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.02/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.02/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.02/1.66 c_Polynomial_OpCons( X, Z, c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Polynomial_OpCons( X, Z,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( T, X, Y,
% 1.02/1.66 Z, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.66 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.66 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, Z, Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.66 c_Polynomial_OpCons( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Y,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = c_Polynomial_OpCons( X, Y
% 1.02/1.66 , c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! Z = Y, hAPP( c_Polynomial_Ocoeff( X, Z ), T
% 1.02/1.66 ) = hAPP( c_Polynomial_Ocoeff( X, Y ), T ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ), skol2( X
% 1.02/1.66 , Y, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ), skol2( X, Y, Z ) ), Z = Y
% 1.02/1.66 }.
% 1.02/1.66 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.02/1.66 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.02/1.66 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.02/1.66 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_Ocoeff( X, Z ) =
% 1.02/1.66 c_Polynomial_Ocoeff( X, Y ), Z = Y }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! Z = Y, c_Polynomial_Ocoeff( X, Z ) =
% 1.02/1.66 c_Polynomial_Ocoeff( X, Y ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.66 c_Polynomial_OpCons( X, Z, Y ) ), c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Nat_Onat ) ) = Z }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.66 c_Polynomial_Omonom( X, Y, T ) ), Z ) = Y }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), T = Z, hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.66 c_Polynomial_Omonom( X, Y, T ) ), Z ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.02/1.66 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.02/1.66 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.02/1.66 c_Polynomial_OpCons( X, Z, Y ), U = Z }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! c_Polynomial_OpCons( X, U, T ) =
% 1.02/1.66 c_Polynomial_OpCons( X, Z, Y ), T = Y }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! U = Z, ! T = Y, c_Polynomial_OpCons( X, U, T
% 1.02/1.66 ) = c_Polynomial_OpCons( X, Z, Y ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osmult( X, T, Y ) =
% 1.02/1.66 c_Polynomial_OpCons( X, Z, Y ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Opoly__rec( W, X, U, T,
% 1.02/1.66 c_Polynomial_OpCons( X, Z, Y ) ) = hAPP( hAPP( hAPP( T, Z ), Y ), c_If( W
% 1.02/1.66 , c_fequal( Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) )
% 1.02/1.66 , U, c_Polynomial_Opoly__rec( W, X, U, T, Y ) ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.02/1.66 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.66 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! hAPP( hAPP( hAPP( Z,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) ), Y ) = Y, c_Polynomial_Opoly__rec( W, X, Y,
% 1.02/1.66 Z, c_Polynomial_OpCons( X, U, T ) ) = hAPP( hAPP( hAPP( Z, U ), T ),
% 1.02/1.66 c_Polynomial_Opoly__rec( W, X, Y, Z, T ) ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.66 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.02/1.66 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Polynomial_OpCons( X, hAPP(
% 1.02/1.66 c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z, Y )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Ocoeff( X, c_Polynomial_OpCons( X
% 1.02/1.66 , Z, Y ) ) = c_Nat_Onat_Onat__case( X, Z, c_Polynomial_Ocoeff( X, Y ) ) }
% 1.02/1.66 .
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ),
% 1.02/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X,
% 1.02/1.66 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Y,
% 1.02/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ),
% 1.02/1.66 c_Polynomial_OpCons( X, T,
% 1.02/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, Z, Y ) ) ) }
% 1.02/1.66 .
% 1.02/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X, Z, c_Nat_OSuc( Y ) ) =
% 1.02/1.66 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.66 c_Polynomial_Omonom( X, Z, Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.66 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.66 c_Polynomial_Opcompose( X, T, Z ) ), Y ) = hAPP( c_Polynomial_Opoly( X, T
% 1.02/1.66 ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.02/1.66 ( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ),
% 1.02/1.66 alpha1( X, Y, T ) }.
% 1.02/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.02/1.66 ( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ),
% 1.02/1.66 alpha19( X, Y, Z, T ) }.
% 1.02/1.66 { ! class_Fields_Ofield( X ), ! alpha1( X, Y, T ), ! alpha19( X, Y, Z, T )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.02/1.66 , c_Polynomial_Osmult( X, T, Z ) ), Y ) ) }.
% 1.02/1.66 { ! alpha19( X, Y, Z, T ), T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.02/1.66 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.02/1.66 ) ) }.
% 1.02/1.66 { ! T = c_Groups_Ozero__class_Ozero( X ), alpha19( X, Y, Z, T ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.02/1.66 , Z ), Y ) ), alpha19( X, Y, Z, T ) }.
% 1.02/1.66 { ! alpha1( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { Z = c_Groups_Ozero__class_Ozero( X ), alpha1( X, Y, Z ) }.
% 1.02/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha1( X
% 1.02/1.66 , Y, Z ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.66 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.66 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.66 c_Polynomial_Odegree( X, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero
% 1.02/1.66 ( tc_Polynomial_Opoly( X ) ) ) ), hBOOL( hAPP( Y, skol3( Z, Y ) ) ),
% 1.02/1.66 hBOOL( hAPP( Y, T ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero
% 1.02/1.66 ( tc_Polynomial_Opoly( X ) ) ) ), ! hBOOL( hAPP( Y, c_Polynomial_OpCons(
% 1.02/1.66 X, skol18( X, Y ), skol3( X, Y ) ) ) ), hBOOL( hAPP( Y, Z ) ) }.
% 1.02/1.66 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.66 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 T, Y ), Z = Y }.
% 1.02/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 T, Y ) }.
% 1.02/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 Y, Z ), T = Y }.
% 1.02/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 Y, Z ) }.
% 1.02/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 T, Y ), Z = Y }.
% 1.02/1.66 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 T, Y ), Z = Y }.
% 1.02/1.66 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 Y, T ), Z = Y }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.02/1.66 c_Polynomial_Odegree( X, Z ) ) = hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.66 c_Polynomial_Odegree( X, Y ) ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL
% 1.02/1.66 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Y ),
% 1.02/1.66 Z ) ), Z = Y }.
% 1.02/1.66 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.02/1.66 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, U, Z ), c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.66 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.66 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.66 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y ),
% 1.02/1.66 hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.02/1.66 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.66 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.02/1.66 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Osynthetic__div( X
% 1.02/1.66 , Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.66 c_Polynomial_Odegree( X, Z ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.66 }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Polynomial_Odegree( X, Z ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Polynomial_Osynthetic__div
% 1.02/1.66 ( X, Z, Y ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.02/1.66 ( X, Z, Y ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Y ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.02/1.66 ( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, c_Polynomial_OpCons
% 1.02/1.66 ( X, Y, Z ) ) = c_Nat_OSuc( c_Polynomial_Odegree( X, Z ) ) }.
% 1.02/1.66 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.66 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.66 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.02/1.66 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.66 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.66 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult
% 1.02/1.66 ( X, T, Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), hBOOL(
% 1.02/1.66 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 1.02/1.66 c_Polynomial_Osmult( X, T, Y ) ) ) }.
% 1.02/1.66 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.02/1.66 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.02/1.66 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.66 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.66 c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) ) =
% 1.02/1.66 c_Polynomial_Odegree( X, Y ) }.
% 1.02/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.02/1.66 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Osmult( X, Z, Y ) ) ), Z
% 1.02/1.66 = c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }.
% 1.02/1.66 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.02/1.66 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), T = c_Groups_Ozero__class_Ozero
% 1.02/1.66 ( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.02/1.66 X ) ), c_Polynomial_Osmult( X, T, Z ) ), Y ) ) }.
% 1.02/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 1.02/1.66 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.66 c_Polynomial_Osmult( X, Y, Z ) ) ), hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Z ) ) }.
% 1.02/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! hBOOL
% 1.02/1.66 ( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.66 Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly(
% 1.02/1.66 X ) ), T ), c_Polynomial_Osmult( X, Y, Z ) ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_Odegree( X, c_Polynomial_OpCons(
% 1.02/1.66 X, Y, c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.66 c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Y, Z ) ) = Z }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.02/1.66 c_Polynomial_OpCons( X, Y, Z ), Y = hAPP( c_Polynomial_Opoly( X, U ), T )
% 1.02/1.66 }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), ! c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), U, c_Polynomial_Osmult( X, T, Z ) ) =
% 1.02/1.66 c_Polynomial_OpCons( X, Y, Z ), Z = c_Polynomial_Osynthetic__div( X, U, T
% 1.02/1.66 ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, Y,
% 1.02/1.66 c_Polynomial_Osynthetic__div( X, Z, Y ) ) ) = c_Polynomial_OpCons( X,
% 1.02/1.66 hAPP( c_Polynomial_Opoly( X, Z ), Y ), c_Polynomial_Osynthetic__div( X, Z
% 1.02/1.66 , Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osynthetic__div( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.66 c_Polynomial_OpCons( X, T, Z ) ), c_Nat_OSuc( Y ) ) = hAPP(
% 1.02/1.66 c_Polynomial_Ocoeff( X, Z ), Y ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.66 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( X, T, Z ) ), Y
% 1.02/1.66 ) = hAPP( c_Polynomial_Opoly( X, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.66 , Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) )
% 1.02/1.66 }.
% 1.02/1.66 { hAPP( c_Nat_Onat_Onat__case( T, Z, Y ), c_Nat_OSuc( X ) ) = hAPP( Y, X )
% 1.02/1.66 }.
% 1.02/1.66 { hAPP( c_Nat_Onat_Onat__case( Z, Y, X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Nat_Onat ) ) = Y }.
% 1.02/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.02/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.02/1.66 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.02/1.66 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, Y, T
% 1.02/1.66 ) ) ) }.
% 1.02/1.66 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), c_Nat_OSuc(
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) ) }.
% 1.02/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.02/1.66 ( tc_Nat_Onat ) ) = X }.
% 1.02/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Nat_Onat ), X ) = X }.
% 1.02/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.02/1.66 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.66 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 1.02/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.02/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.66 { ! X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hBOOL(
% 1.02/1.66 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Nat_OSuc(
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha2( X, Y ), alpha20( X
% 1.02/1.66 , Y ) }.
% 1.02/1.66 { ! alpha2( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.66 { ! alpha20( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.66 { ! alpha20( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! alpha20( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Nat_Onat ) ) }.
% 1.02/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha20( X, Y ) }.
% 1.02/1.66 { ! alpha2( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Nat_Onat ) ) }.
% 1.02/1.66 { ! alpha2( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha2( X, Y ) }.
% 1.02/1.66 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha3( X, Y ), alpha21
% 1.02/1.66 ( X, Y ) }.
% 1.02/1.66 { ! alpha3( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.66 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.66 { ! alpha21( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.66 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.66 { ! alpha21( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! alpha21( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Nat_Onat ) ) }.
% 1.02/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha21( X, Y ) }.
% 1.02/1.66 { ! alpha3( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Nat_Onat ) ) }.
% 1.02/1.66 { ! alpha3( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha3( X, Y ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Y ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Y ), T ) ), hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ) }.
% 1.02/1.66 { ! X = c_Nat_OSuc( X ) }.
% 1.02/1.66 { ! c_Nat_OSuc( X ) = X }.
% 1.02/1.66 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.02/1.66 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.02/1.66 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) )
% 1.02/1.66 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.66 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.66 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.66 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.02/1.66 { ! class_Groups_Ozero( X ), c_Polynomial_OpCons( X, Z, Y ) =
% 1.02/1.66 c_Polynomial_OAbs__poly( X, c_Nat_Onat_Onat__case( X, Z,
% 1.02/1.66 c_Polynomial_Ocoeff( X, Y ) ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Opcompose( X,
% 1.02/1.66 c_Polynomial_OpCons( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, T,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.02/1.66 c_Polynomial_Opcompose( X, Z, Y ) ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.66 c_Polynomial_OpCons( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, Z, T ),
% 1.02/1.66 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) ) }
% 1.02/1.66 .
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.66 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.02/1.66 c_Polynomial_OpCons( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ) ) }
% 1.02/1.66 .
% 1.02/1.66 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.66 tc_Nat_Onat, c_Polynomial_Oorder( X, Z, Y ), c_Polynomial_Odegree( X, Y )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), Z ), Y ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.66 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.02/1.66 }.
% 1.02/1.66 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), X ) ) }
% 1.02/1.66 .
% 1.02/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.66 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha4( X, Y
% 1.02/1.66 , Z ), alpha22( X, Y, Z ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha4( X, Y, Z ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha22( X, Y, Z ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.66 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.66 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.66 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ), alpha22( X, Y, Z ) }.
% 1.02/1.66 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.66 { ! alpha4( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Y ), alpha4( X, Y, Z ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.66 ( X ) ), alpha5( X, Y, Z ), alpha23( X, Y, Z ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha5( X, Y, Z ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.66 ( X ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha23( X, Y, Z ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.66 ( X ) ) }.
% 1.02/1.66 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.66 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.66 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.02/1.66 ( X ), Y ), alpha23( X, Y, Z ) }.
% 1.02/1.66 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.66 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ), alpha5( X, Y, Z ) }.
% 1.02/1.66 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.66 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.66 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.66 ( X ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.66 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.66 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.66 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.66 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.66 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__semiring( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.66 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.66 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.66 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.66 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.66 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.66 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.66 ( X ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.02/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.02/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.02/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.02/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.02/1.66 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.02/1.66 ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.02/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.02/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.02/1.66 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.02/1.66 ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.02/1.66 ), Z ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! X = Z, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.02/1.66 Z ), Y ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! X = Y }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! Y = X }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.02/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.02/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , ! Y = X }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.02/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.02/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.02/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X )
% 1.02/1.66 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y
% 1.02/1.66 ) ) }.
% 1.02/1.66 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.02/1.66 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.02/1.66 ), X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.02/1.66 ), Z ) ) }.
% 1.02/1.66 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.02/1.66 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.02/1.66 ), X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.02/1.66 Z ), Y ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Z )
% 1.02/1.66 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.02/1.66 ), Y = X }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.02/1.66 ), Y = X }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , ! X = Z, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.02/1.66 ), Z ) ) }.
% 1.02/1.66 { ! Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.02/1.66 ), Z ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y
% 1.02/1.66 ), Z ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.02/1.66 , X ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.02/1.66 ), Y ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , Y = X }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.02/1.66 ), Y = X }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.02/1.66 ), X = Y }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , ! X = Y, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.02/1.66 ), Y ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.66 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.02/1.66 , X ) ) }.
% 1.02/1.66 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.02/1.66 , X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.02/1.66 , X ) ) }.
% 1.02/1.66 { Y = X, ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.02/1.66 , X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X
% 1.02/1.66 ), Y ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.02/1.66 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.02/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.02/1.66 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.02/1.66 { ! alpha6( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.66 tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.66 { ! alpha6( X, Y ), ! Y = X }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , Y = X, alpha6( X, Y ) }.
% 1.02/1.66 { ! alpha6( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.66 tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.66 { ! alpha6( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.66 tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , alpha6( X, Y ) }.
% 1.02/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.66 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.02/1.66 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ), hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , alpha7( X, Y ), Y = X }.
% 1.02/1.66 { ! alpha7( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.66 tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.66 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.02/1.66 , X ) ) }.
% 1.02/1.66 { ! alpha7( X, Y ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.66 tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.66 { ! alpha7( X, Y ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.66 tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y ) )
% 1.02/1.66 , alpha7( X, Y ) }.
% 1.02/1.66 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y )
% 1.02/1.66 , X ) ) }.
% 1.02/1.66 { ! Y = X, hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X )
% 1.02/1.66 , Y ) ) }.
% 1.02/1.66 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.66 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), Y )
% 1.02/1.66 ), Y = X }.
% 1.02/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol4( X, Y ) ) }.
% 1.02/1.66 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.02/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.02/1.66 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.02/1.66 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.02/1.66 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ),
% 1.02/1.66 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.66 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.66 ), U = Z, T = Y }.
% 1.02/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.66 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.66 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.02/1.66 ) ), Z ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.66 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.66 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.66 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.66 ), ! U = T }.
% 1.02/1.66 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.66 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.02/1.66 ), ! Z = Y }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.02/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.02/1.66 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.02/1.66 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.02/1.66 ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.66 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.02/1.66 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.02/1.66 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.66 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 }.
% 1.02/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 }.
% 1.02/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.66 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.02/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.02/1.66 ) ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.02/1.66 Z ), c_Polynomial_Odegree( X, Y ) ) ) = hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.02/1.66 c_Polynomial_Odegree( X, Z ) ) ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.66 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.02/1.66 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.66 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.66 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.02/1.66 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.02/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.02/1.66 ) ), T ), Y ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.66 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.66 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.66 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.66 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.66 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.66 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.66 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.66 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.66 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.66 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.66 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.66 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.02/1.66 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), T ), Z ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 1.02/1.66 ), Z ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), Z ), T ) ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X
% 1.02/1.66 ), Z ), Y ) ) }.
% 1.02/1.66 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), Y ), T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), Z
% 1.02/1.66 ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), U ), T ) ), hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.66 ( X ), Z ), U ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T
% 1.02/1.66 ) ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.02/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.02/1.66 c_Rings_Odvd__class_Odvd( X ), Z ), hAPP( hAPP(
% 1.02/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.02/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.02/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.02/1.66 ) }.
% 1.02/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.02/1.67 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.02/1.67 }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.02/1.67 c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.02/1.67 ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.02/1.67 , c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.67 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.67 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.67 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.02/1.67 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.02/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! class_Groups_Ozero( X ), c_Polynomial_OAbs__poly( X,
% 1.02/1.67 c_Polynomial_Ocoeff( X, Y ) ) = Y }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.67 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.67 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.67 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.67 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 Z, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 Y, Z ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.02/1.67 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.67 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.02/1.67 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Z =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), T ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.02/1.67 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 X ), T ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), T =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ), hBOOL(
% 1.02/1.67 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 X ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Polynomial_Odegree( X, Y ),
% 1.02/1.67 c_Polynomial_Odegree( X, Z ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.67 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), c_Polynomial_Osmult( X, T,
% 1.02/1.67 Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.67 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Ocoeff( X, Z
% 1.02/1.67 ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.02/1.67 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Osmult( X, Z, Y ) )
% 1.02/1.67 , c_Polynomial_Odegree( X, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.67 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.02/1.67 , Y ) ) }.
% 1.02/1.67 { ! class_Groups_Ocomm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.02/1.67 Z ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.67 c_Polynomial_Odegree( X, T ), Y ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.67 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.02/1.67 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.02/1.67 , c_Polynomial_Odegree( X, c_Polynomial_Omonom( X, Z, Y ) ), Y ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.67 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.02/1.67 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.67 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.02/1.67 { ! class_Groups_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.67 tc_Nat_Onat, Y, c_Polynomial_Odegree( X, Z ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.67 c_Polynomial_OpCons( X, T, Z ) ), Y ) = c_Groups_Oplus__class_Oplus( X, T
% 1.02/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.02/1.67 c_Polynomial_Opoly( X, Z ), Y ) ) ) }.
% 1.02/1.67 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.02/1.67 , c_Polynomial_Odegree( X, c_Polynomial_OpCons( X, Z, Y ) ), c_Nat_OSuc(
% 1.02/1.67 c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.02/1.67 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.02/1.67 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.02/1.67 hAPP( Z, skol5( U, W, Z ) ) ) }.
% 1.02/1.67 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.02/1.67 Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) ), hBOOL(
% 1.02/1.67 hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, skol5( X, Y, Z ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) ) ) ) }.
% 1.02/1.67 { ! class_Rings_Odvd( X ), ! class_Rings_Osemiring__0( X ), ! hBOOL( hAPP(
% 1.02/1.67 hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.67 , T, c_Groups_Ozero__class_Ozero( X ) ) ) ), ! hBOOL( hAPP( Z, T ) ),
% 1.02/1.67 hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.02/1.67 skol19( X, Y, Z ) ) ) ) }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.02/1.67 , Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol6( X, Y ) ) }.
% 1.02/1.67 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.67 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.02/1.67 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.02/1.67 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.67 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.02/1.67 .
% 1.02/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.02/1.67 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.67 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.02/1.67 .
% 1.02/1.67 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.02/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.02/1.67 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.02/1.67 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.67 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.02/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.67 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.02/1.67 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.67 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.02/1.67 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.67 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.02/1.67 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.02/1.67 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.02/1.67 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.67 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.67 ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.67 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.02/1.67 hAPP( Y, U ) ) }.
% 1.02/1.67 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.02/1.67 ( Z, skol7( X, Y, Z ) ), hAPP( Y, skol7( X, Y, Z ) ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.02/1.67 ( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.02/1.67 ( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.67 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.02/1.67 hAPP( Y, U ) ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.67 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.02/1.67 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.02/1.67 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.67 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.67 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.67 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.02/1.67 hAPP( Y, U ) ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__0( X ), c_Orderings_Oord__class_Oless__eq
% 1.02/1.67 ( tc_Nat_Onat, c_Polynomial_Odegree( X, c_Polynomial_Opcompose( X, Z, Y )
% 1.02/1.67 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 c_Polynomial_Odegree( X, Z ) ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), Z =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.67 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ) }.
% 1.02/1.67 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.02/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), ! hAPP(
% 1.02/1.67 c_Polynomial_Ocoeff( X, Z ), Y ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Z )
% 1.02/1.67 , Y ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oorder_Omono( tc_Nat_Onat, X
% 1.02/1.67 , c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), T ), Z ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 1.02/1.67 { c_Nat_Onat_Onat__size( c_Nat_OSuc( X ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Nat_Onat, c_Nat_Onat_Onat__size( X ), c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.67 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Nat_OSuc( X ) ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_Osize__class_Osize(
% 1.02/1.67 tc_Nat_Onat, X ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.67 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.02/1.67 ), Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.02/1.67 X ) ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.02/1.67 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.67 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.67 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.67 , Y ), X ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.02/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Nat_Onat ) }.
% 1.02/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Nat_Onat ) }.
% 1.02/1.67 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.02/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.67 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.67 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.67 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.67 tc_Nat_Onat ), X ), Y ) }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.67 Y ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.67 Y ), ! Z = Y }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.67 Z ), ! Z = Y }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.67 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.67 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.67 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.67 , ! Z = Y }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.67 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.67 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.67 , ! Z = Y }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.67 , ! Y = Z }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.67 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.02/1.67 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.02/1.67 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.67 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.67 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.67 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.67 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.67 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.02/1.67 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.02/1.67 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.02/1.67 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, Y, Z ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.67 { alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.02/1.67 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.02/1.67 { alpha35( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.02/1.67 ( X, Y ), Z ) ) }.
% 1.02/1.67 { ! alpha35( X, Y, Z ), alpha38( X, Y, Z ), Z = Y }.
% 1.02/1.67 { ! alpha35( X, Y, Z ), alpha38( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! alpha38( X, Y, Z ), alpha35( X, Y, Z ) }.
% 1.02/1.67 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha35( X, Y, Z ) }.
% 1.02/1.67 { ! alpha38( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.02/1.67 }.
% 1.02/1.67 { ! alpha38( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.02/1.67 X, Y ), Z ) ), alpha38( X, Y, Z ) }.
% 1.02/1.67 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.02/1.67 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.67 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.02/1.67 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.02/1.67 { c_Nat_Osize__class_Osize( tc_Nat_Onat, X ) = X }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 X ), Y ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.02/1.67 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 Y ), X ) ), X ) ), Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.02/1.67 hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ), X ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) = c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.67 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.67 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.67 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.67 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.67 , ! Z = Y }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.67 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.67 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.67 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.67 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.02/1.67 ( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.67 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.02/1.67 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.67 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.67 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.67 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.67 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.67 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.02/1.67 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.67 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.67 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.02/1.67 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.67 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.67 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.67 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.02/1.67 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.67 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.67 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, T, Y ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.67 , Y, Z ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, Z, Y ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.67 , T, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.67 , Y, T ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.67 , T, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.67 , T ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, Z, Y ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, Z, Y ) }.
% 1.02/1.67 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.67 = Y }.
% 1.02/1.67 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.67 = Y }.
% 1.02/1.67 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.67 = Y }.
% 1.02/1.67 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.67 = Y }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.02/1.67 = Y }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.67 = Y }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), c_Groups_Oone__class_Oone( X ) ), Y ) ) }
% 1.02/1.67 .
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.02/1.67 .
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), Z ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.67 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.02/1.67 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 Y ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.02/1.67 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.02/1.67 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.02/1.67 .
% 1.02/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.02/1.67 .
% 1.02/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.02/1.67 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.02/1.67 X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.02/1.67 }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.67 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.02/1.67 ), X ) ) }.
% 1.02/1.67 { c_Nat_Osize__class_Osize( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ) ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.02/1.67 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.02/1.67 , X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.02/1.67 .
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.02/1.67 .
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.02/1.67 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.02/1.67 .
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ),
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.67 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), X ), c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Nat_Onat ) ) ) }.
% 1.02/1.67 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ),
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.02/1.67 , Y ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z
% 1.02/1.67 ), Y ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 X ), Z ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X )
% 1.02/1.67 , Y ) ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.02/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.02/1.67 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.67 { c_Nat_Onat_Onat__size( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone
% 1.02/1.67 ( tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), hAPP( c_Polynomial_Ocoeff( X, c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.02/1.67 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.02/1.67 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha8( X, Y, Z, T ),
% 1.02/1.67 alpha24( X, Y, Z, T ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z, T ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha24( X, Y, Z, T ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! alpha24( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! alpha24( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha24( X, Y, Z, T ) }.
% 1.02/1.67 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.67 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.67 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha8( X, Y, Z, T ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha9( X, Y, Z, T ),
% 1.02/1.67 alpha25( X, Y, Z, T ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha9( X, Y, Z, T ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha25( X, Y, Z, T ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.67 { ! alpha25( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! alpha25( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha25( X, Y, Z, T ) }.
% 1.02/1.67 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.02/1.67 { ! alpha9( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.02/1.67 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha9( X, Y, Z, T ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.67 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.67 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( X ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.67 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( X ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.67 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( X ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.67 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.67 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.67 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.67 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.67 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.02/1.67 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.02/1.67 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.67 , Y, T ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.67 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.67 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.67 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol8( X ) ) }.
% 1.02/1.67 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha10( X, Y ) }.
% 1.02/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.02/1.67 c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { ! alpha10( X, Y ), Y = c_Nat_OSuc( skol9( Z, Y ) ) }.
% 1.02/1.67 { ! alpha10( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol9( X,
% 1.02/1.67 Y ), X ) }.
% 1.02/1.67 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.02/1.67 ), alpha10( X, Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.02/1.67 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Nat_Onat ), Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.02/1.67 ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.02/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.02/1.67 ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.02/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) ) }.
% 1.02/1.67 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.02/1.67 .
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.67 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.02/1.67 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.02/1.67 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.02/1.67 X, c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.02/1.67 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), Z, Y ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.02/1.67 { ! class_Groups_Ocomm__monoid__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.67 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Polynomial_Odegree( X, Y ) )
% 1.02/1.67 , c_Polynomial_Odegree( X, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), Y, Z ) ) = c_Polynomial_Odegree( X, Y ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.67 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.02/1.67 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.67 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.02/1.67 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.02/1.67 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.02/1.67 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.67 , ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.02/1.67 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.02/1.67 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.02/1.67 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Polynomial_Odegree( X, Z ), Y ), hAPP( c_Polynomial_Ocoeff( X, Z ), Y )
% 1.02/1.67 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Osynthetic__div( X, Y, Z )
% 1.02/1.67 ), c_Polynomial_OpCons( X, hAPP( c_Polynomial_Opoly( X, Y ), Z ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) = Y }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.67 , U = c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), T ), Y )
% 1.02/1.67 }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.67 , alpha33( X, Y, Z, T ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! U = c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), Z ), T ), Y ), ! alpha33( X, Y, Z, T ),
% 1.02/1.67 c_Polynomial_Opdivmod__rel( X, U, T, Z, Y ) }.
% 1.02/1.67 { ! alpha33( X, Y, Z, T ), alpha11( X, Z, T ) }.
% 1.02/1.67 { ! alpha33( X, Y, Z, T ), alpha26( X, Y, T ) }.
% 1.02/1.67 { ! alpha11( X, Z, T ), ! alpha26( X, Y, T ), alpha33( X, Y, Z, T ) }.
% 1.02/1.67 { ! alpha26( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), alpha34( X, Y, Z ) }.
% 1.02/1.67 { ! Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha26( X
% 1.02/1.67 , Y, Z ) }.
% 1.02/1.67 { ! alpha34( X, Y, Z ), alpha26( X, Y, Z ) }.
% 1.02/1.67 { ! alpha34( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Polynomial_Odegree( X, Y ), c_Polynomial_Odegree( X, Z ) ) }.
% 1.02/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha34( X
% 1.02/1.67 , Y, Z ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, Y
% 1.02/1.67 ), c_Polynomial_Odegree( X, Z ) ), alpha34( X, Y, Z ) }.
% 1.02/1.67 { ! alpha11( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { Z = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X,
% 1.02/1.67 Y, Z ) }.
% 1.02/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha11( X
% 1.02/1.67 , Y, Z ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.02/1.67 ( c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , c_Groups_Ozero__class_Ozero( X ), hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.67 c_Polynomial_Odegree( X, Y ) ) ), c_Polynomial_Opos__poly( X, Y ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.67 c_Polynomial_OpCons( X, Z, Y ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.67 alpha12( X, Y, Z ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.67 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! alpha12( X, Y, Z ),
% 1.02/1.67 c_Polynomial_Opos__poly( X, c_Polynomial_OpCons( X, Z, Y ) ) }.
% 1.02/1.67 { ! alpha12( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.67 alpha12( X, Y, Z ) }.
% 1.02/1.67 { ! class_Groups_Ozero( X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.02/1.67 , skol11( T, U, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.67 c_Polynomial_Odegree( X, Y ), Z ) }.
% 1.02/1.67 { ! class_Groups_Ozero( X ), ! hAPP( c_Polynomial_Ocoeff( X, Y ), skol11( X
% 1.02/1.67 , Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.02/1.67 Y ), Z ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) =
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.02/1.67 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Ocoeff( X, Z ), Y
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ) ), Y ) =
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.67 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Z = V0 }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.67 , ! c_Polynomial_Opdivmod__rel( X, U, T, V0, W ), Y = W }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, U, Y )
% 1.02/1.67 , ! c_Polynomial_Opdivmod__rel( X, T, Z, V0, W ), Y = W }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T, Z, Y, U )
% 1.02/1.67 , ! c_Polynomial_Opdivmod__rel( X, T, Z, W, V0 ), Y = W }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.67 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.67 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.67 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.02/1.67 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, Z, Y ) ) =
% 1.02/1.67 c_Polynomial_OpCons( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.67 c_Polynomial_Opos__poly( X, c_Groups_Ouminus__class_Ouminus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), Y ) ) }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.02/1.67 c_Polynomial_Omonom( X, c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.67 = Y }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.67 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( X ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Y ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 = Y }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.02/1.67 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.02/1.67 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Y ), Z ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.67 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Z ), Y ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.67 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.67 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.67 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.67 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.02/1.67 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.02/1.67 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.02/1.67 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.67 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.02/1.67 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.67 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.67 ) ), Y ) }.
% 1.02/1.67 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 Z, Y ) ) = Y }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.67 Y ) ) = Y }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.02/1.67 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.02/1.67 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.67 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.67 ) ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 1.02/1.67 , Y ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), c_Groups_Ouminus__class_Ouminus( X, Z ) )
% 1.02/1.67 , Y ) ) }.
% 1.02/1.67 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.02/1.67 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.02/1.67 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.02/1.67 }.
% 1.02/1.67 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.02/1.67 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), c_Polynomial_Odegree( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.02/1.67 c_Polynomial_Odegree( X, Y ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, Z,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ),
% 1.02/1.67 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X, Y,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opdivmod__rel( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Z =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, T,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ), Y = T }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), ! Y = T, c_Polynomial_Opdivmod__rel( X, T,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z, Y ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Z =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ), Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opdivmod__rel( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), T, Z, Y ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.67 , c_Polynomial_Opdivmod__rel( X, c_Polynomial_Osmult( X, W, U ), T,
% 1.02/1.67 c_Polynomial_Osmult( X, W, Z ), c_Polynomial_Osmult( X, W, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Y ), Y ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.67 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 , Y ) }.
% 1.02/1.67 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.67 , Y ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.67 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.02/1.67 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.67 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 X ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.67 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Y ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.67 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.67 Z ) = Y }.
% 1.02/1.67 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.02/1.67 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.67 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.67 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.67 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.67 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.02/1.67 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.67 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X, Y ),
% 1.02/1.67 ! c_Polynomial_Opos__poly( X, Z ), c_Polynomial_Opos__poly( X, hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ), Z ) ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.67 , ! c_Polynomial_Opdivmod__rel( X, Z, V1, V0, W ),
% 1.02/1.67 c_Polynomial_Opdivmod__rel( X, U, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), V1 ), V0
% 1.02/1.67 , c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), W ), Y )
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons
% 1.02/1.67 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ) ) ), Z ) ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.02/1.67 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X, Z,
% 1.02/1.67 c_Polynomial_OpCons( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ),
% 1.02/1.67 hAPP( c_Polynomial_Opoly( X, Y ), c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.02/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Y ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ) ) = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X
% 1.02/1.67 ) ), c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.02/1.67 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Z ) }.
% 1.02/1.67 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.02/1.67 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.02/1.67 Y ) ) ) ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.02/1.67 ( tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ) ) ), c_Nat_OSuc( c_Polynomial_Oorder( X, Z,
% 1.02/1.67 Y ) ) ) ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Nat_Onat ) ) = Y }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.02/1.67 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.02/1.67 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.02/1.67 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.67 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.67 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.02/1.67 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.02/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.02/1.67 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.02/1.67 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.02/1.67 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Orderings_Oord__class_Oless__eq
% 1.02/1.67 ( tc_Nat_Onat, c_Polynomial_Odegree( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), Z ), Y ) ),
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 c_Polynomial_Odegree( X, Z ) ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.67 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Odegree( X, hAPP(
% 1.02/1.67 hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.02/1.67 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ) = Y }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Ocoeff( X, hAPP
% 1.02/1.67 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ),
% 1.02/1.67 c_Polynomial_OpCons( X, Z, c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ) ) ), Y ) ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.67 ( X ) }.
% 1.02/1.67 { ! class_Rings_Oidom( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) ) ) ), c_Polynomial_Oorder( X, Z, Y ) ) ), Y )
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.67 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.67 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), hBOOL( hAPP
% 1.02/1.67 ( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.02/1.67 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.02/1.67 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 1.02/1.67 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) ), Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ), hBOOL( hAPP(
% 1.02/1.67 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.02/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.02/1.67 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.67 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.67 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.02/1.67 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.02/1.67 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.02/1.67 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.02/1.67 ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.02/1.67 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.02/1.67 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.02/1.67 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), Y ) }.
% 1.02/1.67 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.02/1.67 ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ), hBOOL( hAPP(
% 1.02/1.67 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.02/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.02/1.67 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) ), Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), hAPP( hAPP
% 1.02/1.67 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.02/1.67 ) }.
% 1.02/1.67 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( X ) }.
% 1.02/1.67 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.02/1.67 = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.67 X ), Z ), T ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T )
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.02/1.67 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Nat_Onat ) ) = Y }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.67 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.67 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.02/1.67 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.67 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.67 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.67 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.67 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Nat_Onat ) }.
% 1.02/1.67 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.02/1.67 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.02/1.67 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.02/1.67 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.02/1.67 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.67 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.67 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.02/1.67 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.02/1.67 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.02/1.67 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.02/1.67 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.67 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.02/1.67 X ), T ), Z ) ), Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.02/1.67 , U, Z ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), U ) ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ), hBOOL( hAPP( hAPP
% 1.02/1.67 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.02/1.67 ( X ), Z ), U ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T
% 1.02/1.67 ) ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP
% 1.02/1.67 ( c_Rings_Odvd__class_Odvd( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.02/1.67 ( X ), T ), Z ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y
% 1.02/1.67 ) ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.02/1.67 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 X ), Y ), Z = Y }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.67 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.02/1.67 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.67 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.67 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.02/1.67 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.02/1.67 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.02/1.67 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.02/1.67 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.02/1.67 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.02/1.67 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.02/1.67 c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.02/1.67 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.02/1.67 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.02/1.67 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.02/1.67 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.02/1.67 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.02/1.67 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.02/1.67 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.02/1.67 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.67 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.67 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.02/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ), hBOOL( hAPP
% 1.02/1.67 ( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) )
% 1.02/1.67 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.02/1.67 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), T ) ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.02/1.67 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Int_Oint, U, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint )
% 1.02/1.67 , Z ), X ) ), T ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Int_Oint ), Y ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, T ) ) )
% 1.02/1.67 }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) ), Z =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), X ), Y ) ), ! hBOOL( hAPP( hAPP
% 1.02/1.67 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ), X = Y }.
% 1.02/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ) }.
% 1.02/1.67 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) ), hBOOL( hAPP(
% 1.02/1.67 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.02/1.67 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) ), hBOOL( hAPP(
% 1.02/1.67 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.02/1.67 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) ), hBOOL( hAPP( hAPP
% 1.02/1.67 ( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y
% 1.02/1.67 ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.67 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.02/1.67 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.02/1.67 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.02/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Y ), X ) )
% 1.02/1.67 , ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.02/1.67 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.02/1.67 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.02/1.67 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.02/1.67 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.02/1.67 { ! class_Lattices_Oab__semigroup__idem__mult( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = Y }.
% 1.02/1.67 { ! class_Lattices_Oboolean__algebra( X ), !
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Y ), Z = Y }.
% 1.02/1.67 { ! class_Lattices_Oboolean__algebra( X ), ! Z = Y,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( X, Z ) = c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, Y ) }.
% 1.02/1.67 { ! class_Groups_Ouminus( X ), hAPP( c_Groups_Ouminus__class_Ouminus(
% 1.02/1.67 tc_fun( T, X ), Z ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( Z, Y
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! class_Lattices_Oboolean__algebra( X ), c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( X, c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.67 }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Z, Y ) ), c_Polynomial_Odegree( X,
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) = c_Groups_Oone__class_Oone( X ) }
% 1.02/1.67 .
% 1.02/1.67 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.02/1.67 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol12( Z, Y
% 1.02/1.67 ), Y ) }.
% 1.02/1.67 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.02/1.67 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.67 skol12( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.02/1.67 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.02/1.67 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.02/1.67 , skol12( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.67 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 Z, c_Polynomial_Odegree( X, Y ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.67 tc_Nat_Onat, Z, skol13( T, U, Z ) ) }.
% 1.02/1.67 { ! class_Groups_Ozero( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.67 Z, c_Polynomial_Odegree( X, Y ) ), ! hAPP( c_Polynomial_Ocoeff( X, Y ),
% 1.02/1.67 skol13( X, Y, Z ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Z ) ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Fields_Ofield( X ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) ), Y ) ) }
% 1.02/1.67 .
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.02/1.67 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ), T ) ), hBOOL(
% 1.02/1.67 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), Z ),
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Y, T ) ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.02/1.67 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 1.02/1.67 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.02/1.67 , T ), Z ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.02/1.67 ( tc_Polynomial_Opoly( X ) ), T ), c_Polynomial_Opoly__gcd( X, Z, Y ) ) )
% 1.02/1.67 , hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.02/1.67 , T ), Y ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.02/1.67 ( tc_Polynomial_Opoly( X ) ), T ), Z ) ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ), Y ) ), hBOOL(
% 1.02/1.67 hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), T ),
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Z, Y ) ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.02/1.67 .
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Int_Oint ) ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.02/1.67 }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Int_Oint ) ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.02/1.67 }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Int_Oint ) ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Int_Oint ), X ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.02/1.67 = X }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Int_Oint ) ) ) }.
% 1.02/1.67 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Int_Oint ) ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.02/1.67 .
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.67 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.02/1.67 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.67 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.02/1.67 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.02/1.67 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Z ), Y ) =
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z,
% 1.02/1.67 c_Groups_Ouminus__class_Ouminus( tc_Polynomial_Opoly( X ), Y ) ) =
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Z, Y ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ), Y ) =
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.02/1.67 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Int_Oint ), X ) = X }.
% 1.02/1.67 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Int_Oint ) ) = X }.
% 1.02/1.67 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.02/1.67 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.02/1.67 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, T, Z ), Y ) = c_Polynomial_Opoly__gcd( X, T,
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Z, Y ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, T,
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Z, Y ) ) = c_Polynomial_Opoly__gcd( X, Z,
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, T, Y ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Y, Z ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), c_Polynomial_Opoly__gcd( X, Z, Y ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.02/1.67 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.02/1.67 ( tc_Int_Oint ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.67 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.02/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.02/1.67 ( tc_Int_Oint ), Y ) }.
% 1.02/1.67 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.67 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.02/1.67 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.02/1.67 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.67 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.02/1.67 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.02/1.67 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.02/1.67 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.67 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.02/1.67 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Int_Oint ) ) }.
% 1.02/1.67 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.02/1.67 tc_Int_Oint ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Int_Oint, X, Y ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.02/1.67 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha39( X, Y, Z, T ), ! Y =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! T =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.02/1.67 c_Polynomial_Opoly__gcd( X, Y, T ) = Z }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd
% 1.02/1.67 ( tc_Polynomial_Opoly( X ) ), Z ), Y ) ), alpha39( X, Y, Z, T ), ! hAPP(
% 1.02/1.67 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.02/1.67 c_Groups_Oone__class_Oone( X ), c_Polynomial_Opoly__gcd( X, Y, T ) = Z }
% 1.02/1.67 .
% 1.02/1.67 { ! alpha39( X, Y, Z, T ), alpha40( X, Y, Z, T ), alpha36( X, Y, T ) }.
% 1.02/1.67 { ! alpha39( X, Y, Z, T ), alpha40( X, Y, Z, T ), ! hAPP(
% 1.02/1.67 c_Polynomial_Ocoeff( X, Z ), c_Polynomial_Odegree( X, Z ) ) =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.67 { ! alpha40( X, Y, Z, T ), alpha39( X, Y, Z, T ) }.
% 1.02/1.67 { ! alpha36( X, Y, T ), hAPP( c_Polynomial_Ocoeff( X, Z ),
% 1.02/1.67 c_Polynomial_Odegree( X, Z ) ) = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.67 alpha39( X, Y, Z, T ) }.
% 1.02/1.67 { ! alpha40( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), Z ), T ) ), alpha41( X, Y, Z, T ) }.
% 1.02/1.67 { hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ),
% 1.02/1.67 Z ), T ) ), alpha40( X, Y, Z, T ) }.
% 1.02/1.67 { ! alpha41( X, Y, Z, T ), alpha40( X, Y, Z, T ) }.
% 1.02/1.67 { ! alpha41( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), skol14( X, Y, U, W ) ), Y ) ) }.
% 1.02/1.67 { ! alpha41( X, Y, Z, T ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), skol14( X, Y, U, T ) ), T ) ) }.
% 1.02/1.67 { ! alpha41( X, Y, Z, T ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), skol14( X, Y, Z, T ) ), Z ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) )
% 1.02/1.67 , U ), Y ) ), ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ), U ), T ) ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ) ), U ), Z ) ), alpha41
% 1.02/1.67 ( X, Y, Z, T ) }.
% 1.02/1.67 { ! alpha36( X, Y, Z ), Y = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! alpha36( X, Y, Z ), Z = c_Groups_Ozero__class_Ozero(
% 1.02/1.67 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! Z =
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), alpha36( X, Y, Z
% 1.02/1.67 ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Int_Oint ), X ), hBOOL( hAPP( Y, skol15( Z, Y ) ) ), !
% 1.02/1.67 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! hBOOL( hAPP( Y, U ) )
% 1.02/1.67 , hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint, U, hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), X ) ) ) ) }.
% 1.02/1.67 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.02/1.67 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus(
% 1.02/1.67 tc_Int_Oint, skol15( X, Y ), X ) ) ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.67 ( tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! hBOOL(
% 1.02/1.67 hAPP( Y, T ) ), hBOOL( hAPP( Y, c_Groups_Oplus__class_Oplus( tc_Int_Oint
% 1.02/1.67 , T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) )
% 1.02/1.67 ) ) }.
% 1.02/1.67 { ! class_Fields_Ofield( X ), c_Polynomial_Opoly__gcd( X, Y,
% 1.02/1.67 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.02/1.67 c_Polynomial_Osmult( X, c_Rings_Oinverse__class_Oinverse( X, hAPP(
% 1.02/1.67 c_Polynomial_Ocoeff( X, Y ), c_Polynomial_Odegree( X, Y ) ) ), Y ) }.
% 1.02/1.67 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.67 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.02/1.67 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), c_Groups_Ominus__class_Ominus(
% 1.02/1.67 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) =
% 1.02/1.67 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.02/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.67 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.67 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 1.02/1.67 ) ), Y ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.67 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.67 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.67 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.67 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.67 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__ring__1( X ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), T ) ), hBOOL( hAPP( hAPP(
% 1.02/1.67 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.02/1.67 T ) ) ) }.
% 1.02/1.67 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), X ) )
% 1.02/1.67 , ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ), Z )
% 1.02/1.67 ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Y ),
% 1.02/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.02/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.02/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.02/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.02/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.67 { ! class_Groups_Ominus( X ), hAPP( c_Groups_Ominus__class_Ominus( tc_fun(
% 1.02/1.67 U, X ), T, Z ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( T, Y ),
% 1.02/1.67 hAPP( Z, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.02/1.67 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.67 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.02/1.67 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.67 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.67 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Ocoeff( X, T ), Y )
% 1.02/1.67 , hAPP( c_Polynomial_Ocoeff( X, Z ), Y ) ) }.
% 1.02/1.67 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.02/1.67 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.02/1.67 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.02/1.67 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.67 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.67 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, U, T ),
% 1.02/1.67 c_Polynomial_OpCons( X, Z, Y ) ) = c_Polynomial_OpCons( X,
% 1.02/1.67 c_Groups_Ominus__class_Ominus( X, U, Z ), c_Groups_Ominus__class_Ominus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), T, Y ) ) }.
% 1.02/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.02/1.67 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.67 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.02/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 1.02/1.67 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.02/1.67 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 1.02/1.67 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.67 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.67 , Y ) ) = Y }.
% 1.02/1.67 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.67 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.02/1.67 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.02/1.67 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.02/1.67 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.67 ( tc_Nat_Onat, c_Nat_OSuc( Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.02/1.67 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.67 ( tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.67 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.02/1.67 X ) ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.68 , Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.68 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.68 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.68 ( X ) ) }.
% 1.02/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.68 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.68 , Z, Y ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.68 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.02/1.68 = Y }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.68 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.02/1.68 ( X ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 1.02/1.68 X, Y ) ) = Y }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.68 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.68 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.68 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.68 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.68 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.02/1.68 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.02/1.68 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.02/1.68 ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.02/1.68 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.02/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.02/1.68 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.02/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.02/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.02/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.02/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.02/1.68 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), !
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.02/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, X ) =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.02/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.68 tc_Nat_Onat ), X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, Y, X ), X ) = Y }.
% 1.02/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, Y, X ), Y ) = X }.
% 1.02/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( tc_Nat_Onat, Z, Y ), X ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.68 Z, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) }.
% 1.02/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.68 ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X = Z }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = Y }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, Z ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ) }.
% 1.02/1.68 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( tc_Nat_Onat, Y, Z ), X ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( tc_Nat_Onat, Z, X ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.68 ) }.
% 1.02/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.02/1.68 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.68 Y ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, Y, Z ) }.
% 1.02/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) }.
% 1.02/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.02/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, X, Z ), Y ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) = X }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Nat_Onat, X, Y ), Y ) = X }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z, X =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) = Z }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, Z, X ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Nat_Onat, X, Y ), Z ) = c_Groups_Ominus__class_Ominus( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ), Y ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.02/1.68 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 1.02/1.68 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 1.02/1.68 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ) }.
% 1.02/1.68 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ), ! hBOOL( hAPP(
% 1.02/1.68 hAPP( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), X ) ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), hBOOL( hAPP( hAPP
% 1.02/1.68 ( c_Rings_Odvd__class_Odvd( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.68 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( tc_Nat_Onat, X, Y ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y )
% 1.02/1.68 ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( tc_Nat_Onat, Y, Z ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z )
% 1.02/1.68 ) }.
% 1.02/1.68 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) = Y }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, Z, X ), Y ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.02/1.68 ( tc_Nat_Onat, Z, X ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z
% 1.02/1.68 , c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) =
% 1.02/1.68 c_Nat_OSuc( c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.68 { ! c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.68 { c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.68 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.68 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.68 ( tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.02/1.68 tc_Nat_Onat ), c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.02/1.68 ) = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus(
% 1.02/1.68 X, Y ) ) }.
% 1.02/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.68 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.02/1.68 X, Z, Y ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X, Z
% 1.02/1.68 , Y ) = c_Groups_Oplus__class_Oplus( X, Z,
% 1.02/1.68 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.02/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Z, Y )
% 1.02/1.68 = c_Groups_Oplus__class_Oplus( X, Z, c_Groups_Ouminus__class_Ouminus( X
% 1.02/1.68 , Y ) ) }.
% 1.02/1.68 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.68 X, Y ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 1.02/1.68 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 1.02/1.68 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.68 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.68 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.68 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.68 Z ) ), Y ) ) }.
% 1.02/1.68 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.68 Z ) ), U ), T ) = Y }.
% 1.02/1.68 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.68 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), Z ), U ), Y ) }.
% 1.02/1.68 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.68 W ) ), U ), Y ) }.
% 1.02/1.68 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.68 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.68 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), Z ), U ), Y ) }.
% 1.02/1.68 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.68 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.68 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.02/1.68 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.02/1.68 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.68 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.02/1.68 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.68 ) ), Z ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.68 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 1.02/1.68 ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.02/1.68 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.68 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.68 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.02/1.68 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.68 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.68 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.68 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.68 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.02/1.68 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.02/1.68 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.02/1.68 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.68 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.02/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( X, Z, W ) ), U ), Y ) ) }.
% 1.02/1.68 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.02/1.68 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.68 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.02/1.68 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.68 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.68 X, W, Z ) ), U ), T ), Y ) }.
% 1.02/1.68 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.02/1.68 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), Z ), U ), Y ) ) }.
% 1.02/1.68 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.02/1.68 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.02/1.68 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.02/1.68 .
% 1.02/1.68 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.02/1.68 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.02/1.68 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, U, T
% 1.02/1.68 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.02/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.02/1.68 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.02/1.68 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ), hBOOL( hAPP(
% 1.02/1.68 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.68 , U, T ) ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.02/1.68 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.02/1.68 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X, U, T
% 1.02/1.68 ) ) ), hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( X ), Z ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.02/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), ! hBOOL( hAPP(
% 1.02/1.68 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), Y ) ), ! hBOOL( hAPP( hAPP(
% 1.02/1.68 c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, U, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) ), hBOOL( hAPP(
% 1.02/1.68 hAPP( c_Rings_Odvd__class_Odvd( X ), Z ), c_Groups_Oplus__class_Oplus( X
% 1.02/1.68 , U, T ) ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.68 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.68 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Nat_Onat, X, c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) )
% 1.02/1.68 ) ) = X }.
% 1.02/1.68 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.68 , alpha13( X, Y, Z ) }.
% 1.02/1.68 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.68 , alpha27( X, Y, Z ) }.
% 1.02/1.68 { ! alpha13( X, Y, Z ), ! alpha27( X, Y, Z ), hBOOL( hAPP( Z,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.68 { ! alpha27( X, Y, Z ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.68 T ), hBOOL( hAPP( Z, T ) ) }.
% 1.02/1.68 { ! hBOOL( hAPP( Z, skol16( T, U, Z ) ) ), alpha27( X, Y, Z ) }.
% 1.02/1.68 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, skol16( X, Y, Z ) ),
% 1.02/1.68 alpha27( X, Y, Z ) }.
% 1.02/1.68 { ! alpha13( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.02/1.68 ), hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.02/1.68 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha13( X, Y, Z ) }
% 1.02/1.68 .
% 1.02/1.68 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha13
% 1.02/1.68 ( X, Y, Z ) }.
% 1.02/1.68 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.68 , ! alpha14( X, Y, Z ) }.
% 1.02/1.68 { ! hBOOL( hAPP( Z, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) )
% 1.02/1.68 , ! alpha28( X, Y, Z ) }.
% 1.02/1.68 { alpha14( X, Y, Z ), alpha28( X, Y, Z ), hBOOL( hAPP( Z,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.02/1.68 { ! alpha28( X, Y, Z ), ! hBOOL( hAPP( Z, skol17( T, U, Z ) ) ) }.
% 1.02/1.68 { ! alpha28( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.02/1.68 skol17( X, Y, Z ) ) }.
% 1.02/1.68 { ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, T ), hBOOL( hAPP( Z, T
% 1.02/1.68 ) ), alpha28( X, Y, Z ) }.
% 1.02/1.68 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.02/1.68 }.
% 1.02/1.68 { ! alpha14( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.02/1.68 tc_Nat_Onat ) ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha14( X, Y, Z ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, c_Nat_OSuc(
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ) ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, Z, Y ), c_Nat_OSuc( X ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc(
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), Z ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( X ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ), T =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.02/1.68 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, T,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), T ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ) = Z,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.02/1.68 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.02/1.68 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.02/1.68 c_Polynomial_Opdivmod__rel( X, W, U, T, Z ), c_Polynomial_Opdivmod__rel(
% 1.02/1.68 X, W, c_Polynomial_Osmult( X, Y, U ), c_Polynomial_Osmult( X,
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ), T ), Z ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Odegree( X,
% 1.02/1.68 c_Polynomial_Osynthetic__div( X, Z, Y ) ) = c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), c_Groups_Oone__class_Oone(
% 1.02/1.68 tc_Nat_Onat ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.68 ( tc_Nat_Onat ), X ), c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) = X }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.02/1.68 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) }.
% 1.02/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = X }.
% 1.02/1.68 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Nat_Onat, Y, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.02/1.68 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), Z ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y
% 1.02/1.68 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), Z ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.02/1.68 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ) ), U ), T ), Z ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.02/1.68 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X
% 1.02/1.68 ), U ), T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ), Z ) ) }.
% 1.02/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.02/1.68 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.02/1.68 ( tc_Nat_Onat ) ) ), X ) ) }.
% 1.02/1.68 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.68 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.02/1.68 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.02/1.68 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.02/1.68 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.02/1.68 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone
% 1.02/1.68 ( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP
% 1.02/1.68 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), hAPP( hAPP(
% 1.02/1.68 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) ) = hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.02/1.68 Y ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.02/1.68 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.02/1.68 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.02/1.68 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.68 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.02/1.68 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.02/1.68 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Nat_Onat, Z, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.02/1.68 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.02/1.68 tc_Nat_Onat, Z, Y ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) ) = hAPP
% 1.02/1.68 ( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.68 c_Power_Opower__class_Opower( X ), T ), c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Nat_Onat, Y, Z ) ) ), T ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ), Y ) = c_Groups_Ouminus__class_Ouminus(
% 1.02/1.68 tc_Polynomial_Opoly( X ), Y ) }.
% 1.02/1.68 { ! hBOOL( hAPP( hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) ), ! hBOOL( hAPP(
% 1.02/1.68 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), X ) ), hBOOL( hAPP(
% 1.02/1.68 hAPP( c_Rings_Odvd__class_Odvd( tc_Int_Oint ), Z ), Y ) ) }.
% 1.02/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.02/1.68 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.02/1.68 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.68 ( tc_Polynomial_Opoly( X ), Z, Y ), Z = Y, c_Polynomial_Opos__poly( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), ! Z = Y,
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.02/1.68 { c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.68 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.02/1.68 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.02/1.68 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ominus__class_Ominus
% 1.02/1.68 ( tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ),
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 tc_Polynomial_Opoly( X ), Z, Y ), c_Polynomial_Opos__poly( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), ! c_Polynomial_Opos__poly( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Y, Z ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.02/1.68 ( tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Polynomial_Odegree( X,
% 1.02/1.68 T ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.02/1.68 c_Polynomial_Odegree( X, c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Polynomial_Opoly( X ), Z, T ) ), Y ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 tc_Nat_Onat, c_Polynomial_Odegree( X, Z ), Y ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree( X, T )
% 1.02/1.68 , Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Polynomial_Odegree(
% 1.02/1.68 X, c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, T ) ), Y )
% 1.02/1.68 }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.02/1.68 ( tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.02/1.68 .
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( tc_Int_Oint, X, c_Groups_Oone__class_Oone
% 1.02/1.68 ( tc_Int_Oint ) ) ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.02/1.68 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Z ) ) =
% 1.02/1.68 c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.68 Y ) ), c_Groups_Ominus__class_Ominus( X, Y, Z ) ) ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Z ) ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.68 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.02/1.68 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus(
% 1.02/1.68 X, U, Z ), c_Groups_Ominus__class_Ominus( X, T, Y ) ) }.
% 1.02/1.68 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) }.
% 1.02/1.68 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.02/1.68 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.68 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 1.02/1.68 , Y = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.68 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.02/1.68 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 1.02/1.68 = c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.68 ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.68 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.68 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.02/1.68 ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.68 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.02/1.68 .
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.02/1.68 ( X ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.68 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.02/1.68 .
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.68 , Y ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.68 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.02/1.68 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.68 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.68 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.68 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.68 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.68 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.68 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.02/1.68 , Y ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 1.02/1.68 ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.02/1.68 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 1.02/1.68 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.68 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.02/1.68 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.68 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.68 ) ) }.
% 1.02/1.68 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.02/1.68 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.02/1.68 c_Groups_Oone__class_Oone( X ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.02/1.68 }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.02/1.68 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 1.02/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.02/1.68 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.68 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.02/1.68 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 1.02/1.68 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.02/1.68 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.02/1.68 { ! class_Fields_Ofield( X ), ! c_Polynomial_Opdivmod__rel( X, U, T, Z, Y )
% 1.02/1.68 , T = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), ! V0 =
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, hAPP( c_Polynomial_Ocoeff( X,
% 1.02/1.68 c_Polynomial_OpCons( X, W, Y ) ), c_Polynomial_Odegree( X, T ) ), hAPP(
% 1.02/1.68 c_Polynomial_Ocoeff( X, T ), c_Polynomial_Odegree( X, T ) ) ),
% 1.02/1.68 c_Polynomial_Opdivmod__rel( X, c_Polynomial_OpCons( X, W, U ), T,
% 1.02/1.68 c_Polynomial_OpCons( X, V0, Z ), c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Polynomial_Opoly( X ), c_Polynomial_OpCons( X, W, Y ),
% 1.02/1.68 c_Polynomial_Osmult( X, V0, T ) ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.68 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ominus__class_Ominus(
% 1.02/1.68 tc_Int_Oint, X, Y ) }.
% 1.02/1.68 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.02/1.68 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.02/1.68 ) }.
% 1.02/1.68 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.02/1.68 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.68 { ! class_RealVector_Oreal__normed__field( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.02/1.68 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.68 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.68 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 1.02/1.68 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.02/1.68 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 1.02/1.68 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.02/1.68 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.02/1.68 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 1.02/1.68 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 1.02/1.68 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.02/1.68 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.02/1.68 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 1.02/1.68 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 1.02/1.68 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.02/1.68 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.68 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.02/1.68 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.02/1.68 X ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.68 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.02/1.68 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.02/1.68 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.68 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.02/1.68 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 1.02/1.68 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.02/1.68 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.68 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.68 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.02/1.68 X ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.68 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.02/1.68 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.02/1.68 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.68 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.02/1.68 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.02/1.68 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha15( X, Y, Z ), alpha29
% 1.02/1.68 ( X, Y, Z ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha15( X, Y, Z
% 1.02/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.68 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha29( X, Y, Z
% 1.02/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.02/1.68 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.68 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.68 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ), alpha29( X, Y, Z ) }.
% 1.02/1.68 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.68 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), Y ), alpha15( X, Y, Z ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.02/1.68 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha16( X, Y, Z ), alpha30
% 1.02/1.68 ( X, Y, Z ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha16( X, Y, Z
% 1.02/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.02/1.68 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha30( X, Y, Z
% 1.02/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.02/1.68 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.02/1.68 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.02/1.68 ( X ), Y ), alpha30( X, Y, Z ) }.
% 1.02/1.68 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.68 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ), alpha16( X, Y, Z ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.02/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.02/1.68 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.02/1.68 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.02/1.68 , Y, Z ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.02/1.68 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.02/1.68 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.02/1.68 , Y, Z ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 1.02/1.68 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha17( X, Y, Z ), alpha31( X,
% 1.02/1.68 Y, Z ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha17( X, Y, Z
% 1.02/1.68 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.02/1.68 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha31( X, Y, Z
% 1.02/1.68 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.02/1.68 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.68 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.68 ), alpha31( X, Y, Z ) }.
% 1.02/1.68 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.68 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.68 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 ), alpha17( X, Y, Z ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.02/1.68 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha18( X, Y, Z ), alpha32
% 1.02/1.68 ( X, Y, Z ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha18( X, Y, Z
% 1.02/1.68 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.68 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 1.02/1.68 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.02/1.68 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.02/1.68 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.02/1.68 ), alpha32( X, Y, Z ) }.
% 1.02/1.68 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.02/1.68 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.02/1.68 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.02/1.68 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.02/1.68 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.02/1.68 ), alpha18( X, Y, Z ) }.
% 1.02/1.68 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.02/1.68 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.02/1.68 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.02/1.68 ( X ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__add(
% 1.02/1.68 X ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ocomm__monoid__add( X
% 1.02/1.68 ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring( X ) }
% 1.02/1.68 .
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Omonoid__add( X ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0( X ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero( X ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring( X ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Ozero( X ) }.
% 1.02/1.68 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.68 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.68 { ! class_Lattices_Oboolean__algebra( X ), class_Lattices_Oboolean__algebra
% 1.02/1.68 ( tc_fun( Y, X ) ) }.
% 1.02/1.68 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.02/1.68 ) ) }.
% 1.02/1.68 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.02/1.68 .
% 1.02/1.68 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.02/1.68 { ! class_Groups_Ouminus( X ), class_Groups_Ouminus( tc_fun( Y, X ) ) }.
% 1.02/1.68 { ! class_Groups_Ominus( X ), class_Groups_Ominus( tc_fun( Y, X ) ) }.
% 1.02/1.68 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.68 tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.02/1.68 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.02/1.68 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.02/1.68 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.02/1.68 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.02/1.68 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Ouminus( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Ominus( tc_Int_Oint ) }.
% 1.02/1.68 { class_Power_Opower( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.02/1.68 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.02/1.68 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.02/1.68 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.68 tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Ominus( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.02/1.68 { class_Lattices_Oboolean__algebra( tc_HOL_Obool ) }.
% 1.02/1.68 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.02/1.68 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.02/1.68 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.02/1.68 { class_Groups_Ouminus( tc_HOL_Obool ) }.
% 1.02/1.68 { class_Groups_Ominus( tc_HOL_Obool ) }.
% 1.02/1.68 { ! class_Rings_Oidom( X ),
% 1.02/1.68 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.02/1.68 ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.02/1.68 X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.02/1.68 ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.02/1.68 }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.68 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ),
% 1.02/1.68 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.02/1.68 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.02/1.68 ( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.02/1.68 ( tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), class_Groups_Ouminus(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Groups_Oab__group__add( X ), class_Groups_Ominus(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.02/1.68 }.
% 1.02/1.68 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.02/1.68 ) ) }.
% 1.02/1.68 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.02/1.68 .
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.02/1.68 tc_Polynomial_Opoly( X ) ) }.
% 1.02/1.68 { ! hBOOL( c_fequal( Y, X ) ), Y = X }.
% 1.02/1.68 { ! Y = X, hBOOL( c_fequal( Y, X ) ) }.
% 1.02/1.68 { alpha37, v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) )
% 1.02/1.68 }.
% 1.02/1.68 { alpha37, ! c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a
% 1.02/1.68 , v_p, v_h ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) )
% 1.02/1.68 }.
% 1.02/1.68 { ! alpha37, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a
% 1.02/1.68 , v_p, v_h ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) )
% 1.02/1.68 }.
% 1.02/1.68 { ! alpha37, ! v_p = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a
% 1.02/1.68 ) ) }.
% 1.02/1.68 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly( t_a, v_p, v_h
% 1.02/1.68 ) = c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ), v_p =
% 1.02/1.68 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( t_a ) ), alpha37 }.
% 1.02/1.68 { class_Rings_Ocomm__semiring__0( t_a ) }.
% 1.02/1.68
% 1.02/1.68 *** allocated 15000 integers for clauses
% 1.02/1.68 *** allocated 22500 integers for clauses
% 1.02/1.68 *** allocated 33750 integers for clauses
% 1.02/1.68 *** allocated 50625 integers for clauses
% 1.02/1.68 *** allocated 75937 integers for clauses
% 1.02/1.68 percentage equality = 0.255789, percentage horn = 0.897541
% 1.02/1.68 This is a problem with some equality
% 1.02/1.68
% 1.02/1.68
% 1.02/1.68
% 1.02/1.68 Options Used:
% 1.02/1.68
% 1.02/1.68 useres = 1
% 1.02/1.68 useparamod = 1
% 1.02/1.68 useeqrefl = 1
% 1.02/1.68 useeqfact = 1
% 1.02/1.68 usefactor = 1
% 1.02/1.68 usesimpsplitting = 0
% 1.02/1.68 usesimpdemod = 5
% 1.02/1.68 usesimpres = 3
% 1.02/1.68
% 1.02/1.68 resimpinuse = 1000
% 1.02/1.68 resimpclauses = 20000
% 1.02/1.68 substype = eqrewr
% 1.02/1.68 backwardsubs = 1
% 1.02/1.68 selectoldest = 5
% 1.02/1.68
% 1.02/1.68 litorderings [0] = split
% 1.02/1.68 litorderings [1] = extend the termordering, first sorting on arguments
% 1.02/1.68
% 1.02/1.68 termordering = kbo
% 1.02/1.68
% 1.02/1.68 litapriori = 0
% 1.02/1.68 termapriori = 1
% 1.02/1.68 litaposteriori = 0
% 1.02/1.68 termaposteriori = 0
% 1.02/1.68 demodaposteriori = 0
% 1.02/1.68 ordereqreflfact = 0
% 1.02/1.68
% 1.02/1.68 litselect = negord
% 1.02/1.68
% 1.02/1.68 maxweight = 15
% 1.02/1.68 maxdepth = 30000
% 1.02/1.68 maxlength = 115
% 1.02/1.68 maxnrvars = 195
% 1.02/1.68 excuselevel = 1
% 1.02/1.68 increasemaxweight = 1
% 1.02/1.68
% 1.02/1.68 maxselected = 10000000
% 1.02/1.68 maxnrclauses = 10000000
% 1.02/1.68
% 1.02/1.68 showgenerated = 0
% 1.02/1.68 showkept = 0
% 1.02/1.68 showselected = 0
% 1.02/1.68 showdeleted = 0
% 1.02/1.68 showresimp = 1
% 1.02/1.68 showstatus = 2000
% 1.02/1.68
% 1.02/1.68 prologoutput = 0
% 1.02/1.68 nrgoals = 5000000
% 1.02/1.68 totalproof = 1
% 1.02/1.68
% 1.02/1.68 Symbols occurring in the translation:
% 1.02/1.68
% 1.02/1.68 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.02/1.68 . [1, 2] (w:1, o:189, a:1, s:1, b:0),
% 1.02/1.68 ! [4, 1] (w:0, o:106, a:1, s:1, b:0),
% 1.02/1.68 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.68 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.68 hAPP [38, 2] (w:1, o:213, a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Ocomm__semiring__0 [41, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.02/1.68 tc_Polynomial_Opoly [42, 1] (w:1, o:115, a:1, s:1, b:0),
% 1.02/1.68 c_Groups_Ozero__class_Ozero [43, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.02/1.68 c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly [44, 3] (w:1
% 1.02/1.68 , o:241, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Ozero [47, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.02/1.68 c_Polynomial_OpCons [49, 3] (w:1, o:245, a:1, s:1, b:0),
% 1.02/1.68 c_Polynomial_Opoly__rec [52, 5] (w:1, o:300, a:1, s:1, b:0),
% 1.02/1.68 c_Polynomial_Omonom [54, 3] (w:1, o:246, a:1, s:1, b:0),
% 1.02/1.68 c_Polynomial_Opoly [58, 2] (w:1, o:214, a:1, s:1, b:0),
% 1.02/1.68 c_Polynomial_Ocoeff [59, 2] (w:1, o:215, a:1, s:1, b:0),
% 1.02/1.68 c_Polynomial_Osmult [61, 3] (w:1, o:247, a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Oidom [63, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.02/1.68 tc_Nat_Onat [64, 0] (w:1, o:45, a:1, s:1, b:0),
% 1.02/1.68 class_Int_Oring__char__0 [67, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.02/1.68 c_fequal [72, 2] (w:1, o:216, a:1, s:1, b:0),
% 1.02/1.68 c_If [73, 4] (w:1, o:288, a:1, s:1, b:0),
% 1.02/1.68 c_Polynomial_Oorder [74, 3] (w:1, o:244, a:1, s:1, b:0),
% 1.02/1.68 c_Polynomial_Osynthetic__div [75, 3] (w:1, o:248, a:1, s:1, b:0),
% 1.02/1.68 c_Nat_Onat_Onat__case [76, 3] (w:1, o:249, a:1, s:1, b:0),
% 1.02/1.68 c_Groups_Oplus__class_Oplus [77, 3] (w:1, o:250, a:1, s:1, b:0),
% 1.02/1.68 c_Nat_OSuc [78, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.02/1.68 c_Polynomial_Opcompose [80, 3] (w:1, o:251, a:1, s:1, b:0),
% 1.02/1.68 class_Fields_Ofield [81, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.02/1.68 c_Rings_Odvd__class_Odvd [82, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.02/1.68 hBOOL [83, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.02/1.68 c_Polynomial_Odegree [84, 2] (w:1, o:217, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Oab__semigroup__add [89, 1] (w:1, o:127, a:1, s:1, b:0)
% 1.02/1.68 ,
% 1.02/1.68 class_Groups_Ocancel__semigroup__add [91, 1] (w:1, o:128, a:1, s:1
% 1.02/1.68 , b:0),
% 1.02/1.68 class_Groups_Ocancel__ab__semigroup__add [92, 1] (w:1, o:129, a:1, s:
% 1.02/1.68 1, b:0),
% 1.02/1.68 class_Groups_Ocomm__monoid__add [93, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.02/1.68
% 1.02/1.68 class_Groups_Omonoid__add [94, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Olinordered__ab__group__add [95, 1] (w:1, o:131, a:1, s:
% 1.02/1.68 1, b:0),
% 1.02/1.68 class_Rings_Ocomm__semiring__1 [96, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.02/1.68 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.02/1.68 107, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.02/1.68 c_Polynomial_OAbs__poly [108, 2] (w:1, o:218, a:1, s:1, b:0),
% 1.02/1.68 c_Groups_Otimes__class_Otimes [109, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.02/1.68 c_Orderings_Oord__class_Oless__eq [110, 3] (w:1, o:242, a:1, s:1, b:0
% 1.02/1.68 ),
% 1.02/1.68 class_Rings_Olinordered__ring [111, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Olinordered__ring__strict [112, 1] (w:1, o:135, a:1, s:1
% 1.02/1.68 , b:0),
% 1.02/1.68 class_Rings_Oordered__cancel__semiring [113, 1] (w:1, o:137, a:1, s:1
% 1.02/1.68 , b:0),
% 1.02/1.68 class_Rings_Oordered__ring [114, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Oordered__semiring [115, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.02/1.68
% 1.02/1.68 class_Rings_Oordered__comm__semiring [116, 1] (w:1, o:140, a:1, s:1
% 1.02/1.68 , b:0),
% 1.02/1.68 class_Groups_Oab__semigroup__mult [124, 1] (w:1, o:165, a:1, s:1, b:0
% 1.02/1.68 ),
% 1.02/1.68 class_Rings_Omult__zero [131, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Oring__no__zero__divisors [132, 1] (w:1, o:149, a:1, s:1
% 1.02/1.68 , b:0),
% 1.02/1.68 class_Rings_Ono__zero__divisors [133, 1] (w:1, o:136, a:1, s:1, b:0)
% 1.02/1.68 ,
% 1.02/1.68 class_Rings_Osemiring [135, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Ocomm__semiring [136, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Oordered__ab__semigroup__add__imp__le [137, 1] (w:1, o:
% 1.02/1.68 166, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Oordered__ab__semigroup__add [138, 1] (w:1, o:167, a:1
% 1.02/1.68 , s:1, b:0),
% 1.02/1.68 class_Rings_Odvd [139, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Oordered__comm__monoid__add [140, 1] (w:1, o:168, a:1
% 1.02/1.68 , s:1, b:0),
% 1.02/1.68 class_Rings_Osemiring__0 [142, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.02/1.68 class_Orderings_Opreorder [143, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.02/1.68 class_RealVector_Oreal__normed__algebra [145, 1] (w:1, o:157, a:1, s:
% 1.02/1.68 1, b:0),
% 1.02/1.68 class_Orderings_Oord [148, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.02/1.68 tc_fun [149, 2] (w:1, o:228, a:1, s:1, b:0),
% 1.02/1.68 class_Orderings_Olinorder [150, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.02/1.68 class_Orderings_Oorder [151, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.02/1.68 c_Orderings_Oord__class_Oless [153, 3] (w:1, o:243, a:1, s:1, b:0),
% 1.02/1.68 c_Orderings_Oorder_Omono [154, 4] (w:1, o:289, a:1, s:1, b:0),
% 1.02/1.68 c_Nat_Onat_Onat__size [156, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.02/1.68 c_Nat_Osize__class_Osize [157, 2] (w:1, o:229, a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Olinordered__semiring__1 [160, 1] (w:1, o:141, a:1, s:1
% 1.02/1.68 , b:0),
% 1.02/1.68 c_Groups_Oone__class_Oone [161, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Olinordered__semidom [162, 1] (w:1, o:142, a:1, s:1, b:0)
% 1.02/1.68 ,
% 1.02/1.68 class_Rings_Olinordered__idom [163, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Oone [166, 1] (w:1, o:175, a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Ozero__neq__one [167, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Oordered__cancel__ab__semigroup__add [168, 1] (w:1, o:
% 1.02/1.68 176, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Omonoid__mult [169, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Ocomm__monoid__mult [170, 1] (w:1, o:178, a:1, s:1, b:0)
% 1.02/1.68 ,
% 1.02/1.68 class_Rings_Olinordered__semiring__1__strict [171, 1] (w:1, o:144, a:
% 1.02/1.68 1, s:1, b:0),
% 1.02/1.68 class_Rings_Olinordered__semiring__strict [172, 1] (w:1, o:145, a:1
% 1.02/1.68 , s:1, b:0),
% 1.02/1.68 class_Rings_Olinordered__comm__semiring__strict [173, 1] (w:1, o:146
% 1.02/1.68 , a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Olinordered__semiring [176, 1] (w:1, o:147, a:1, s:1, b:0
% 1.02/1.68 ),
% 1.02/1.68 class_Rings_Ocomm__ring__1 [177, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.02/1.68 c_Groups_Ouminus__class_Ouminus [178, 2] (w:1, o:230, a:1, s:1, b:0)
% 1.02/1.68 ,
% 1.02/1.68 c_Polynomial_Opdivmod__rel [180, 5] (w:1, o:301, a:1, s:1, b:0),
% 1.02/1.68 c_Polynomial_Opos__poly [181, 2] (w:1, o:231, a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Ocomm__ring [183, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Oab__group__add [184, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Ogroup__add [189, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.02/1.68 class_Groups_Oordered__ab__group__add [190, 1] (w:1, o:181, a:1, s:1
% 1.02/1.68 , b:0),
% 1.02/1.68 class_Rings_Oring [191, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Oring__1__no__zero__divisors [192, 1] (w:1, o:151, a:1
% 1.02/1.68 , s:1, b:0),
% 1.02/1.68 c_Power_Opower__class_Opower [195, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.02/1.68 tc_Int_Oint [196, 0] (w:1, o:89, a:1, s:1, b:0),
% 1.02/1.68 class_Power_Opower [197, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.02/1.68 class_Rings_Oring__1 [198, 1] (w:1, o:152, a:1, s:1, b:0),
% 3.68/4.03 c_Power_Opower_Opower [200, 3] (w:1, o:252, a:1, s:1, b:0),
% 3.68/4.03 class_Lattices_Oboolean__algebra [201, 1] (w:1, o:185, a:1, s:1, b:0)
% 3.68/4.03 ,
% 3.68/4.03 class_Lattices_Oab__semigroup__idem__mult [209, 1] (w:1, o:184, a:1
% 3.68/4.03 , s:1, b:0),
% 3.68/4.03 class_Groups_Ouminus [211, 1] (w:1, o:186, a:1, s:1, b:0),
% 3.68/4.03 c_Polynomial_Opoly__gcd [212, 3] (w:1, o:253, a:1, s:1, b:0),
% 3.68/4.03 c_Rings_Oinverse__class_Oinverse [215, 2] (w:1, o:232, a:1, s:1, b:0)
% 3.68/4.03 ,
% 3.68/4.03 c_Groups_Ominus__class_Ominus [216, 3] (w:1, o:254, a:1, s:1, b:0),
% 3.68/4.03 class_Rings_Odivision__ring__inverse__zero [217, 1] (w:1, o:159, a:1
% 3.68/4.03 , s:1, b:0),
% 3.68/4.03 class_Groups_Ominus [219, 1] (w:1, o:187, a:1, s:1, b:0),
% 3.68/4.03 class_Rings_Odivision__ring [220, 1] (w:1, o:160, a:1, s:1, b:0),
% 3.68/4.03 class_Fields_Olinordered__field [227, 1] (w:1, o:118, a:1, s:1, b:0)
% 3.68/4.03 ,
% 3.68/4.03 class_Fields_Ofield__inverse__zero [228, 1] (w:1, o:119, a:1, s:1, b:
% 3.68/4.03 0),
% 3.68/4.03 class_Fields_Olinordered__field__inverse__zero [229, 1] (w:1, o:120
% 3.68/4.03 , a:1, s:1, b:0),
% 3.68/4.03 c_Rings_Oinverse__class_Odivide [230, 3] (w:1, o:255, a:1, s:1, b:0)
% 3.68/4.03 ,
% 3.68/4.03 c_Nat__Transfer_Otsub [231, 2] (w:1, o:233, a:1, s:1, b:0),
% 3.68/4.03 class_RealVector_Oreal__normed__field [232, 1] (w:1, o:161, a:1, s:1
% 3.68/4.03 , b:0),
% 3.68/4.03 class_RealVector_Oreal__field [233, 1] (w:1, o:162, a:1, s:1, b:0),
% 3.68/4.03 class_Groups_Ocancel__comm__monoid__add [236, 1] (w:1, o:188, a:1, s:
% 3.68/4.03 1, b:0),
% 3.68/4.03 tc_HOL_Obool [238, 0] (w:1, o:88, a:1, s:1, b:0),
% 3.68/4.03 t_a [239, 0] (w:1, o:102, a:1, s:1, b:0),
% 3.68/4.03 v_p [240, 0] (w:1, o:103, a:1, s:1, b:0),
% 3.68/4.03 v_h [241, 0] (w:1, o:104, a:1, s:1, b:0),
% 3.68/4.03 alpha1 [242, 3] (w:1, o:256, a:1, s:1, b:1),
% 3.68/4.03 alpha2 [243, 2] (w:1, o:235, a:1, s:1, b:1),
% 3.68/4.03 alpha3 [244, 2] (w:1, o:238, a:1, s:1, b:1),
% 3.68/4.03 alpha4 [245, 3] (w:1, o:264, a:1, s:1, b:1),
% 3.68/4.03 alpha5 [246, 3] (w:1, o:265, a:1, s:1, b:1),
% 3.68/4.03 alpha6 [247, 2] (w:1, o:239, a:1, s:1, b:1),
% 3.68/4.03 alpha7 [248, 2] (w:1, o:240, a:1, s:1, b:1),
% 3.68/4.03 alpha8 [249, 4] (w:1, o:290, a:1, s:1, b:1),
% 3.68/4.03 alpha9 [250, 4] (w:1, o:291, a:1, s:1, b:1),
% 3.68/4.03 alpha10 [251, 2] (w:1, o:234, a:1, s:1, b:1),
% 3.68/4.03 alpha11 [252, 3] (w:1, o:266, a:1, s:1, b:1),
% 3.68/4.03 alpha12 [253, 3] (w:1, o:267, a:1, s:1, b:1),
% 3.68/4.03 alpha13 [254, 3] (w:1, o:268, a:1, s:1, b:1),
% 3.68/4.03 alpha14 [255, 3] (w:1, o:269, a:1, s:1, b:1),
% 3.68/4.03 alpha15 [256, 3] (w:1, o:270, a:1, s:1, b:1),
% 3.68/4.03 alpha16 [257, 3] (w:1, o:271, a:1, s:1, b:1),
% 3.68/4.03 alpha17 [258, 3] (w:1, o:272, a:1, s:1, b:1),
% 3.68/4.03 alpha18 [259, 3] (w:1, o:273, a:1, s:1, b:1),
% 3.68/4.03 alpha19 [260, 4] (w:1, o:292, a:1, s:1, b:1),
% 3.68/4.03 alpha20 [261, 2] (w:1, o:236, a:1, s:1, b:1),
% 3.68/4.03 alpha21 [262, 2] (w:1, o:237, a:1, s:1, b:1),
% 3.68/4.03 alpha22 [263, 3] (w:1, o:274, a:1, s:1, b:1),
% 3.68/4.03 alpha23 [264, 3] (w:1, o:275, a:1, s:1, b:1),
% 3.68/4.03 alpha24 [265, 4] (w:1, o:293, a:1, s:1, b:1),
% 3.68/4.03 alpha25 [266, 4] (w:1, o:294, a:1, s:1, b:1),
% 3.68/4.03 alpha26 [267, 3] (w:1, o:276, a:1, s:1, b:1),
% 3.68/4.03 alpha27 [268, 3] (w:1, o:277, a:1, s:1, b:1),
% 3.68/4.04 alpha28 [269, 3] (w:1, o:278, a:1, s:1, b:1),
% 3.68/4.04 alpha29 [270, 3] (w:1, o:279, a:1, s:1, b:1),
% 3.68/4.04 alpha30 [271, 3] (w:1, o:257, a:1, s:1, b:1),
% 3.68/4.04 alpha31 [272, 3] (w:1, o:258, a:1, s:1, b:1),
% 3.68/4.04 alpha32 [273, 3] (w:1, o:259, a:1, s:1, b:1),
% 3.68/4.04 alpha33 [274, 4] (w:1, o:295, a:1, s:1, b:1),
% 3.68/4.04 alpha34 [275, 3] (w:1, o:260, a:1, s:1, b:1),
% 3.68/4.04 alpha35 [276, 3] (w:1, o:261, a:1, s:1, b:1),
% 3.68/4.04 alpha36 [277, 3] (w:1, o:262, a:1, s:1, b:1),
% 3.68/4.04 alpha37 [278, 0] (w:1, o:105, a:1, s:1, b:1),
% 3.68/4.04 alpha38 [279, 3] (w:1, o:263, a:1, s:1, b:1),
% 3.68/4.04 alpha39 [280, 4] (w:1, o:296, a:1, s:1, b:1),
% 3.68/4.04 alpha40 [281, 4] (w:1, o:297, a:1, s:1, b:1),
% 3.68/4.04 alpha41 [282, 4] (w:1, o:298, a:1, s:1, b:1),
% 3.68/4.04 skol1 [283, 2] (w:1, o:219, a:1, s:1, b:1),
% 3.68/4.04 skol2 [284, 3] (w:1, o:285, a:1, s:1, b:1),
% 3.68/4.04 skol3 [285, 2] (w:1, o:220, a:1, s:1, b:1),
% 3.68/4.04 skol4 [286, 2] (w:1, o:221, a:1, s:1, b:1),
% 3.68/4.04 skol5 [287, 3] (w:1, o:286, a:1, s:1, b:1),
% 3.68/4.04 skol6 [288, 2] (w:1, o:222, a:1, s:1, b:1),
% 23.24/23.59 skol7 [289, 3] (w:1, o:287, a:1, s:1, b:1),
% 23.24/23.59 skol8 [290, 1] (w:1, o:114, a:1, s:1, b:1),
% 23.24/23.59 skol9 [291, 2] (w:1, o:223, a:1, s:1, b:1),
% 23.24/23.59 skol10 [292, 2] (w:1, o:224, a:1, s:1, b:1),
% 23.24/23.59 skol11 [293, 3] (w:1, o:280, a:1, s:1, b:1),
% 23.24/23.59 skol12 [294, 2] (w:1, o:225, a:1, s:1, b:1),
% 23.24/23.59 skol13 [295, 3] (w:1, o:281, a:1, s:1, b:1),
% 23.24/23.59 skol14 [296, 4] (w:1, o:299, a:1, s:1, b:1),
% 23.24/23.59 skol15 [297, 2] (w:1, o:226, a:1, s:1, b:1),
% 23.24/23.59 skol16 [298, 3] (w:1, o:282, a:1, s:1, b:1),
% 23.24/23.59 skol17 [299, 3] (w:1, o:283, a:1, s:1, b:1),
% 23.24/23.59 skol18 [300, 2] (w:1, o:227, a:1, s:1, b:1),
% 23.24/23.59 skol19 [301, 3] (w:1, o:284, a:1, s:1, b:1).
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Starting Search:
% 23.24/23.59
% 23.24/23.59 *** allocated 113905 integers for clauses
% 23.24/23.59 *** allocated 170857 integers for clauses
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 3084
% 23.24/23.59 Kept: 2015
% 23.24/23.59 Inuse: 51
% 23.24/23.59 Deleted: 0
% 23.24/23.59 Deletedinuse: 0
% 23.24/23.59
% 23.24/23.59 *** allocated 256285 integers for clauses
% 23.24/23.59 *** allocated 170857 integers for termspace/termends
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 9134
% 23.24/23.59 Kept: 4029
% 23.24/23.59 Inuse: 135
% 23.24/23.59 Deleted: 2
% 23.24/23.59 Deletedinuse: 1
% 23.24/23.59
% 23.24/23.59 *** allocated 384427 integers for clauses
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 *** allocated 256285 integers for termspace/termends
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 15294
% 23.24/23.59 Kept: 6041
% 23.24/23.59 Inuse: 175
% 23.24/23.59 Deleted: 3
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 *** allocated 576640 integers for clauses
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 *** allocated 384427 integers for termspace/termends
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 21399
% 23.24/23.59 Kept: 8341
% 23.24/23.59 Inuse: 225
% 23.24/23.59 Deleted: 3
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 26406
% 23.24/23.59 Kept: 10696
% 23.24/23.59 Inuse: 265
% 23.24/23.59 Deleted: 3
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 *** allocated 864960 integers for clauses
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 31325
% 23.24/23.59 Kept: 12806
% 23.24/23.59 Inuse: 298
% 23.24/23.59 Deleted: 5
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 *** allocated 576640 integers for termspace/termends
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 38105
% 23.24/23.59 Kept: 14847
% 23.24/23.59 Inuse: 323
% 23.24/23.59 Deleted: 5
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 46185
% 23.24/23.59 Kept: 16882
% 23.24/23.59 Inuse: 345
% 23.24/23.59 Deleted: 5
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 *** allocated 1297440 integers for clauses
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 52234
% 23.24/23.59 Kept: 18920
% 23.24/23.59 Inuse: 378
% 23.24/23.59 Deleted: 5
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 Resimplifying clauses:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 56931
% 23.24/23.59 Kept: 20951
% 23.24/23.59 Inuse: 410
% 23.24/23.59 Deleted: 203
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 *** allocated 864960 integers for termspace/termends
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 63165
% 23.24/23.59 Kept: 23201
% 23.24/23.59 Inuse: 443
% 23.24/23.59 Deleted: 203
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 70494
% 23.24/23.59 Kept: 25858
% 23.24/23.59 Inuse: 458
% 23.24/23.59 Deleted: 203
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 *** allocated 1946160 integers for clauses
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 76629
% 23.24/23.59 Kept: 27972
% 23.24/23.59 Inuse: 473
% 23.24/23.59 Deleted: 203
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 86195
% 23.24/23.59 Kept: 30012
% 23.24/23.59 Inuse: 513
% 23.24/23.59 Deleted: 203
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 *** allocated 1297440 integers for termspace/termends
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 92896
% 23.24/23.59 Kept: 33052
% 23.24/23.59 Inuse: 528
% 23.24/23.59 Deleted: 203
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 98826
% 23.24/23.59 Kept: 35093
% 23.24/23.59 Inuse: 548
% 23.24/23.59 Deleted: 203
% 23.24/23.59 Deletedinuse: 2
% 23.24/23.59
% 23.24/23.59 Resimplifying inuse:
% 23.24/23.59 Done
% 23.24/23.59
% 23.24/23.59
% 23.24/23.59 Intermediate Status:
% 23.24/23.59 Generated: 104786
% 23.24/23.59 Kept: 38251
% 23.24/23.59 Inuse: 563
% 83.69/84.05 Deleted: 203
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 109600
% 83.69/84.05 Kept: 41284
% 83.69/84.05 Inuse: 573
% 83.69/84.05 Deleted: 203
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying clauses:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 *** allocated 2919240 integers for clauses
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 120765
% 83.69/84.05 Kept: 44431
% 83.69/84.05 Inuse: 588
% 83.69/84.05 Deleted: 263
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 126641
% 83.69/84.05 Kept: 47517
% 83.69/84.05 Inuse: 603
% 83.69/84.05 Deleted: 263
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 133774
% 83.69/84.05 Kept: 49749
% 83.69/84.05 Inuse: 633
% 83.69/84.05 Deleted: 263
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 139911
% 83.69/84.05 Kept: 51927
% 83.69/84.05 Inuse: 658
% 83.69/84.05 Deleted: 263
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 *** allocated 1946160 integers for termspace/termends
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 146164
% 83.69/84.05 Kept: 53958
% 83.69/84.05 Inuse: 708
% 83.69/84.05 Deleted: 263
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 152692
% 83.69/84.05 Kept: 56195
% 83.69/84.05 Inuse: 753
% 83.69/84.05 Deleted: 263
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 158646
% 83.69/84.05 Kept: 58225
% 83.69/84.05 Inuse: 773
% 83.69/84.05 Deleted: 263
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 169016
% 83.69/84.05 Kept: 60366
% 83.69/84.05 Inuse: 793
% 83.69/84.05 Deleted: 263
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying clauses:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 181998
% 83.69/84.05 Kept: 62850
% 83.69/84.05 Inuse: 823
% 83.69/84.05 Deleted: 478
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 190959
% 83.69/84.05 Kept: 64869
% 83.69/84.05 Inuse: 857
% 83.69/84.05 Deleted: 478
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 200525
% 83.69/84.05 Kept: 67382
% 83.69/84.05 Inuse: 868
% 83.69/84.05 Deleted: 478
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 *** allocated 4378860 integers for clauses
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 209934
% 83.69/84.05 Kept: 69723
% 83.69/84.05 Inuse: 878
% 83.69/84.05 Deleted: 478
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 219323
% 83.69/84.05 Kept: 73318
% 83.69/84.05 Inuse: 893
% 83.69/84.05 Deleted: 478
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 228159
% 83.69/84.05 Kept: 75343
% 83.69/84.05 Inuse: 926
% 83.69/84.05 Deleted: 478
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 *** allocated 2919240 integers for termspace/termends
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 234477
% 83.69/84.05 Kept: 78290
% 83.69/84.05 Inuse: 928
% 83.69/84.05 Deleted: 478
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 242244
% 83.69/84.05 Kept: 80298
% 83.69/84.05 Inuse: 965
% 83.69/84.05 Deleted: 478
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 254610
% 83.69/84.05 Kept: 83186
% 83.69/84.05 Inuse: 988
% 83.69/84.05 Deleted: 478
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying clauses:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 264997
% 83.69/84.05 Kept: 85509
% 83.69/84.05 Inuse: 1018
% 83.69/84.05 Deleted: 748
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 297844
% 83.69/84.05 Kept: 89271
% 83.69/84.05 Inuse: 1033
% 83.69/84.05 Deleted: 748
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 307360
% 83.69/84.05 Kept: 91397
% 83.69/84.05 Inuse: 1053
% 83.69/84.05 Deleted: 748
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 314330
% 83.69/84.05 Kept: 93620
% 83.69/84.05 Inuse: 1063
% 83.69/84.05 Deleted: 748
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
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% 83.69/84.05
% 83.69/84.05 Resimplifying inuse:
% 83.69/84.05 Done
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 321303
% 83.69/84.05 Kept: 95653
% 83.69/84.05 Inuse: 1074
% 83.69/84.05 Deleted: 748
% 83.69/84.05 Deletedinuse: 2
% 83.69/84.05
% 83.69/84.05
% 83.69/84.05 Intermediate Status:
% 83.69/84.05 Generated: 339543
% 83.69/84.05 Kept: 98455
% 83.69/84.05 Inuse: 1083
% 205.45/205.85 Deleted: 748
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 360961
% 205.45/205.85 Kept: 101829
% 205.45/205.85 Inuse: 1098
% 205.45/205.85 Deleted: 748
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 *** allocated 6568290 integers for clauses
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying clauses:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 368701
% 205.45/205.85 Kept: 104015
% 205.45/205.85 Inuse: 1123
% 205.45/205.85 Deleted: 847
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 376031
% 205.45/205.85 Kept: 106181
% 205.45/205.85 Inuse: 1148
% 205.45/205.85 Deleted: 847
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 *** allocated 4378860 integers for termspace/termends
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 383344
% 205.45/205.85 Kept: 108478
% 205.45/205.85 Inuse: 1163
% 205.45/205.85 Deleted: 847
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 390164
% 205.45/205.85 Kept: 110877
% 205.45/205.85 Inuse: 1183
% 205.45/205.85 Deleted: 847
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 395847
% 205.45/205.85 Kept: 113578
% 205.45/205.85 Inuse: 1188
% 205.45/205.85 Deleted: 847
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 402137
% 205.45/205.85 Kept: 115722
% 205.45/205.85 Inuse: 1198
% 205.45/205.85 Deleted: 847
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 410703
% 205.45/205.85 Kept: 117834
% 205.45/205.85 Inuse: 1228
% 205.45/205.85 Deleted: 847
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 449079
% 205.45/205.85 Kept: 122065
% 205.45/205.85 Inuse: 1253
% 205.45/205.85 Deleted: 847
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 459596
% 205.45/205.85 Kept: 124763
% 205.45/205.85 Inuse: 1268
% 205.45/205.85 Deleted: 847
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying clauses:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 467521
% 205.45/205.85 Kept: 126775
% 205.45/205.85 Inuse: 1277
% 205.45/205.85 Deleted: 943
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 484514
% 205.45/205.85 Kept: 130194
% 205.45/205.85 Inuse: 1298
% 205.45/205.85 Deleted: 943
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 496338
% 205.45/205.85 Kept: 132291
% 205.45/205.85 Inuse: 1308
% 205.45/205.85 Deleted: 943
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 511160
% 205.45/205.85 Kept: 136142
% 205.45/205.85 Inuse: 1333
% 205.45/205.85 Deleted: 943
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 517834
% 205.45/205.85 Kept: 138163
% 205.45/205.85 Inuse: 1347
% 205.45/205.85 Deleted: 943
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 525542
% 205.45/205.85 Kept: 140260
% 205.45/205.85 Inuse: 1348
% 205.45/205.85 Deleted: 943
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 556887
% 205.45/205.85 Kept: 145103
% 205.45/205.85 Inuse: 1363
% 205.45/205.85 Deleted: 943
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying clauses:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 564513
% 205.45/205.85 Kept: 147137
% 205.45/205.85 Inuse: 1383
% 205.45/205.85 Deleted: 995
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 *** allocated 6568290 integers for termspace/termends
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 572728
% 205.45/205.85 Kept: 149146
% 205.45/205.85 Inuse: 1405
% 205.45/205.85 Deleted: 995
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 584186
% 205.45/205.85 Kept: 151580
% 205.45/205.85 Inuse: 1438
% 205.45/205.85 Deleted: 995
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 589766
% 205.45/205.85 Kept: 153819
% 205.45/205.85 Inuse: 1448
% 205.45/205.85 Deleted: 995
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85 *** allocated 9852435 integers for clauses
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 597767
% 205.45/205.85 Kept: 155834
% 205.45/205.85 Inuse: 1469
% 205.45/205.85 Deleted: 995
% 205.45/205.85 Deletedinuse: 2
% 205.45/205.85
% 205.45/205.85 Resimplifying inuse:
% 205.45/205.85 Done
% 205.45/205.85
% 205.45/205.85
% 205.45/205.85 Intermediate Status:
% 205.45/205.85 Generated: 629524
% 205.45/205.85 Kept: 158875
% 205.45/205.85 Inuse: 1473
% 205.45/205.85 Deleted: 995
% 205.45/205.85 DCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------